Factoring - Simplifying Fraction Division with Factors - Composite to Factored (Level 1)

This math topic focuses on employing factorization techniques to simplify fraction divisions by converting composite numbers into their factored forms and identifying cancelable factors. The problems involve detailed steps showing how to factorize numerator and denominator terms, then invert the divisor, further factorizing if necessary, and finally simplifying by canceling out common factors. This practices essential skills in factoring, multiplication, division, and working with fractions, helping learners to improve their understanding and manipulation of algebraic expressions involving fractions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Simplifying Fraction Division with Factors - Composite to Factored

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out

1542÷54\frac{15}{42} \div \frac{5}{4}

Factoring - Simplifying Fraction Division with Factors - Composite to Factored Worksheet

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Math worksheet on 'Factoring - Simplifying Fraction Division with Factors - Composite to Factored (Level 1)'. Part of a broader unit on 'Factoring, Multiplication, Division, Fractions - Advanced' Learn online: app.mobius.academy/math/units/factoring_multiplication_division_fractions_advanced/
1
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 21 over 90 divided by 1 over 15
a A LaTex expression showing 3 multiplied by 7 over 2 multiplied by 3 multiplied by 3 multiplied by 5 multiplied by 3 multiplied by 5 over 1
b A LaTex expression showing 3 multiplied by 7 over 2 multiplied by 3 multiplied by 3 multiplied by 5 multiplied by 3 multiplied by 5 over 13
c A LaTex expression showing 3 multiplied by 7 over 2 multiplied by 3 multiplied by 3 multiplied by 5 multiplied by 5 over 1
d A LaTex expression showing 3 multiplied by 7 over 2 multiplied by 3 multiplied by 5 multiplied by 3 multiplied by 5 over 1
e A LaTex expression showing 11 multiplied by 7 over 2 multiplied by 3 multiplied by 13 multiplied by 5 multiplied by 3 multiplied by 5 over 1
f A LaTex expression showing 3 multiplied by 7 over 2 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 5 multiplied by 7 multiplied by 5 over 3
2
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 4 over 5 divided by 28 over 14
a A LaTex expression showing 2 multiplied by 2 over 5 multiplied by 2 multiplied by 7 over 2 multiplied by 2 multiplied by 7
b A LaTex expression showing 2 multiplied by 2 multiplied by 11 over 11 multiplied by 2 multiplied by 7 over 11 multiplied by 2 multiplied by 2 multiplied by 7
c A LaTex expression showing 2 multiplied by 2 over 5 multiplied by 2 multiplied by 2 multiplied by 7 over 2 multiplied by 2 multiplied by 7
d A LaTex expression showing 7 multiplied by 2 multiplied by 2 over 5 multiplied by 2 multiplied by 7 multiplied by 7 over 2 multiplied by 2 multiplied by 13
e A LaTex expression showing 5 over 5 multiplied by 2 multiplied by 2 multiplied by 13 over 11 multiplied by 2 multiplied by 2 multiplied by 13
f A LaTex expression showing 5 multiplied by 2 over 2 multiplied by 2 multiplied by 7 over 2 multiplied by 7
3
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 42 over 21 divided by 9 over 3
a A LaTex expression showing 2 over 3 multiplied by 7 multiplied by 3 over 3
b A LaTex expression showing 2 multiplied by 3 multiplied by 7 over 3 multiplied by 7 multiplied by 3 over 3 multiplied by 3
c A LaTex expression showing 2 multiplied by 2 multiplied by 3 multiplied by 7 over 3 multiplied by 3 multiplied by 3 over 3 multiplied by 3
d A LaTex expression showing 2 multiplied by 2 multiplied by 3 multiplied by 7 over 3 multiplied by 7 multiplied by 3 over 3 multiplied by 3 multiplied by 2
e A LaTex expression showing 2 multiplied by 2 multiplied by 13 multiplied by 7 over 3 multiplied by 7 multiplied by 3 over 3 multiplied by 3
f A LaTex expression showing 2 multiplied by 2 multiplied by 13 multiplied by 7 over 3 multiplied by 7 multiplied by 3 over 3 multiplied by 3
4
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 1 over 3 divided by 42 over 84
a A LaTex expression showing 1 over 3 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 7 over 2 multiplied by 3 multiplied by 7
b A LaTex expression showing 1 over 3 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 7 over 2 multiplied by 3 multiplied by 7
c A LaTex expression showing 1 over 3 multiplied by 13 multiplied by 2 multiplied by 2 multiplied by 7 multiplied by 7 over 2 multiplied by 3 multiplied by 7
d A LaTex expression showing 1 over 3 multiplied by 2 multiplied by 3 multiplied by 7 over 2 multiplied by 3
e A LaTex expression showing 1 over 3 multiplied by 7 multiplied by 2 multiplied by 13 multiplied by 7 over 2 multiplied by 5 multiplied by 13
5
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 49 over 7 divided by 63 over 6
a A LaTex expression showing 7 multiplied by 7 over 7 multiplied by 2 multiplied by 3 over 7 multiplied by 13
b A LaTex expression showing 7 multiplied by 7 over 7 multiplied by 2 multiplied by 11 over 3 multiplied by 7
c A LaTex expression showing 3 multiplied by 7 over 13 multiplied by 7 multiplied by 3 over 3 multiplied by 3 multiplied by 3 multiplied by 7
d A LaTex expression showing 7 multiplied by 7 over 2 multiplied by 2 multiplied by 3 over 3 multiplied by 3 multiplied by 7
e A LaTex expression showing 7 multiplied by 7 over 7 multiplied by 2 multiplied by 3 over 3 multiplied by 3 multiplied by 7
f A LaTex expression showing 7 over 7 multiplied by 2 over 3 multiplied by 3 multiplied by 7
6
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 3 over 24 divided by 1 over 12
a A LaTex expression showing 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 2 over 3
b A LaTex expression showing 3 over 2 multiplied by 2 multiplied by 2 multiplied by 11 multiplied by 2 multiplied by 5 multiplied by 3 over 1 multiplied by 1
c A LaTex expression showing 3 multiplied by 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 2 multiplied by 3 over 3
d A LaTex expression showing 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 2 multiplied by 3 over 1
e A LaTex expression showing 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 3 over 1
7
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 35 over 63 divided by 7 over 21
a A LaTex expression showing 5 multiplied by 7 over 3 multiplied by 3 multiplied by 7 multiplied by 7 multiplied by 3 multiplied by 7 over 7
b A LaTex expression showing 5 multiplied by 7 over 3 multiplied by 3 multiplied by 3 over 7
c A LaTex expression showing 7 over 3 multiplied by 7 multiplied by 7 multiplied by 3 multiplied by 7 over 5
d A LaTex expression showing 5 multiplied by 7 multiplied by 7 over 3 multiplied by 3 multiplied by 13 multiplied by 3 multiplied by 7 over 7
e A LaTex expression showing 5 multiplied by 7 over 3 multiplied by 3 multiplied by 7 multiplied by 3 multiplied by 7 over 7