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

These math problems focus on simplifying fractions by factoring both the numerator and the denominator to identify common factors that can be cancelled out. This topic involves skills in multiplication, division, identification of factors, and manipulation of fractions. The exercises challenge the students to factorize composite numbers into their prime or simplest components and then simplify the fractions by cancelling out common terms. The problems are structured to provide multiple choices, requiring a clear understanding of elementary factors and fraction simplification.

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

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Simplifying Fractions with Factors - Composite to Factored

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


Use factorization to show what factors in this fraction can be cancelled out

6×1030×5\frac{6 \times 10}{30 \times 5}

Factoring - Simplifying Fractions with Factors - Composite to Factored Worksheet

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Math worksheet on 'Factoring - Simplifying Fractions 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 show what factors in this fraction can be cancelled out
A LaTex expression showing 5 multiplied by 20 over 4 multiplied by 35
a A LaTex expression showing 2 multiplied by 5 over 2 multiplied by 2 multiplied by 5 multiplied by 5 multiplied by 7
b A LaTex expression showing 5 multiplied by 2 multiplied by 7 multiplied by 5 over 2 multiplied by 2 multiplied by 5 multiplied by 7
c A LaTex expression showing 5 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 2 multiplied by 5 multiplied by 7
d A LaTex expression showing 5 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 2 multiplied by 2 multiplied by 5 multiplied by 7
e A LaTex expression showing 5 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 5 over 2 multiplied by 2 multiplied by 5 multiplied by 7
f A LaTex expression showing 5 multiplied by 2 multiplied by 5 multiplied by 5 over 2 multiplied by 5 multiplied by 7
2
Use factorization to show what factors in this fraction can be cancelled out
A LaTex expression showing 15 multiplied by 6 over 12 multiplied by 5
a A LaTex expression showing 3 multiplied by 5 multiplied by 5 over 2 multiplied by 2 multiplied by 5
b A LaTex expression showing 7 multiplied by 5 multiplied by 2 multiplied by 3 over 2 multiplied by 2 multiplied by 3 multiplied by 5
c A LaTex expression showing 3 multiplied by 5 multiplied by 2 multiplied by 3 over 2 multiplied by 2 multiplied by 13 multiplied by 5
d A LaTex expression showing 3 multiplied by 5 multiplied by 2 multiplied by 3 over 2 multiplied by 2 multiplied by 3 multiplied by 5
e A LaTex expression showing 11 multiplied by 5 multiplied by 2 multiplied by 3 over 2 multiplied by 3 multiplied by 5 multiplied by 5
f A LaTex expression showing 11 multiplied by 5 multiplied by 11 over 2 multiplied by 2 multiplied by 3 multiplied by 5
3
Use factorization to show what factors in this fraction can be cancelled out
A LaTex expression showing 15 multiplied by 15 over 2 multiplied by 75
a A LaTex expression showing 3 multiplied by 5 multiplied by 3 multiplied by 5 over 2 multiplied by 3 multiplied by 5 multiplied by 5 multiplied by 5
b A LaTex expression showing 11 multiplied by 5 multiplied by 3 multiplied by 2 over 3 multiplied by 5
c A LaTex expression showing 3 multiplied by 5 multiplied by 3 multiplied by 5 over 3 multiplied by 3 multiplied by 5 multiplied by 5
d A LaTex expression showing 3 multiplied by 5 multiplied by 5 multiplied by 3 multiplied by 5 over 2 multiplied by 3 multiplied by 3 multiplied by 5
e A LaTex expression showing 3 multiplied by 5 multiplied by 3 multiplied by 5 over 2 multiplied by 3 multiplied by 5 multiplied by 3
