qu.env.lastSaved= Jul 30, 2005 12:21:19 PM @ qu.env.validTest= false @ qu.1.topic=4_1 Prime Factors (3)@ qu.1.1.mode=Multi Formula@ qu.1.1.name=30@ qu.1.1.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $a; $b; $c

@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=$a=2; $b=3; $c=5; $num=$a*$b*$c;@ qu.1.1.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.1.answer=$a; $b; $c@ qu.1.2.mode=Multi Formula@ qu.1.2.name=42@ qu.1.2.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $a; $b; $c

@ qu.1.2.editing=useHTML@ qu.1.2.algorithm=$a=2; $b=3; $c=7; $num=$a*$b*$c;@ qu.1.2.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.2.answer=$a; $b; $c@ qu.1.3.mode=Multi Formula@ qu.1.3.name=66@ qu.1.3.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $a; $b; $c

@ qu.1.3.editing=useHTML@ qu.1.3.algorithm=$a=2; $b=3; $c=11; $num=$a*$b*$c;@ qu.1.3.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.3.answer=$a; $b; $c@ qu.1.4.mode=Multi Formula@ qu.1.4.name=45@ qu.1.4.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $a; $b; $c

@ qu.1.4.editing=useHTML@ qu.1.4.algorithm=$a=3; $b=3; $c=5; $num=$a*$b*$c;@ qu.1.4.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.4.answer=$a; $b; $c@ qu.1.5.mode=Multi Formula@ qu.1.5.name=75@ qu.1.5.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $c; $b; $a

@ qu.1.5.editing=useHTML@ qu.1.5.algorithm=$a=5; $b=5; $c=3; $num=$a*$b*$c;@ qu.1.5.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.5.answer=$c; $b; $a@ qu.1.6.mode=Multi Formula@ qu.1.6.name=12@ qu.1.6.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $a; $b; $c

@ qu.1.6.editing=useHTML@ qu.1.6.algorithm=$a=2; $b=2; $c=3; $num=$a*$b*$c;@ qu.1.6.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.6.answer=$a; $b; $c@ qu.1.7.mode=Multi Formula@ qu.1.7.name=105@ qu.1.7.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $b; $a; $c

@ qu.1.7.editing=useHTML@ qu.1.7.algorithm=$a=5; $b=3; $c=7; $num=$a*$b*$c;@ qu.1.7.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.7.answer=$b; $a; $c@ qu.1.8.mode=Multi Formula@ qu.1.8.name=28@ qu.1.8.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $a; $b; $c

@ qu.1.8.editing=useHTML@ qu.1.8.algorithm=$a=2; $b=2; $c=7; $num=$a*$b*$c;@ qu.1.8.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.8.answer=$a; $b; $c@ qu.1.9.mode=Multi Formula@ qu.1.9.name=78@ qu.1.9.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $c; $b; $a

@ qu.1.9.editing=useHTML@ qu.1.9.algorithm=$a=13; $b=3; $c=2; $num=$a*$b*$c;@ qu.1.9.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.9.answer=$c; $b; $a@ qu.1.10.mode=Multi Formula@ qu.1.10.name=52@ qu.1.10.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • $c =
$a • $b • $c
Enter the prime factors as $c; $b; $a

@ qu.1.10.editing=useHTML@ qu.1.10.algorithm=$a=13; $b=2; $c=2; $num=$a*$b*$c;@ qu.1.10.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.1.10.answer=$c; $b; $a@ qu.2.topic=4_1 Prime Factors (4)@ qu.2.1.mode=Multi Formula@ qu.2.1.name=210@ qu.2.1.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b*$c} • $d =
(${$a*$b} • $c) • $d =
($a • $b) • $c • $d =
$a • $b • $c • $d =
Enter the prime factors as $a; $d; $b; $c

@ qu.2.1.editing=useHTML@ qu.2.1.algorithm=$a=2; $b=5; $c=7;$d=3; $num=$a*$b*$c*$d;@ qu.2.1.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.1.answer=$a; $d; $b; $c@ qu.2.2.mode=Multi Formula@ qu.2.2.name=36@ qu.2.2.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $a; $b; $c; $d

@ qu.2.2.editing=useHTML@ qu.2.2.algorithm=$a=2; $b=2; $c=3;$d=3; $num=$a*$b*$c*$d;@ qu.2.2.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.2.answer=$a; $b; $c; $d@ qu.2.3.mode=Multi Formula@ qu.2.3.name=60@ qu.2.3.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $a; $c; $b; $d

@ qu.2.3.editing=useHTML@ qu.2.3.algorithm=$a=2; $b=3; $c=2;$d=5; $num=$a*$b*$c*$d;@ qu.2.3.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.3.answer=$a; $c; $b; $d@ qu.2.4.mode=Multi Formula@ qu.2.4.name=84@ qu.2.4.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $c; $d; $a; $b

@ qu.2.4.editing=useHTML@ qu.2.4.algorithm=$a=3; $b=7; $c=2;$d=2; $num=$a*$b*$c*$d;@ qu.2.4.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.4.answer=$c; $d; $a; $b@ qu.2.5.mode=Multi Formula@ qu.2.5.name=90@ qu.2.5.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $c; $b; $a; $d

@ qu.2.5.editing=useHTML@ qu.2.5.algorithm=$a=3; $b=3; $c=2;$d=5; $num=$a*$b*$c*$d;@ qu.2.5.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.5.answer=$c; $b; $a; $d@ qu.2.6.mode=Multi Formula@ qu.2.6.name=150@ qu.2.6.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b*$c} • $d =
(${$a*$b} • $c) • $d =
($a • $b) • $c • $d =
$a • $b • $c • $d =
Enter the prime factors as $a; $d; $c; $b

@ qu.2.6.editing=useHTML@ qu.2.6.algorithm=$a=2; $b=5; $c=5;$d=3; $num=$a*$b*$c*$d;@ qu.2.6.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.6.answer=$a; $d; $c; $b@ qu.2.7.mode=Multi Formula@ qu.2.7.name=441@ qu.2.7.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $a; $c; $b; $d

@ qu.2.7.editing=useHTML@ qu.2.7.algorithm=$a=3; $b=7; $c=3;$d=7; $num=$a*$b*$c*$d;@ qu.2.7.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.7.answer=$a; $c; $b; $d@ qu.2.8.mode=Multi Formula@ qu.2.8.name=54@ qu.2.8.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $a; $b; $c; $d

@ qu.2.8.editing=useHTML@ qu.2.8.algorithm=$a=2; $b=3; $c=3;$d=3; $num=$a*$b*$c*$d;@ qu.2.8.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.8.answer=$a; $b; $c; $d@ qu.2.9.mode=Multi Formula@ qu.2.9.name=126@ qu.2.9.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b} • ${$c*$d} =
($a • $b) • ($c • $d) =
$a • $b • $c • $d
Enter the prime factors as $a; $b; $c; $d

@ qu.2.9.editing=useHTML@ qu.2.9.algorithm=$a=2; $b=3; $c=3;$d=7; $num=$a*$b*$c*$d;@ qu.2.9.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.9.answer=$a; $b; $c; $d@ qu.2.10.mode=Multi Formula@ qu.2.10.name=330@ qu.2.10.comment=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

$num =
${$a*$b*$c} • $d =
(${$a*$b} • $c) • $d =
($a • $b) • $c • $d =
$a • $b • $c • $d =
Enter the prime factors as $a; $d; $b; $c

@ qu.2.10.editing=useHTML@ qu.2.10.algorithm=$a=2; $b=5; $c=11;$d=3; $num=$a*$b*$c*$d;@ qu.2.10.question=

Write the prime factors of $num.
Write the value separated by a semi-colon ; as 3; 5; 7

