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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

1242÷57\frac{12}{42} \div \frac{5}{7}

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 - Intro' Learn online: app.mobius.academy/math/units/factoring_multiplication_division_fractions_intro/
1
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 2 divided by 50 over 15
a A LaTex expression showing 2 over 2 multiplied by 3 over 2 multiplied by 2 multiplied by 5 multiplied by 5
b A LaTex expression showing 2 multiplied by 2 over 2 multiplied by 3 multiplied by 5 over 2 multiplied by 5 multiplied by 5
c A LaTex expression showing 2 multiplied by 2 over 13 multiplied by 3 multiplied by 5 over 5 multiplied by 5
d A LaTex expression showing 2 over 2 multiplied by 3 multiplied by 5 multiplied by 5 over 2 multiplied by 5 multiplied by 5
e A LaTex expression showing 2 multiplied by 5 over 2 multiplied by 3 multiplied by 5 over 2 multiplied by 5
f A LaTex expression showing 11 multiplied by 2 over 2 multiplied by 3 multiplied by 5 over 5 multiplied by 5 multiplied by 5
2
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 5 over 9 divided by 15 over 18
a A LaTex expression showing 5 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 5
b A LaTex expression showing 5 over 3 multiplied by 3 multiplied by 2 multiplied by 3 over 3 multiplied by 3 multiplied by 5
c A LaTex expression showing 5 over 3 multiplied by 3 multiplied by 2 multiplied by 3 multiplied by 3 over 3 multiplied by 5
d A LaTex expression showing 2 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 5
e A LaTex expression showing 7 over 3 multiplied by 2 multiplied by 3 multiplied by 3 over 3 multiplied by 13
3
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 30 over 21 divided by 25 over 7
a A LaTex expression showing 2 multiplied by 2 multiplied by 3 multiplied by 5 over 3 multiplied by 3 multiplied by 7 multiplied by 7 over 5 multiplied by 5
b A LaTex expression showing 2 multiplied by 3 multiplied by 5 over 3 multiplied by 7 multiplied by 7 multiplied by 7 over 5 multiplied by 5 multiplied by 5
c A LaTex expression showing 2 multiplied by 2 multiplied by 3 multiplied by 5 multiplied by 5 over 3 multiplied by 7 multiplied by 7 over 5 multiplied by 5
d A LaTex expression showing 2 multiplied by 2 multiplied by 5 over 3 multiplied by 7 multiplied by 7 over 5 multiplied by 5
e A LaTex expression showing 2 multiplied by 3 over 3 multiplied by 7 over 5
f A LaTex expression showing 2 multiplied by 3 multiplied by 5 over 3 multiplied by 7 multiplied by 7 over 5 multiplied by 5
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 63 over 81
a A LaTex expression showing 1 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 3 multiplied by 7
b A LaTex expression showing 11 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 3 multiplied by 7
c A LaTex expression showing 1 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 3 multiplied by 7
d A LaTex expression showing 1 over 2 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 3
e A LaTex expression showing 1 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 3 multiplied by 3 multiplied by 7
5
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 20 over 30 divided by 2 over 7
a A LaTex expression showing 2 over 2 multiplied by 3 multiplied by 3 multiplied by 11 multiplied by 7 over 2
b A LaTex expression showing 2 multiplied by 2 multiplied by 5 over 2 multiplied by 3 multiplied by 5 multiplied by 7 over 2
c A LaTex expression showing 2 multiplied by 2 multiplied by 3 over 2 multiplied by 3 multiplied by 5 multiplied by 5 multiplied by 7 multiplied by 7 over 2
d A LaTex expression showing 2 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 3 multiplied by 13 multiplied by 7 over 2
e A LaTex expression showing 2 multiplied by 5 over 2 multiplied by 3 multiplied by 5 multiplied by 5 multiplied by 7 multiplied by 7 over 2
f A LaTex expression showing 2 multiplied by 2 over 2 multiplied by 3 multiplied by 5 multiplied by 7 multiplied by 7 over 3
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 multiplied by 3 over 1
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 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
d A LaTex expression showing 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 2 over 3
e 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
7
Use factorization to simplify. Invert and factor to show what factors in this fraction division can be cancelled out
A LaTex expression showing 6 over 7 divided by 12 over 10
a A LaTex expression showing 2 multiplied by 11 over 7 multiplied by 2 multiplied by 5 over 2 multiplied by 3
b A LaTex expression showing 2 multiplied by 3 multiplied by 3 over 7 multiplied by 2 multiplied by 5 over 5 multiplied by 2 multiplied by 3
c A LaTex expression showing 2 multiplied by 3 multiplied by 3 over 3 multiplied by 2 multiplied by 5 over 2 multiplied by 2 multiplied by 3
d A LaTex expression showing 7 multiplied by 3 over 7 multiplied by 2 multiplied by 5 over 2 multiplied by 2 multiplied by 2 multiplied by 5
e A LaTex expression showing 2 multiplied by 3 over 7 multiplied by 2 multiplied by 5 over 2 multiplied by 2 multiplied by 3