Simplifying Fraction Multiplication with Factors - Composite to Factored (Level 2)

This math topic focuses on simplifying fraction multiplication through factorization. Students practice identifying and cancelling out common factors in the numerators and denominators of multiple fractions that are multiplied together. The problems encourage students to apply their knowledge of factoring, multiplication, and division skills within the context of fractions. Each question provides a visual representation of fraction multiplication involving large numbers and composite factors, along with multiple-choice answers that demonstrate different factorization outcomes.

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

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

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Factoring - Simplifying Fraction Multiplication with Factors - Composite to Factored
1
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 14 over 5 multiplied by 30 over 5 multiplied by 3 over 84
a A LaTex expression showing 2 multiplied by 2 multiplied by 7 over 3 multiplied by 2 multiplied by 3 multiplied by 2 over 5 multiplied by 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2
b A LaTex expression showing 2 multiplied by 7 over 5 multiplied by 2 multiplied by 3 multiplied by 5 over 5 multiplied by 3 over 2 multiplied by 2 multiplied by 3 multiplied by 7
c A LaTex expression showing 2 multiplied by 7 over 5 multiplied by 2 multiplied by 3 multiplied by 5 over 5 multiplied by 5 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 7
2
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 15 over 14 multiplied by 1 over 25 multiplied by 40 over 6
a A LaTex expression showing 3 multiplied by 5 over 2 multiplied by 7 multiplied by 1 over 5 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 3
b A LaTex expression showing 3 multiplied by 5 over 2 multiplied by 7 multiplied by 1 multiplied by 1 over 5 multiplied by 5 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 3 multiplied by 3
c A LaTex expression showing 3 multiplied by 5 over 2 multiplied by 7 multiplied by 1 over 5 multiplied by 5 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 3
3
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 3 over 90 multiplied by 15 over 2 multiplied by 42 over 7
a A LaTex expression showing 3 over 2 multiplied by 3 multiplied by 3 multiplied by 5 multiplied by 3 multiplied by 5 over 2 multiplied by 2 multiplied by 3 multiplied by 7 over 7
b A LaTex expression showing 3 over 3 multiplied by 3 multiplied by 5 multiplied by 3 multiplied by 5 over 2 multiplied by 2 multiplied by 3 multiplied by 7 over 11
c A LaTex expression showing 3 over 2 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 5 multiplied by 3 over 2 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 7 over 7
4
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 5 over 42 multiplied by 21 over 2 multiplied by 8 over 35
a A LaTex expression showing 5 over 2 multiplied by 3 multiplied by 7 multiplied by 3 multiplied by 7 over 2 multiplied by 2 multiplied by 2 multiplied by 2 over 5 multiplied by 7
b A LaTex expression showing 5 over 3 multiplied by 7 multiplied by 7 over 2 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 2 over 5 multiplied by 7
5
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 63 over 9 multiplied by 2 over 1 multiplied by 21 over 84
a A LaTex expression showing 3 multiplied by 11 over 3 multiplied by 3 multiplied by 3 multiplied by 2 multiplied by 2 over 1 multiplied by 3 multiplied by 7 over 2 multiplied by 13 multiplied by 3 multiplied by 3 multiplied by 7
b A LaTex expression showing 3 multiplied by 3 multiplied by 13 multiplied by 7 over 3 multiplied by 3 multiplied by 2 over 1 multiplied by 7 over 2 multiplied by 2 multiplied by 3 multiplied by 7
c A LaTex expression showing 3 multiplied by 3 multiplied by 7 over 3 multiplied by 3 multiplied by 2 over 1 multiplied by 3 multiplied by 7 over 2 multiplied by 2 multiplied by 3 multiplied by 7
6
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 90 over 3 multiplied by 1 over 12 multiplied by 6 over 9
a A LaTex expression showing 7 multiplied by 3 multiplied by 3 multiplied by 5 over 3 multiplied by 1 over 11 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 3 over 3
b A LaTex expression showing 2 multiplied by 3 multiplied by 3 multiplied by 5 over 5 multiplied by 1 over 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 3 over 13
c A LaTex expression showing 2 multiplied by 3 multiplied by 3 multiplied by 5 over 3 multiplied by 1 over 2 multiplied by 2 multiplied by 3 multiplied by 2 multiplied by 3 over 3 multiplied by 3
7
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 10 over 7 multiplied by 18 over 24 multiplied by 2 over 5
a A LaTex expression showing 2 multiplied by 5 over 7 multiplied by 2 multiplied by 3 multiplied by 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 over 5
b A LaTex expression showing 2 multiplied by 5 over 7 multiplied by 7 multiplied by 2 multiplied by 3 multiplied by 3 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 2 over 5
c A LaTex expression showing 2 multiplied by 5 over 11 multiplied by 2 multiplied by 5 multiplied by 3 over 2 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 5 over 5
8
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 4 over 2 multiplied by 3 over 1 multiplied by 8 over 72
a A LaTex expression showing 2 over 2 multiplied by 3 over 1 multiplied by 2 multiplied by 2 over 5 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 3
b A LaTex expression showing 2 multiplied by 2 over 2 multiplied by 2 multiplied by 3 over 1 multiplied by 2 multiplied by 2 over 2 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 3
c A LaTex expression showing 2 multiplied by 2 over 2 multiplied by 3 over 1 multiplied by 2 multiplied by 2 multiplied by 2 over 2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 3