@ qu.2.10.answer=$a; $d; $b; $c@ qu.3.topic=4_2 Greatest Common Factor (3)@ qu.3.1.question=Find the greatest common factor of $num1 and $num2.@ qu.3.1.answer.num=$g@ qu.3.1.answer.units=@ qu.3.1.showUnits=false@ qu.3.1.grading=exact_value@ qu.3.1.negStyle=minus@ qu.3.1.numStyle=thousands scientific dollars arithmetic@ qu.3.1.mode=Numeric@ qu.3.1.name=30, 42@ qu.3.1.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=$a=2; $b=3; $c=5; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.2.question=Find the greatest common factor of $num1 and $num2.@ qu.3.2.answer.num=$g@ qu.3.2.answer.units=@ qu.3.2.showUnits=false@ qu.3.2.grading=exact_value@ qu.3.2.negStyle=minus@ qu.3.2.numStyle=thousands scientific dollars arithmetic@ qu.3.2.mode=Numeric@ qu.3.2.name=20, 28@ qu.3.2.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=$a=2; $b=2; $c=5; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.3.question=Find the greatest common factor of $num1 and $num2.@ qu.3.3.answer.num=$g@ qu.3.3.answer.units=@ qu.3.3.showUnits=false@ qu.3.3.grading=exact_value@ qu.3.3.negStyle=minus@ qu.3.3.numStyle=thousands scientific dollars arithmetic@ qu.3.3.mode=Numeric@ qu.3.3.name=30, 70@ qu.3.3.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $c • $b
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.3.editing=useHTML@ qu.3.3.algorithm=$a=2; $b=5; $c=3; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.4.question=Find the greatest common factor of $num1 and $num2.@ qu.3.4.answer.num=$g@ qu.3.4.answer.units=@ qu.3.4.showUnits=false@ qu.3.4.grading=exact_value@ qu.3.4.negStyle=minus@ qu.3.4.numStyle=thousands scientific dollars arithmetic@ qu.3.4.mode=Numeric@ qu.3.4.name=45, 105@ qu.3.4.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $c • $b
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.4.editing=useHTML@ qu.3.4.algorithm=$a=3; $b=5; $c=3; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.5.question=Find the greatest common factor of $num1 and $num2.@ qu.3.5.answer.num=$g@ qu.3.5.answer.units=@ qu.3.5.showUnits=false@ qu.3.5.grading=exact_value@ qu.3.5.negStyle=minus@ qu.3.5.numStyle=thousands scientific dollars arithmetic@ qu.3.5.mode=Numeric@ qu.3.5.name=70, 105@ qu.3.5.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $c • $b • $a
$num2 = $d • $b • $a
Multiply the common prime factors.
G.C.F. = $b • $a = $g

@ qu.3.5.editing=useHTML@ qu.3.5.algorithm=$a=7; $b=5; $c=2; $d=3; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.6.question=Find the greatest common factor of $num1 and $num2.@ qu.3.6.answer.num=$g@ qu.3.6.answer.units=@ qu.3.6.showUnits=false@ qu.3.6.grading=exact_value@ qu.3.6.negStyle=minus@ qu.3.6.numStyle=thousands scientific dollars arithmetic@ qu.3.6.mode=Numeric@ qu.3.6.name=63, 231@ qu.3.6.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $c • $b
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.6.editing=useHTML@ qu.3.6.algorithm=$a=3; $b=7; $c=3; $d=11; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.7.question=Find the greatest common factor of $num1 and $num2.@ qu.3.7.answer.num=$g@ qu.3.7.answer.units=@ qu.3.7.showUnits=false@ qu.3.7.grading=exact_value@ qu.3.7.negStyle=minus@ qu.3.7.numStyle=thousands scientific dollars arithmetic@ qu.3.7.mode=Numeric@ qu.3.7.name=75, 175@ qu.3.7.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $c • $b • $a
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.7.editing=useHTML@ qu.3.7.algorithm=$a=5; $b=5; $c=3; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.8.question=Find the greatest common factor of $num1 and $num2.@ qu.3.8.answer.num=$g@ qu.3.8.answer.units=@ qu.3.8.showUnits=false@ qu.3.8.grading=exact_value@ qu.3.8.negStyle=minus@ qu.3.8.numStyle=thousands scientific dollars arithmetic@ qu.3.8.mode=Numeric@ qu.3.8.name=70, 175@ qu.3.8.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $c • $a • $b
$num2 = $a • $d • $b
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.8.editing=useHTML@ qu.3.8.algorithm=$a=5; $b=7; $c=2; $d=5; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.9.question=Find the greatest common factor of $num1 and $num2.@ qu.3.9.answer.num=$g@ qu.3.9.answer.units=@ qu.3.9.showUnits=false@ qu.3.9.grading=exact_value@ qu.3.9.negStyle=minus@ qu.3.9.numStyle=thousands scientific dollars arithmetic@ qu.3.9.mode=Numeric@ qu.3.9.name=110, 154@ qu.3.9.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $c • $b
$num2 = $a • $d • $b
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.9.editing=useHTML@ qu.3.9.algorithm=$a=2; $b=11; $c=5; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.3.10.question=Find the greatest common factor of $num1 and $num2.@ qu.3.10.answer.num=$g@ qu.3.10.answer.units=@ qu.3.10.showUnits=false@ qu.3.10.grading=exact_value@ qu.3.10.negStyle=minus@ qu.3.10.numStyle=thousands scientific dollars arithmetic@ qu.3.10.mode=Numeric@ qu.3.10.name=45, 63@ qu.3.10.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c
$num2 = $a • $b • $d
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.3.10.editing=useHTML@ qu.3.10.algorithm=$a=3; $b=3; $c=5; $d=7; $num1=$a*$b*$c; $num2=$a*$b*$d; $g=$a*$b;@ qu.4.topic=4_2 Greatest Common Factor (4)@ qu.4.1.question=Find the greatest common factor of $num1 and $num2.@ qu.4.1.answer.num=$g@ qu.4.1.answer.units=@ qu.4.1.showUnits=false@ qu.4.1.grading=exact_value@ qu.4.1.negStyle=minus@ qu.4.1.numStyle=thousands scientific dollars arithmetic@ qu.4.1.mode=Numeric@ qu.4.1.name=150, 210@ qu.4.1.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c • $d
$num2 = $a • $b • $c • $e
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=$a=2; $b=3; $c=5; $d=5; $e=7; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.2.question=Find the greatest common factor of $num1 and $num2.@ qu.4.2.answer.num=$g@ qu.4.2.answer.units=@ qu.4.2.showUnits=false@ qu.4.2.grading=exact_value@ qu.4.2.negStyle=minus@ qu.4.2.numStyle=thousands scientific dollars arithmetic@ qu.4.2.mode=Numeric@ qu.4.2.name=36, 60@ qu.4.2.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c • $d
$num2 = $a • $b • $c • $e
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=$a=2; $b=2; $c=3; $d=3; $e=5; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.3.question=Find the greatest common factor of $num1 and $num2.@ qu.4.3.answer.num=$g@ qu.4.3.answer.units=@ qu.4.3.showUnits=false@ qu.4.3.grading=exact_value@ qu.4.3.negStyle=minus@ qu.4.3.numStyle=thousands scientific dollars arithmetic@ qu.4.3.mode=Numeric@ qu.4.3.name=54, 90@ qu.4.3.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c • $d
$num2 = $a • $b • $c • $e
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.3.editing=useHTML@ qu.4.3.algorithm=$a=2; $b=3; $c=3; $d=3; $e=5; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.4.question=Find the greatest common factor of $num1 and $num2.@ qu.4.4.answer.num=$g@ qu.4.4.answer.units=@ qu.4.4.showUnits=false@ qu.4.4.grading=exact_value@ qu.4.4.negStyle=minus@ qu.4.4.numStyle=thousands scientific dollars arithmetic@ qu.4.4.mode=Numeric@ qu.4.4.name=24, 40@ qu.4.4.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c • $d
$num2 = $a • $b • $c • $e
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.4.editing=useHTML@ qu.4.4.algorithm=$a=2; $b=2; $c=2; $d=3; $e=5; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.5.question=Find the greatest common factor of $num1 and $num2.@ qu.4.5.answer.num=$g@ qu.4.5.answer.units=@ qu.4.5.showUnits=false@ qu.4.5.grading=exact_value@ qu.4.5.negStyle=minus@ qu.4.5.numStyle=thousands scientific dollars arithmetic@ qu.4.5.mode=Numeric@ qu.4.5.name=36, 84@ qu.4.5.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c • $d
$num2 = $a • $b • $c • $e
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.5.editing=useHTML@ qu.4.5.algorithm=$a=2; $b=2; $c=3; $d=3; $e=7; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.6.question=Find the greatest common factor of $num1 and $num2.@ qu.4.6.answer.num=$g@ qu.4.6.answer.units=@ qu.4.6.showUnits=false@ qu.4.6.grading=exact_value@ qu.4.6.negStyle=minus@ qu.4.6.numStyle=thousands scientific dollars arithmetic@ qu.4.6.mode=Numeric@ qu.4.6.name=36, 140@ qu.4.6.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $c • $d
$num2 = $a • $b • $e • $f
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.4.6.editing=useHTML@ qu.4.6.algorithm=$a=2; $b=2; $c=3; $d=3; $e=5; $f=7; $num1=$a*$b*$c*$d; $num2=$a*$b*$e*$f; $g=$a*$b;@ qu.4.7.question=Find the greatest common factor of $num1 and $num2.@ qu.4.7.answer.num=$g@ qu.4.7.answer.units=@ qu.4.7.showUnits=false@ qu.4.7.grading=exact_value@ qu.4.7.negStyle=minus@ qu.4.7.numStyle=thousands scientific dollars arithmetic@ qu.4.7.mode=Numeric@ qu.4.7.name=60, 100@ qu.4.7.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $d • $c
$num2 = $a • $b • $c • $e
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.7.editing=useHTML@ qu.4.7.algorithm=$a=2; $b=2; $c=5; $d=3; $e=5; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.8.question=Find the greatest common factor of $num1 and $num2.@ qu.4.8.answer.num=$g@ qu.4.8.answer.units=@ qu.4.8.showUnits=false@ qu.4.8.grading=exact_value@ qu.4.8.negStyle=minus@ qu.4.8.numStyle=thousands scientific dollars arithmetic@ qu.4.8.mode=Numeric@ qu.4.8.name=198, 330@ qu.4.8.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $b • $d • $c
$num2 = $a • $b • $e • $c
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.8.editing=useHTML@ qu.4.8.algorithm=$a=2; $b=3; $c=11; $d=3; $e=5; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.9.question=Find the greatest common factor of $num1 and $num2.@ qu.4.9.answer.num=$g@ qu.4.9.answer.units=@ qu.4.9.showUnits=false@ qu.4.9.grading=exact_value@ qu.4.9.negStyle=minus@ qu.4.9.numStyle=thousands scientific dollars arithmetic@ qu.4.9.mode=Numeric@ qu.4.9.name=100, 150@ qu.4.9.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $d • $c • $b
$num2 = $a • $e • $c • $b
Multiply the common prime factors.
G.C.F. = $a • $b • $c = $g

