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

This math topic covers the skill of simplifying fraction multiplication through factorization, specifically transitioning from composite numbers to their factored forms. Students practice identifying and cancelling out common factors in multiplicative fractions and express their operations on various complex fractions. The focus is on recognizing factorable numbers in the numerator and denominator of fractions, optimizing them to simpler terms. This set of problems enhances understanding of multiplication and division within the framework of fractions and factorization.

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
A LaTex expression showing 14 over 2 multiplied by 9 over 45
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
a A LaTex expression showing 2 multiplied by 7 over 2 multiplied by 3 multiplied by 3 over 3 multiplied by 3 multiplied by 3 multiplied by 5
b A LaTex expression showing 2 multiplied by 7 over 2 multiplied by 3 multiplied by 3 over 3 multiplied by 3 multiplied by 5
2
A LaTex expression showing 35 over 21 multiplied by 9 over 21
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
a A LaTex expression showing 5 multiplied by 7 over 3 multiplied by 7 multiplied by 3 multiplied by 3 over 3 multiplied by 7
b A LaTex expression showing 5 multiplied by 7 over 3 multiplied by 11 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 3 multiplied by 7
3
A LaTex expression showing 2 over 21 multiplied by 42 over 14
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
a A LaTex expression showing 2 over 3 multiplied by 7 multiplied by 2 multiplied by 3 multiplied by 7 over 2 multiplied by 7
b A LaTex expression showing 2 over 2 multiplied by 7 multiplied by 2 multiplied by 3 multiplied by 7 over 2 multiplied by 7 multiplied by 7
4
A LaTex expression showing 21 over 63 multiplied by 6 over 3
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
a A LaTex expression showing 3 multiplied by 7 multiplied by 7 over 3 multiplied by 7 multiplied by 7 multiplied by 2 multiplied by 3 multiplied by 3 over 3
b A LaTex expression showing 3 multiplied by 7 over 3 multiplied by 3 multiplied by 7 multiplied by 2 multiplied by 3 over 3
5
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 15 over 70 multiplied by 35 over 3
a A LaTex expression showing 3 multiplied by 5 over 2 multiplied by 5 multiplied by 7 over 3
b A LaTex expression showing 3 multiplied by 5 over 2 multiplied by 5 multiplied by 7 multiplied by 5 multiplied by 5 multiplied by 7 over 3
c A LaTex expression showing 3 multiplied by 5 over 2 multiplied by 5 multiplied by 7 multiplied by 5 multiplied by 7 over 3
6
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 100 over 6 multiplied by 1 over 10
a A LaTex expression showing 2 multiplied by 2 multiplied by 5 multiplied by 5 over 2 multiplied by 3 multiplied by 1 over 2 multiplied by 5
b A LaTex expression showing 2 multiplied by 5 multiplied by 5 over 2 multiplied by 3 multiplied by 1 over 2 multiplied by 5
c A LaTex expression showing 2 multiplied by 2 multiplied by 5 multiplied by 5 over 2 multiplied by 3 multiplied by 13 over 2 multiplied by 5
7
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 1 over 3 multiplied by 54 over 30
a A LaTex expression showing 1 over 3 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 3 over 2 multiplied by 3 multiplied by 5
b A LaTex expression showing 1 multiplied by 1 over 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 multiplied by 3 over 2 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 5
c A LaTex expression showing 7 over 3 multiplied by 7 multiplied by 3 multiplied by 3 multiplied by 3 over 2
8
Use factorization to simplify by showing what factors in this fraction multiplication can be cancelled out
A LaTex expression showing 10 over 50 multiplied by 14 over 2
a A LaTex expression showing 5 over 2 multiplied by 5 multiplied by 13 multiplied by 13 multiplied by 7 over 7
b A LaTex expression showing 2 multiplied by 5 over 2 multiplied by 5 multiplied by 5 multiplied by 2 multiplied by 7 over 2
c A LaTex expression showing 2 multiplied by 5 over 2 multiplied by 5 multiplied by 5 multiplied by 2 multiplied by 7 over 13