f A LaTex expression showing 3 multiplied by 5 multiplied by 3 multiplied by 5 over 2 multiplied by 3 multiplied by 5 multiplied by 5
4
Use factorization to show what factors in this fraction can be cancelled out
A LaTex expression showing 4 multiplied by 35 over 3 multiplied by 70
a A LaTex expression showing 2 multiplied by 2 multiplied by 3 over 3 multiplied by 2 multiplied by 5 multiplied by 7
b A LaTex expression showing 2 multiplied by 2 multiplied by 5 multiplied by 7 over 2 multiplied by 2 multiplied by 5 multiplied by 5 multiplied by 7
c A LaTex expression showing 2 multiplied by 2 multiplied by 5 multiplied by 7 over 3 multiplied by 2 multiplied by 5 multiplied by 7
d A LaTex expression showing 2 multiplied by 2 multiplied by 5 multiplied by 7 over 7 multiplied by 2 multiplied by 5
e A LaTex expression showing 2 multiplied by 3 multiplied by 5 multiplied by 3 over 3 multiplied by 5 multiplied by 7
5
Use factorization to show what factors in this fraction can be cancelled out
A LaTex expression showing 35 multiplied by 14 over 3 multiplied by 98
a A LaTex expression showing 5 multiplied by 7 multiplied by 13 multiplied by 5 over 3 multiplied by 2 multiplied by 7 multiplied by 7 multiplied by 7
b A LaTex expression showing 5 multiplied by 7 multiplied by 5 multiplied by 5 over 3 multiplied by 2 multiplied by 7 multiplied by 7 multiplied by 7
c A LaTex expression showing 5 multiplied by 2 multiplied by 2 multiplied by 7 over 3 multiplied by 2 multiplied by 7 multiplied by 7 multiplied by 7
d A LaTex expression showing 5 multiplied by 7 multiplied by 2 over 3 multiplied by 2 multiplied by 2 multiplied by 11
e A LaTex expression showing 5 multiplied by 7 multiplied by 2 multiplied by 7 over 3 multiplied by 2 multiplied by 7 multiplied by 7
f A LaTex expression showing 5 multiplied by 7 multiplied by 3 multiplied by 5 over 3 multiplied by 2 multiplied by 7
6
Use factorization to show what factors in this fraction can be cancelled out
A LaTex expression showing 3 multiplied by 42 over 21 multiplied by 15
a A LaTex expression showing 13 multiplied by 2 multiplied by 7 over 3 multiplied by 7 multiplied by 3 multiplied by 5
b A LaTex expression showing 3 multiplied by 3 multiplied by 2 multiplied by 3 multiplied by 7 over 3 multiplied by 7 multiplied by 7 multiplied by 3 multiplied by 5 multiplied by 5
c A LaTex expression showing 3 multiplied by 2 multiplied by 3 multiplied by 7 over 3 multiplied by 7 multiplied by 3 multiplied by 5
d A LaTex expression showing 5 multiplied by 2 multiplied by 3 multiplied by 7 over 3 multiplied by 7 multiplied by 3 multiplied by 3 multiplied by 5
e A LaTex expression showing 3 multiplied by 2 multiplied by 2 multiplied by 2 multiplied by 13 over 3 multiplied by 7
7
Use factorization to show what factors in this fraction can be cancelled out
A LaTex expression showing 15 multiplied by 35 over 30 multiplied by 5
a A LaTex expression showing 5 multiplied by 5 multiplied by 7 over 5 multiplied by 3 multiplied by 5 multiplied by 5
b A LaTex expression showing 3 multiplied by 5 multiplied by 5 multiplied by 7 over 2 multiplied by 3 multiplied by 5 multiplied by 5
c A LaTex expression showing 3 multiplied by 5 multiplied by 5 multiplied by 7 over 2 multiplied by 3 multiplied by 5 multiplied by 5 multiplied by 5
d A LaTex expression showing 3 multiplied by 5 multiplied by 5 multiplied by 7 multiplied by 7 over 2 multiplied by 3 multiplied by 5 multiplied by 13
e A LaTex expression showing 3 multiplied by 5 multiplied by 5 multiplied by 7 over 7 multiplied by 3 multiplied by 5 multiplied by 11
f A LaTex expression showing 3 multiplied by 3 multiplied by 5 multiplied by 5 multiplied by 7 over 2 multiplied by 3 multiplied by 5 multiplied by 5