@ qu.4.9.editing=useHTML@ qu.4.9.algorithm=$a=2; $b=5; $c=5; $d=2; $e=3; $num1=$a*$b*$c*$d; $num2=$a*$b*$c*$e; $g=$a*$b*$c;@ qu.4.10.question=Find the greatest common factor of $num1 and $num2.@ qu.4.10.answer.num=$g@ qu.4.10.answer.units=@ qu.4.10.showUnits=false@ qu.4.10.grading=exact_value@ qu.4.10.negStyle=minus@ qu.4.10.numStyle=thousands scientific dollars arithmetic@ qu.4.10.mode=Numeric@ qu.4.10.name=294, 350@ qu.4.10.comment=

Find the greatest common factor of $num1 and $num2.

Find the prime factors of each number.
$num1 = $a • $d • $c • $b
$num2 = $a • $f • $e • $b
Multiply the common prime factors.
G.C.F. = $a • $b = $g

@ qu.4.10.editing=useHTML@ qu.4.10.algorithm=$a=2; $b=7; $c=7; $d=3; $e=5; $f=5; $num1=$a*$b*$c*$d; $num2=$a*$b*$e*$f; $g=$a*$b;@ qu.5.topic=4_2 Greatest CF with variables@ qu.5.1.mode=Formula@ qu.5.1.name=x^a y^b@ qu.5.1.comment=

Find the greatest common factor of x$x1y$y1 and x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y.
The LCM is x$xy$y entered as x^$x y^$y.

@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2);@ qu.5.1.question=Find the greatest common factor of x$x1y$y1 and x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.5.1.answer=x^$x y^$y@ qu.5.2.mode=Formula@ qu.5.2.name=x^a y^b z^c@ qu.5.2.comment=

Find the greatest common factor of x$x1y$y1z$z1 and x$x2y$y2z$z2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x, the lowest power of y is $y and the lowest power of z is $z.
The LCM is x$xy$yz$z entered as x^$x y^$y z^$z.

@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2); $z1=range(2,10,1); $z2=range(2,10,1); $z=min($z1,$z2);@ qu.5.2.question=

Find the greatest common factor of x$x1y$y1z$z1 and x$x2y$y2z$z2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

@ qu.5.2.answer=x^$x y^$y z^$z@ qu.5.3.mode=Formula@ qu.5.3.name=x^a y^b x^dy^fz^g@ qu.5.3.comment=

Find the greatest common factor of x$x1y$y1 and x$x2y$y2z$z1
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y. The lowest power of z is $z.
The LCM is x$xy$y entered as x^$x y^$y.

@ qu.5.3.editing=useHTML@ qu.5.3.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2); $z1=range(2,10,1); $z2=0; $z=min($z1,$z2);@ qu.5.3.question=Find the greatest common factor of x$x1y$y1 and x$x2y$y2z$z1
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.5.3.answer=x^$x y^$y@ qu.5.4.mode=Formula@ qu.5.4.name=x^a y^bz^c x^dy^f@ qu.5.4.comment=

Find the greatest common factor of x$x1y$y1z$z1 and x$x2y$y2
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y. The lowest power of z is $z.
The LCM is x$xy$y entered as x^$x y^$y.

@ qu.5.4.editing=useHTML@ qu.5.4.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2); $z1=range(2,10,1); $z2=0; $z=min($z1,$z2);@ qu.5.4.question=Find the greatest common factor of x$x1y$y1z$z1 and x$x2y$y2
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.5.4.answer=x^$x y^$y@ qu.6.topic=4_2 GCF with numbers and 1 variable@ qu.6.1.mode=Formula@ qu.6.1.name=cf2-3 x^a@ qu.6.1.comment=

Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of the variable.
The lowest power of x is $x.
The LCM is ${$g}x$x entered as $g x^$x.

@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=$x1=range(2,6,1); $y1=range(2,6,1); $x2=range(2,6,1); $y2=range(2,6,1); $x=min($x1,$x2); $y=min($y1,$y2);$cf=range(2,36,1);$c1=range(2,5,1)*$cf;$c2=range(2,6,1)*$cf;condition:ne($c1,$c2);$g=$gcd($c1,$c2);@ qu.6.1.question=Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.6.1.answer=$g x^$x@ qu.6.2.mode=Formula@ qu.6.2.name=cf3-4 x^a@ qu.6.2.comment=

Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of the variable.
The lowest power of x is $x.
The LCM is ${$g}x$x entered as $g x^$x.

@ qu.6.2.editing=useHTML@ qu.6.2.algorithm=$x1=range(2,6,1); $y1=range(2,6,1); $x2=range(2,6,1); $y2=range(2,6,1); $x=min($x1,$x2); $y=min($y1,$y2);$cf=range(3,4,1);$c1=range(2,5,1)*$cf;$c2=range(2,6,1)*$cf;condition:ne($c1,$c2);$g=$gcd($c1,$c2);@ qu.6.2.question=Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.6.2.answer=$g x^$x@ qu.6.3.mode=Formula@ qu.6.3.name=cf5-6 x^a@ qu.6.3.comment=

Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of the variable.
The lowest power of x is $x.
The LCM is ${$g}x$x entered as $g x^$x.

@ qu.6.3.editing=useHTML@ qu.6.3.algorithm=$x1=range(2,6,1); $y1=range(2,6,1); $x2=range(2,6,1); $y2=range(2,6,1); $x=min($x1,$x2); $y=min($y1,$y2);$cf=range(5,6,1);$c1=range(2,5,1)*$cf;$c2=range(2,6,1)*$cf;condition:ne($c1,$c2);$g=$gcd($c1,$c2);@ qu.6.3.question=Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.6.3.answer=$g x^$x@ qu.6.4.mode=Formula@ qu.6.4.name=cf7-8 x^a@ qu.6.4.comment=

Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of the variable.
The lowest power of x is $x.
The LCM is ${$g}x$x entered as $g x^$x.

@ qu.6.4.editing=useHTML@ qu.6.4.algorithm=$x1=range(2,6,1); $y1=range(2,6,1); $x2=range(2,6,1); $y2=range(2,6,1); $x=min($x1,$x2); $y=min($y1,$y2);$cf=range(7,8,1);$c1=range(2,5,1)*$cf;$c2=range(2,6,1)*$cf;condition:ne($c1,$c2);$g=$gcd($c1,$c2);@ qu.6.4.question=Find the greatest common factor of ${$c1}x$x1 and ${$c2}x$x2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.6.4.answer=$g x^$x@ qu.7.topic=4_2 GCF with numbers and variables@ qu.7.1.mode=Formula@ qu.7.1.name=cf2-3 x^a y^b@ qu.7.1.comment=

Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y.
The LCM is ${$g}x$xy$y entered as $g x^$x y^$y.

@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2);$cf=range(2,6,1);$c1=range(2,5,1)*$cf;$c2=range(2,6,1)*$cf;condition:ne($c1,$c2);$g=$gcd($c1,$c2);@ qu.7.1.question=Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.7.1.answer=$g x^$x y^$y@ qu.7.2.mode=Formula@ qu.7.2.name=cf3-4 x^a y^b@ qu.7.2.comment=

Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y.
The LCM is ${$g}x$xy$y entered as $g x^$x y^$y.

@ qu.7.2.editing=useHTML@ qu.7.2.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2); $cf=range(3,4,1); $c1=range(2,6,1)*$cf; $c2=range(2,6,1)*$cf; condition:ne($c1,$c2); $g=$gcd($c1,$c2);@ qu.7.2.question=Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.7.2.answer=$g x^$x y^$y@ qu.7.3.mode=Formula@ qu.7.3.name=cf5-6 x^a y^b@ qu.7.3.comment=

Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y.
The LCM is ${$g}x$xy$y entered as $g x^$x y^$y.

@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2); $cf=range(5,6,1); $c1=range(2,6,1)*$cf; $c2=range(2,6,1)*$cf; condition:ne($c1,$c2); $g=$gcd($c1,$c2);@ qu.7.3.question=Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.7.3.answer=$g x^$x y^$y@ qu.7.4.mode=Formula@ qu.7.4.name=cf7-8 x^a y^b@ qu.7.4.comment=

Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The GCF of $c1 and $c2 is $g.
The GCF is the lowest power of each variable. If the variable is not present, the exponent is 0 and is not included in the GCF
The lowest power of x is $x and the lowest power of y is $y.
The LCM is ${$g}x$xy$y entered as $g x^$x y^$y.

@ qu.7.4.editing=useHTML@ qu.7.4.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=min($x1,$x2); $y=min($y1,$y2); $cf=range(5,6,1); $c1=range(2,6,1)*$cf; $c2=range(2,6,1)*$cf; condition:ne($c1,$c2); $g=$gcd($c1,$c2);@ qu.7.4.question=Find the greatest common factor of ${$c1}x$x1y$y1 and ${$c2}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.7.4.answer=$g x^$x y^$y@ qu.8.topic=4_3 Simplify Fractions@ qu.8.1.mode=Blanks@ qu.8.1.name=GCF 2@ qu.8.1.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.1.editing=useHTML@ qu.8.1.algorithm=$a=2; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.1.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.1.blank.1=%24n%2f%24d@ qu.8.1.extra=@ qu.8.1.format.input=text@ qu.8.2.mode=Blanks@ qu.8.2.name=GCF 3@ qu.8.2.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.2.editing=useHTML@ qu.8.2.algorithm=$a=3; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.2.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.2.blank.1=%24n%2f%24d@ qu.8.2.extra=@ qu.8.2.format.input=text@ qu.8.3.mode=Blanks@ qu.8.3.name=GCF 4@ qu.8.3.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.3.editing=useHTML@ qu.8.3.algorithm=$a=4; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.3.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.3.blank.1=%24n%2f%24d@ qu.8.3.extra=@ qu.8.3.format.input=text@ qu.8.4.mode=Blanks@ qu.8.4.name=GCF 5@ qu.8.4.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.4.editing=useHTML@ qu.8.4.algorithm=$a=5; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.4.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.4.blank.1=%24n%2f%24d@ qu.8.4.extra=@ qu.8.4.format.input=text@ qu.8.5.mode=Blanks@ qu.8.5.name=GCF 6@ qu.8.5.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.5.editing=useHTML@ qu.8.5.algorithm=$a=6; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.5.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.5.blank.1=%24n%2f%24d@ qu.8.5.extra=@ qu.8.5.format.input=text@ qu.8.6.mode=Blanks@ qu.8.6.name=GCF 7@ qu.8.6.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.6.editing=useHTML@ qu.8.6.algorithm=$a=7; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.6.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.6.blank.1=%24n%2f%24d@ qu.8.6.extra=@ qu.8.6.format.input=text@ qu.8.7.mode=Blanks@ qu.8.7.name=GCF 8@ qu.8.7.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.7.editing=useHTML@ qu.8.7.algorithm=$a=8; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.7.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.7.blank.1=%24n%2f%24d@ qu.8.7.extra=@ qu.8.7.format.input=text@ qu.8.8.mode=Blanks@ qu.8.8.name=GCF 9@ qu.8.8.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.8.editing=useHTML@ qu.8.8.algorithm=$a=9; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.8.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.8.blank.1=%24n%2f%24d@ qu.8.8.extra=@ qu.8.8.format.input=text@ qu.8.9.mode=Blanks@ qu.8.9.name=GCF 10@ qu.8.9.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.9.editing=useHTML@ qu.8.9.algorithm=$a=10; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.9.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.9.blank.1=%24n%2f%24d@ qu.8.9.extra=@ qu.8.9.format.input=text@ qu.8.10.mode=Blanks@ qu.8.10.name=GCF 11@ qu.8.10.comment=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox.

Find the GCF of $b and $c.
The GCF is $g.
Divide numerator and denominator by $g.
The simplified fraction is $n/$d.

@ qu.8.10.editing=useHTML@ qu.8.10.algorithm=$a=11; $b=$a*range(3,11,2); $c=$a*range(4,12,2); $g=gcd($b,$c); $n=$b/$g; $d=$c/$g; condition:ne($d,1); $ans=$n/$d;@ qu.8.10.question=

Simplify the fraction:
$b
$c

Enter a fraction such as 2/3 in the textbox. Do not use spaces in the answer!

<1>

@ qu.8.10.blank.1=%24n%2f%24d@ qu.8.10.extra=@ qu.8.10.format.input=text@ qu.9.topic=4_4 Find LCM of 2 numbers@ qu.9.1.question=Find the least common multiple of $a and $b.@ qu.9.1.answer.num=$lcm@ qu.9.1.answer.units=@ qu.9.1.showUnits=false@ qu.9.1.grading=exact_value@ qu.9.1.negStyle=minus@ qu.9.1.numStyle=thousands scientific dollars arithmetic@ qu.9.1.mode=Numeric@ qu.9.1.name=2m, 2n@ qu.9.1.comment=

Find the least common multiple of $a and $b.

Write the multiples of each number.
${if(eq($a,$lcm),"","")}$a${if(eq($a,$lcm),"","")},${if(eq($a2,$lcm),"","")} $a2${if(eq($a2,$lcm),"","")},${if(eq($a3,$lcm),"","")} $a3${if(eq($a3,$lcm),"","")},${if(eq($a4,$lcm),"","")} $a4${if(eq($a4,$lcm),"","")},${if(eq($a5,$lcm),"","")} $a5${if(eq($a5,$lcm),"","")},${if(eq($a6,$lcm),"","")} $a6${if(eq($a6,$lcm),"","")},${if(eq($a7,$lcm),"","")} $a7${if(eq($a7,$lcm),"","")},${if(eq($a8,$lcm),"","")} $a8${if(eq($a8,$lcm),"","")},${if(eq($a9,$lcm),"","")} $a9${if(eq($a9,$lcm),"","")},${if(eq($a10,$lcm),"","")} $a10${if(eq($a10,$lcm),"","")},${if(eq($a11,$lcm),"","")} $a11${if(eq($a11,$lcm),"","")},${if(eq($a12,$lcm),"","")} $a12${if(eq($a12,$lcm),"","")},....
${if(eq($b,$lcm),"","")}$b${if(eq($b,$lcm),"","")},${if(eq($b2,$lcm),"","")} $b2${if(eq($b2,$lcm),"","")},${if(eq($b3,$lcm),"","")} $b3${if(eq($b3,$lcm),"","")},${if(eq($b4,$lcm),"","")} $b4${if(eq($b4,$lcm),"","")},${if(eq($b5,$lcm),"","")} $b5${if(eq($b5,$lcm),"","")},${if(eq($b6,$lcm),"","")} $b6${if(eq($b6,$lcm),"","")},${if(eq($b7,$lcm),"","")} $b7${if(eq($b7,$lcm),"","")},${if(eq($b8,$lcm),"","")} $b8${if(eq($b8,$lcm),"","")},${if(eq($b9,$lcm),"","")} $b9${if(eq($b9,$lcm),"","")},${if(eq($b10,$lcm),"","")} $b10${if(eq($b10,$lcm),"","")},${if(eq($b11,$lcm),"","")} $b11${if(eq($b11,$lcm),"","")},${if(eq($b12,$lcm),"","")} $b12${if(eq($b12,$lcm),"","")}, ....
Choose the first number which is displayed in both lists.
The LCM is $lcm.

@ qu.9.1.editing=useHTML@ qu.9.1.algorithm=$a=range(2,20,2); $a2=2*$a; $a3=3*$a; $a4=4*$a; $a5=5*$a; $a6=6*$a; $a7=7*$a; $a8=8*$a; $a9=9*$a; $a10=10*$a; $a11=11*$a; $a12=12*$a; $b=range(2,20,2); $b2=2*$b; $b3=3*$b; $b4=4*$b; $b5=5*$b; $b6=6*$b; $b7=7*$b; $b8=8*$b; $b9=9*$b; $b10=10*$b; $b11=11*$b; $b12=12*$b; $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.9.2.question=Find the least common multiple of $a and $b.@ qu.9.2.answer.num=$lcm@ qu.9.2.answer.units=@ qu.9.2.showUnits=false@ qu.9.2.grading=exact_value@ qu.9.2.negStyle=minus@ qu.9.2.numStyle=thousands scientific dollars arithmetic@ qu.9.2.mode=Numeric@ qu.9.2.name=2m, 3n@ qu.9.2.comment=

Find the least common multiple of $a and $b.

Write the multiples of each number.
${if(eq($a,$lcm),"","")}$a${if(eq($a,$lcm),"","")},${if(eq($a2,$lcm),"","")} $a2${if(eq($a2,$lcm),"","")},${if(eq($a3,$lcm),"","")} $a3${if(eq($a3,$lcm),"","")},${if(eq($a4,$lcm),"","")} $a4${if(eq($a4,$lcm),"","")},${if(eq($a5,$lcm),"","")} $a5${if(eq($a5,$lcm),"","")},${if(eq($a6,$lcm),"","")} $a6${if(eq($a6,$lcm),"","")},${if(eq($a7,$lcm),"","")} $a7${if(eq($a7,$lcm),"","")},${if(eq($a8,$lcm),"","")} $a8${if(eq($a8,$lcm),"","")},${if(eq($a9,$lcm),"","")} $a9${if(eq($a9,$lcm),"","")},${if(eq($a10,$lcm),"","")} $a10${if(eq($a10,$lcm),"","")},${if(eq($a11,$lcm),"","")} $a11${if(eq($a11,$lcm),"","")},${if(eq($a12,$lcm),"","")} $a12${if(eq($a12,$lcm),"","")},....
${if(eq($b,$lcm),"","")}$b${if(eq($b,$lcm),"","")},${if(eq($b2,$lcm),"","")} $b2${if(eq($b2,$lcm),"","")},${if(eq($b3,$lcm),"","")} $b3${if(eq($b3,$lcm),"","")},${if(eq($b4,$lcm),"","")} $b4${if(eq($b4,$lcm),"","")},${if(eq($b5,$lcm),"","")} $b5${if(eq($b5,$lcm),"","")},${if(eq($b6,$lcm),"","")} $b6${if(eq($b6,$lcm),"","")},${if(eq($b7,$lcm),"","")} $b7${if(eq($b7,$lcm),"","")},${if(eq($b8,$lcm),"","")} $b8${if(eq($b8,$lcm),"","")},${if(eq($b9,$lcm),"","")} $b9${if(eq($b9,$lcm),"","")},${if(eq($b10,$lcm),"","")} $b10${if(eq($b10,$lcm),"","")},${if(eq($b11,$lcm),"","")} $b11${if(eq($b11,$lcm),"","")},${if(eq($b12,$lcm),"","")} $b12${if(eq($b12,$lcm),"","")}, ....
Choose the first number which is displayed in both lists.
The LCM is $lcm.

@ qu.9.2.editing=useHTML@ qu.9.2.algorithm=$a=range(2,30,2); $a2=2*$a; $a3=3*$a; $a4=4*$a; $a5=5*$a; $a6=6*$a; $a7=7*$a; $a8=8*$a; $a9=9*$a; $a10=10*$a; $a11=11*$a; $a12=12*$a; $b=range(3,30,6); $b2=2*$b; $b3=3*$b; $b4=4*$b; $b5=5*$b; $b6=6*$b; $b7=7*$b; $b8=8*$b; $b9=9*$b; $b10=10*$b; $b11=11*$b; $b12=12*$b; $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.9.3.question=Find the least common multiple of $a and $b.@ qu.9.3.answer.num=$lcm@ qu.9.3.answer.units=@ qu.9.3.showUnits=false@ qu.9.3.grading=exact_value@ qu.9.3.negStyle=minus@ qu.9.3.numStyle=thousands scientific dollars arithmetic@ qu.9.3.mode=Numeric@ qu.9.3.name=3m, 3n@ qu.9.3.comment=

Find the least common multiple of $a and $b.

Write the multiples of each number.
${if(eq($a,$lcm),"","")}$a${if(eq($a,$lcm),"","")},${if(eq($a2,$lcm),"","")} $a2${if(eq($a2,$lcm),"","")},${if(eq($a3,$lcm),"","")} $a3${if(eq($a3,$lcm),"","")},${if(eq($a4,$lcm),"","")} $a4${if(eq($a4,$lcm),"","")},${if(eq($a5,$lcm),"","")} $a5${if(eq($a5,$lcm),"","")},${if(eq($a6,$lcm),"","")} $a6${if(eq($a6,$lcm),"","")},${if(eq($a7,$lcm),"","")} $a7${if(eq($a7,$lcm),"","")},${if(eq($a8,$lcm),"","")} $a8${if(eq($a8,$lcm),"","")},${if(eq($a9,$lcm),"","")} $a9${if(eq($a9,$lcm),"","")},${if(eq($a10,$lcm),"","")} $a10${if(eq($a10,$lcm),"","")},${if(eq($a11,$lcm),"","")} $a11${if(eq($a11,$lcm),"","")},${if(eq($a12,$lcm),"","")} $a12${if(eq($a12,$lcm),"","")},....
${if(eq($b,$lcm),"","")}$b${if(eq($b,$lcm),"","")},${if(eq($b2,$lcm),"","")} $b2${if(eq($b2,$lcm),"","")},${if(eq($b3,$lcm),"","")} $b3${if(eq($b3,$lcm),"","")},${if(eq($b4,$lcm),"","")} $b4${if(eq($b4,$lcm),"","")},${if(eq($b5,$lcm),"","")} $b5${if(eq($b5,$lcm),"","")},${if(eq($b6,$lcm),"","")} $b6${if(eq($b6,$lcm),"","")},${if(eq($b7,$lcm),"","")} $b7${if(eq($b7,$lcm),"","")},${if(eq($b8,$lcm),"","")} $b8${if(eq($b8,$lcm),"","")},${if(eq($b9,$lcm),"","")} $b9${if(eq($b9,$lcm),"","")},${if(eq($b10,$lcm),"","")} $b10${if(eq($b10,$lcm),"","")},${if(eq($b11,$lcm),"","")} $b11${if(eq($b11,$lcm),"","")},${if(eq($b12,$lcm),"","")} $b12${if(eq($b12,$lcm),"","")}, ....
Choose the first number which is displayed in both lists.
The LCM is $lcm.

@ qu.9.3.editing=useHTML@ qu.9.3.algorithm=$a=range(6,24,3); $a2=2*$a; $a3=3*$a; $a4=4*$a; $a5=5*$a; $a6=6*$a; $a7=7*$a; $a8=8*$a; $a9=9*$a; $a10=10*$a; $a11=11*$a; $a12=12*$a; $b=range(3,21,6); $b2=2*$b; $b3=3*$b; $b4=4*$b; $b5=5*$b; $b6=6*$b; $b7=7*$b; $b8=8*$b; $b9=9*$b; $b10=10*$b; $b11=11*$b; $b12=12*$b; $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.9.4.question=Find the least common multiple of $a and $b.@ qu.9.4.answer.num=$lcm@ qu.9.4.answer.units=@ qu.9.4.showUnits=false@ qu.9.4.grading=exact_value@ qu.9.4.negStyle=minus@ qu.9.4.numStyle=thousands scientific dollars arithmetic@ qu.9.4.mode=Numeric@ qu.9.4.name=3m, 5n@ qu.9.4.comment=

Find the least common multiple of $a and $b.

Write the multiples of each number.
${if(eq($a,$lcm),"","")}$a${if(eq($a,$lcm),"","")},${if(eq($a2,$lcm),"","")} $a2${if(eq($a2,$lcm),"","")},${if(eq($a3,$lcm),"","")} $a3${if(eq($a3,$lcm),"","")},${if(eq($a4,$lcm),"","")} $a4${if(eq($a4,$lcm),"","")},${if(eq($a5,$lcm),"","")} $a5${if(eq($a5,$lcm),"","")},${if(eq($a6,$lcm),"","")} $a6${if(eq($a6,$lcm),"","")},${if(eq($a7,$lcm),"","")} $a7${if(eq($a7,$lcm),"","")},${if(eq($a8,$lcm),"","")} $a8${if(eq($a8,$lcm),"","")},${if(eq($a9,$lcm),"","")} $a9${if(eq($a9,$lcm),"","")},${if(eq($a10,$lcm),"","")} $a10${if(eq($a10,$lcm),"","")},${if(eq($a11,$lcm),"","")} $a11${if(eq($a11,$lcm),"","")},${if(eq($a12,$lcm),"","")} $a12${if(eq($a12,$lcm),"","")},....
${if(eq($b,$lcm),"","")}$b${if(eq($b,$lcm),"","")},${if(eq($b2,$lcm),"","")} $b2${if(eq($b2,$lcm),"","")},${if(eq($b3,$lcm),"","")} $b3${if(eq($b3,$lcm),"","")},${if(eq($b4,$lcm),"","")} $b4${if(eq($b4,$lcm),"","")},${if(eq($b5,$lcm),"","")} $b5${if(eq($b5,$lcm),"","")},${if(eq($b6,$lcm),"","")} $b6${if(eq($b6,$lcm),"","")},${if(eq($b7,$lcm),"","")} $b7${if(eq($b7,$lcm),"","")},${if(eq($b8,$lcm),"","")} $b8${if(eq($b8,$lcm),"","")},${if(eq($b9,$lcm),"","")} $b9${if(eq($b9,$lcm),"","")},${if(eq($b10,$lcm),"","")} $b10${if(eq($b10,$lcm),"","")},${if(eq($b11,$lcm),"","")} $b11${if(eq($b11,$lcm),"","")},${if(eq($b12,$lcm),"","")} $b12${if(eq($b12,$lcm),"","")}, ....
Choose the first number which is displayed in both lists.
The LCM is $lcm.

@ qu.9.4.editing=useHTML@ qu.9.4.algorithm=$a=range(6,24,3); $a2=2*$a; $a3=3*$a; $a4=4*$a; $a5=5*$a; $a6=6*$a; $a7=7*$a; $a8=8*$a; $a9=9*$a; $a10=10*$a; $a11=11*$a; $a12=12*$a; $b=range(5,45,5); $b2=2*$b; $b3=3*$b; $b4=4*$b; $b5=5*$b; $b6=6*$b; $b7=7*$b; $b8=8*$b; $b9=9*$b; $b10=10*$b; $b11=11*$b; $b12=12*$b; $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.10.topic=4_4 Find LCM of variables@ qu.10.1.mode=Formula@ qu.10.1.name=x^a y^b@ qu.10.1.comment=

Find the lowest common multiple of x$x1y$y1 and x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM is the highest power of each variable.
The highest power of x is $x and the highest power of y is $y.
The LCM is x$xy$y entered as x^$x y^$y.

@ qu.10.1.editing=useHTML@ qu.10.1.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2);@ qu.10.1.question=Find the lowest common multiple of x$x1y$y1 and x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.10.1.answer=x^$x y^$y@ qu.10.2.mode=Formula@ qu.10.2.name=x^a y^b z^c@ qu.10.2.comment=

Find the lowest common multiple of x$x1y$y1z$z1 and x$x2y$y2z$z2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM is the highest power of each variable.
The highest power of x is $x, the highest power of y is $y and the highest power of z is $z.
The LCM is x$xy$yz$z entered as x^$x y^$y z^$z.

@ qu.10.2.editing=useHTML@ qu.10.2.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $z1=range(2,10,1); $z2=range(2,10,1); $z=max($z1,$z2);@ qu.10.2.question=

Find the lowest common multiple of x$x1y$y1z$z1 and x$x2y$y2z$z2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

@ qu.10.2.answer=x^$x y^$y z^$z@ qu.10.3.mode=Formula@ qu.10.3.name=x^a y^b x^dy^fz^g@ qu.10.3.comment=

Find the lowest common multiple of x$x1y$y1 and x$x2y$y2z$z1
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM is the highest power of each variable.
The highest power of x is $x and the highest power of y is $y. The highest power of z is $z.
The LCM is x$xy$yz$z entered as x^$x y^$y z^$z.

@ qu.10.3.editing=useHTML@ qu.10.3.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $z1=range(2,10,1); $z2=0; $z=max($z1,$z2);@ qu.10.3.question=Find the lowest common multiple of x$x1y$y1 and x$x2y$y2z$z1
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.10.3.answer=x^$x y^$y z^$z@ qu.10.4.mode=Formula@ qu.10.4.name=x^a y^bz^c x^dy^f@ qu.10.4.comment=

Find the lowest common multiple of x$x1y$y1z$z1 and x$x2y$y2
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM is the highest power of each variable.
The highest power of x is $x and the highest power of y is $y. The highest power of z is $z.
The LCM is x$xy$yz$z entered as x^$x y^$y z^$z.

@ qu.10.4.editing=useHTML@ qu.10.4.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $z1=range(2,10,1); $z2=0; $z=max($z1,$z2);@ qu.10.4.question=Find the lowest common multiple of x$x1y$y1z$z1 and x$x2y$y2
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.10.4.answer=x^$x y^$y z^$z@ qu.11.topic=4_4 Find LCM of numbers and variables@ qu.11.1.mode=Formula@ qu.11.1.name=2m x^a 2n y^b@ qu.11.1.comment=

Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM of $a and $b is $lcm.
The LCM of the variables is the highest exponent of each x$x y$y
Putting the these together, the LCM is ${$lcm}x$x y$y entered as $lcm x^$x y^$y

 

@ qu.11.1.editing=useHTML@ qu.11.1.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $a=range(2,20,2); $b=range(2,20,2); $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.11.1.question=Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.11.1.answer=$lcm x^$x y^$y@ qu.11.2.mode=Formula@ qu.11.2.name=2m x^a 3n y^b@ qu.11.2.comment=

Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM of $a and $b is $lcm.
The LCM of the variables is the highest exponent of each x$x y$y
Putting the these together, the LCM is ${$lcm}x$x y$y entered as $lcm x^$x y^$y

 

@ qu.11.2.editing=useHTML@ qu.11.2.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $a=range(2,20,2); $b=range(3,30,6); $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.11.2.question=Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.11.2.answer=$lcm x^$x y^$y@ qu.11.3.mode=Formula@ qu.11.3.name=3m x^a 3n y^b@ qu.11.3.comment=

Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM of $a and $b is $lcm.
The LCM of the variables is the highest exponent of each x$x y$y
Putting the these together, the LCM is ${$lcm}x$x y$y entered as $lcm x^$x y^$y

 

@ qu.11.3.editing=useHTML@ qu.11.3.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $a=range(6,24,3); $b=range(3,21,6); $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.11.3.question=Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.11.3.answer=$lcm x^$x y^$y@ qu.11.4.mode=Formula@ qu.11.4.name=3m x^a 5n y^b@ qu.11.4.comment=

Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.

The LCM of $a and $b is $lcm.
The LCM of the variables is the highest exponent of each x$x y$y
Putting the these together, the LCM is ${$lcm}x$x y$y entered as $lcm x^$x y^$y

 

@ qu.11.4.editing=useHTML@ qu.11.4.algorithm=$x1=range(2,10,1); $y1=range(2,10,1); $x2=range(2,10,1); $y2=range(2,10,1); $x=max($x1,$x2); $y=max($y1,$y2); $a=range(6,24,3); $b=range(5,45,5); $g=gcd($a,$b); $lcm=($a*$b)/$g; condition:ne($a,$b); condition:lt($lcm,$a*13); condition:lt($lcm,$b*13);@ qu.11.4.question=Find the least common multiple of ${$a}x$x1y$y1 and ${$b}x$x2y$y2.
Enter the exponents using the ^ key. For example a5b6would be entered as a^5 b^6.@ qu.11.4.answer=$lcm x^$x y^$y@ qu.12.topic=4_5 Review Mixed to Improper Fraction@ qu.12.1.mode=Formula@ qu.12.1.name=Denom 2-4@ qu.12.1.comment=
Write $w
$n
  as an improper fraction.  
$d

Enter a fraction into the answer box as 3/5.

$w • $d + $n = $num

The fraction is  
$num
  entered as $num/$d.
$d
@ qu.12.1.editing=useHTML@ qu.12.1.algorithm=$w=range(3,5,1); $d=range(2,4,1); $n=range(1,$d-1,1); $num=$w*$d+$n; condition:eq(gcd($n,$d),1);@ qu.12.1.question=
Write $w
$n
  as an improper fraction.  
$d

Enter a fraction into the answer box as 3/5.

@ qu.12.1.answer=$num/$d@ qu.12.2.mode=Formula@ qu.12.2.name=Denom 5-7@ qu.12.2.comment=
Write $w
$n
  as an improper fraction.  
$d

Enter a fraction into the answer box as 3/5.

$w • $d + $n = $num

The fraction is  
$num
  entered as $num/$d.
$d
@ qu.12.2.editing=useHTML@ qu.12.2.algorithm=$w=range(3,5,1); $d=range(5,7,1); $n=range(1,$d-1,1); $num=$w*$d+$n; condition:eq(gcd($n,$d),1);@ qu.12.2.question=
Write $w
$n
  as an improper fraction.  
$d

Enter a fraction into the answer box as 3/5.

@ qu.12.2.answer=$num/$d@ qu.12.3.mode=Formula@ qu.12.3.name=Denom 8-10@ qu.12.3.comment=
Write $w
$n
  as an improper fraction.  
$d

Enter a fraction into the answer box as 3/5.

$w • $d + $n = $num

The fraction is  
$num
  entered as $num/$d.
$d
@ qu.12.3.editing=useHTML@ qu.12.3.algorithm=$w=range(3,5,1); $d=range(8,10,1); $n=range(1,$d-1,1); $num=$w*$d+$n; condition:eq(gcd($n,$d),1);@ qu.12.3.question=
Write $w
$n
  as an improper fraction.  
$d

Enter a fraction into the answer box as 3/5.

@ qu.12.3.answer=$num/$d@ qu.13.topic=4_5 Compare Fractions@ qu.13.1.mode=Multiple Choice@ qu.13.1.name=lt@ qu.13.1.comment=

Replace ? with <, =, or >.

$n1
$d1
 ? 
$n2
$d2

The least common denominator is $lcd.
Multiply each fraction to get the least common denominator.
$n1•$f1
$d1•$f1
 ? 
$n2•$f2
$d2•$f2

${$n1*$f1}
${$d1*$f1}
 ? 
${$n2*$f2}
${$d2*$f2}

Since ${$n1*$f1} < ${$n2*$f2}, 
${$n1*$f1}
${$d1*$f1}
 < 
${$n2*$f2}
${$d2*$f2}
 and we can say  
$n1
$d1
 ? 
$n2
$d2
@ qu.13.1.editing=useHTML@ qu.13.1.algorithm=$d1=range(3,8,1); $d2=range(5,12,1); condition:ne($d1,$d2); $n1=range(1,$d1-1); $n2=decimal(0,$n1*$d2/$d1); condition:lt($n1*$d2,$d1*$n2); $lcd=$d1*$d2/gcd($d1,$d2); $f1=$lcd/$d1; $f2=$lcd/$d2;@ qu.13.1.question=

Replace ? with <, =, or >.

$n1
$d1
 ? 
$n2
$d2
@ qu.13.1.answer=1@ qu.13.1.choice.1=<@ qu.13.1.choice.2=>@ qu.13.1.choice.3==@ qu.13.2.mode=Multiple Choice@ qu.13.2.name=gt@ qu.13.2.comment=

Replace ? with <, =, or >.

$n1
$d1
 ? 
$n2
$d2

The least common denominator is $lcd.
Multiply each fraction to get the least common denominator.
$n1•$f1
$d1•$f1
 ? 
$n2•$f2
$d2•$f2

${$n1*$f1}
${$d1*$f1}
 ? 
${$n2*$f2}
${$d2*$f2}

Since ${$n1*$f1} > ${$n2*$f2}, 
${$n1*$f1}
${$d1*$f1}
 > 
${$n2*$f2}
${$d2*$f2}
 and we can say  
$n1
$d1
 > 
$n2
$d2
@ qu.13.2.editing=useHTML@ qu.13.2.algorithm=$d1=range(5,12,1); $d2=range(3,8,1); condition:ne($d1,$d2); $n1=range(1,$d1-1); $n2=int(($n1*$d2+$d2)/$d1); condition:gt($n2,0); condition:gt($n1*$d2,$d1*$n2); condition:lt($n2/$d2,1); $g=gcd($d1,$d2); $lcd=$d1*$d2/$g; $f1=$lcd/$d1; $f2=$lcd/$d2;@ qu.13.2.question=

Replace ? with <, =, or >.

$n1
$d1
 ? 
$n2
$d2
@ qu.13.2.answer=2@ qu.13.2.choice.1=<@ qu.13.2.choice.2=>@ qu.13.2.choice.3==@ qu.13.3.mode=Multiple Choice@ qu.13.3.name=eq@ qu.13.3.comment=

Replace ? with <, =, or >.

$n1
$d1
 ? 
$n2
$d2

The least common denominator is $lcd.
Multiply each fraction to get the least common denominator.
$n1•$f1
$d1•$f1
 ? 
$n2•$f2
$d2•$f2

${$n1*$f1}
${$d1*$f1}
 ? 
${$n2*$f2}
${$d2*$f2}

Since ${$n1*$f1} = ${$n2*$f2}, 
${$n1*$f1}
${$d1*$f1}
 = 
${$n2*$f2}
${$d2*$f2}
 and we can say  
$n1
$d1
 = 
$n2
$d2
@ qu.13.3.editing=useHTML@ qu.13.3.algorithm=$d1=range(5,12,1); $n1=range(1,$d1-1); $c=range(3,12,1); $d2=$d1*$c; $n2=$n1*$c; $g=gcd($d1,$d2); $lcd=$d1*$d2/$g; $f1=$lcd/$d1; $f2=$lcd/$d2;@ qu.13.3.question=

Replace ? with <, =, or >.

$n1
$d1
 ? 
$n2
$d2
@ qu.13.3.answer=3@ qu.13.3.choice.1=<@ qu.13.3.choice.2=>@ qu.13.3.choice.3==@ qu.14.topic=4_5 Compare Mixed Fractions@ qu.14.1.mode=Multiple Choice@ qu.14.1.name=lt@ qu.14.1.comment=

Replace ? with <, =, or >.

$w
$nw
$d1
 ? 
$n2
$d2

Convert to a mixed number.
$n1
$d1
 ? 
$n2
$d2

The least common denominator is $lcd.
Multiply each fraction to get the least common denominator.
$n1•$f1
$d1•$f1
 ? 
$n2•$f2
$d2•$f2

${$n1*$f1}
${$d1*$f1}
 ? 
${$n2*$f2}
${$d2*$f2}

Since ${$n1*$f1} < ${$n2*$f2}, 
${$n1*$f1}
${$d1*$f1}
 < 
${$n2*$f2}
${$d2*$f2}
 and we can say  
$n1
$d1
 < 
$n2
$d2
@ qu.14.1.editing=useHTML@ qu.14.1.algorithm=$w=range(2,5,1); $d1=range(3,8,1); $d2=range(5,12,1); condition:ne($d1,$d2); $nw=range(1,$d1-1); $n1=$w*$d1+$nw; $n2=decimal(0,$n1*$d2/$d1); condition:lt($n1*$d2,$d1*$n2); $lcd=$d1*$d2/gcd($d1,$d2); $f1=$lcd/$d1; $f2=$lcd/$d2;@ qu.14.1.question=

Replace ? with <, =, or >.

$w
$nw
$d1
 ? 
$n2
$d2
@ qu.14.1.answer=1@ qu.14.1.choice.1=<@ qu.14.1.choice.2=>@ qu.14.1.choice.3==@ qu.14.2.mode=Multiple Choice@ qu.14.2.name=gt@ qu.14.2.comment=

Replace ? with <, =, or >.

$w
$nw
$d1
 ? 
$n2
$d2

Convert to a mixed number.
$n1
$d1
 ? 
$n2
$d2

The least common denominator is $lcd.
Multiply each fraction to get the least common denominator.
$n1•$f1
$d1•$f1
 ? 
$n2•$f2
$d2•$f2

${$n1*$f1}
${$d1*$f1}
 ? 
${$n2*$f2}
${$d2*$f2}

Since ${$n1*$f1} > ${$n2*$f2}, 
${$n1*$f1}
${$d1*$f1}
 > 
${$n2*$f2}
${$d2*$f2}
 and we can say  
$n1
$d1
 > 
$n2
$d2
@ qu.14.2.editing=useHTML@ qu.14.2.algorithm=$w=range(2,5,1); $d1=range(5,12,1); $d2=range(3,8,1); condition:ne($d1,$d2); $nw=range(1,$d1-1); $n1=$w*$d1+$nw; $n2=int(($n1*$d2+$d2)/$d1); condition:gt($n1*$d2,$d1*$n2); $lcd=$d1*$d2/gcd($d1,$d2); $f1=$lcd/$d1; $f2=$lcd/$d2;@ qu.14.2.question=

Replace ? with <, =, or >.

$w
$nw
$d1
 ? 
$n2
$d2
@ qu.14.2.answer=2@ qu.14.2.choice.1=<@ qu.14.2.choice.2=>@ qu.14.2.choice.3==@ qu.14.3.mode=Multiple Choice@ qu.14.3.name=equal@ qu.14.3.comment=

Replace ? with <, =, or >.

$w
$nw
$d1
 ? 
$n2
$d2

Convert to a mixed number.
$n1
$d1
 ? 
$n2
$d2

The least common denominator is $lcd.
Multiply each fraction to get the least common denominator.
$n1•$f1
$d1•$f1
 ? 
$n2•$f2
$d2•$f2

${$n1*$f1}
${$d1*$f1}
 ? 
${$n2*$f2}
${$d2*$f2}

Since ${$n1*$f1} = ${$n2*$f2}, 
${$n1*$f1}
${$d1*$f1}
 = 
${$n2*$f2}
${$d2*$f2}
 and we can say  
$n1
$d1
 = 
$n2
$d2
@ qu.14.3.editing=useHTML@ qu.14.3.algorithm=$w=range(2,5,1); $d1=range(3,8,1); $nw=range(1,$d1-1); $n1=$w*$d1+$nw; $c=range(3,7,1); $n2=$n1*$c; $d2=$d1*$c; $lcd=$d1*$d2/gcd($d1,$d2); $f1=$lcd/$d1; $f2=$lcd/$d2;@ qu.14.3.question=

Replace ? with <, =, or >.

$w
$nw
$d1
 ? 
$n2
$d2
@ qu.14.3.answer=3@ qu.14.3.choice.1=<@ qu.14.3.choice.2=>@ qu.14.3.choice.3==@ qu.15.topic=4_5 Order Fractions@ qu.15.1.mode=Inline@ qu.15.1.name=1 3 2@ qu.15.1.comment=

Order the fractions from smallest to largest.

$w
$nw
$d1
, 
$n3
$d3
, 
$n2
$d2