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

This math topic focuses on using factorization to simplify fractions by finding and cancelling out common factors. It provides problems related to breaking down composite numbers into their prime factors and then simplifying the fractions by removing identical factors from the numerator and denominator. This is a basic introduction to concepts of factoring, multiplication, and division within the realm of fractions, ideal for learners starting to explore these areas in algebra.

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 Bracketed Factors

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

Use factorization to factor each number and show what factors in this fraction can be cancelled out

70×214×4\frac{70 \times 2}{14 \times 4}

Factoring - Simplifying Fractions with Factors - Composite to Bracketed Factors Worksheet

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Math worksheet on 'Factoring - Simplifying Fractions with Factors - Composite to Bracketed Factors (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 factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 42 multiplied by 5 over 2 multiplied by 70
a A LaTex expression showing (2 multiplied by 7 multiplied by 7) multiplied by (5) over (2) multiplied by (2 multiplied by 2 multiplied by 5 multiplied by 3)
b A LaTex expression showing (2 multiplied by 3 multiplied by 7) multiplied by (5) over (2) multiplied by (2 multiplied by 5 multiplied by 7)
c A LaTex expression showing (2 multiplied by 3 multiplied by 7) multiplied by (7) over (2) multiplied by (2 multiplied by 5 multiplied by 7)
d A LaTex expression showing (11 multiplied by 3 multiplied by 3 multiplied by 7) multiplied by (13) over (2) multiplied by (2 multiplied by 2 multiplied by 11)
e A LaTex expression showing (2 multiplied by 3 multiplied by 7) multiplied by (5) over (3) multiplied by (2 multiplied by 5)
2
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 14 multiplied by 35 over 5 multiplied by 70
a A LaTex expression showing (2 multiplied by 2 multiplied by 7) multiplied by (5 multiplied by 7) over (5) multiplied by (2 multiplied by 5 multiplied by 7)
b A LaTex expression showing (2 multiplied by 7) multiplied by (5 multiplied by 7) over (5) multiplied by (2 multiplied by 5 multiplied by 7)
c A LaTex expression showing (2 multiplied by 7 multiplied by 7) multiplied by (7) over (5) multiplied by (2 multiplied by 7)
d A LaTex expression showing (7 multiplied by 7 multiplied by 7) multiplied by (5 multiplied by 7) over (5) multiplied by (2 multiplied by 7)
e A LaTex expression showing (7) multiplied by (2 multiplied by 7) over (5) multiplied by (2 multiplied by 5 multiplied by 7)
f A LaTex expression showing (2 multiplied by 7 multiplied by 7) multiplied by (7) over (5) multiplied by (2 multiplied by 7)
3
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 10 multiplied by 21 over 75 multiplied by 7
a A LaTex expression showing (2 multiplied by 5) multiplied by (3 multiplied by 7) over (3 multiplied by 5 multiplied by 5 multiplied by 5) multiplied by (11)
b A LaTex expression showing (2 multiplied by 5) multiplied by (3 multiplied by 7) over (3 multiplied by 5 multiplied by 5) multiplied by (7)
c A LaTex expression showing (5) multiplied by (3 multiplied by 7) over (3 multiplied by 5 multiplied by 5) multiplied by (7)
d A LaTex expression showing (2 multiplied by 5) multiplied by (3 multiplied by 7) over (3 multiplied by 5) multiplied by (7)
e A LaTex expression showing (7) multiplied by (3 multiplied by 3) over (3 multiplied by 5 multiplied by 5 multiplied by 5) multiplied by (7)
f A LaTex expression showing (2 multiplied by 5) multiplied by (3 multiplied by 13) over (3 multiplied by 5 multiplied by 5 multiplied by 5) multiplied by (7)
4
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 5 multiplied by 98 over 30 multiplied by 7
a A LaTex expression showing (5) multiplied by (7 multiplied by 7) over (2 multiplied by 3 multiplied by 5) multiplied by (7)
b A LaTex expression showing (5) multiplied by (2 multiplied by 7 multiplied by 7) over (2) multiplied by (7)
c A LaTex expression showing (5) multiplied by (2 multiplied by 7 multiplied by 7) over (2 multiplied by 3 multiplied by 2) multiplied by (7)
d A LaTex expression showing (2) multiplied by (2 multiplied by 5 multiplied by 7) over (2 multiplied by 3 multiplied by 5) multiplied by (7 multiplied by 7)
e A LaTex expression showing (5) multiplied by (2 multiplied by 7 multiplied by 7) over (2 multiplied by 3 multiplied by 5) multiplied by (7)
f A LaTex expression showing (5) multiplied by (2 multiplied by 7 multiplied by 7) over (11 multiplied by 3 multiplied by 5) multiplied by (7)
5
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 6 multiplied by 15 over 45 multiplied by 3
a A LaTex expression showing (2) multiplied by (3 multiplied by 5) over (3 multiplied by 5) multiplied by (3)
b A LaTex expression showing (2 multiplied by 3) multiplied by (3) over (3 multiplied by 3 multiplied by 5) multiplied by (3)
c A LaTex expression showing (3) multiplied by (3 multiplied by 5) over (3 multiplied by 3 multiplied by 3 multiplied by 5) multiplied by (3)
d A LaTex expression showing (2 multiplied by 3) multiplied by (3 multiplied by 5) over (3 multiplied by 3 multiplied by 5) multiplied by (3)
e A LaTex expression showing (3 multiplied by 3) multiplied by (3 multiplied by 3) over (3 multiplied by 3 multiplied by 5) multiplied by (13)
6
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 10 multiplied by 4 over 2 multiplied by 50
a A LaTex expression showing (5) multiplied by (2 multiplied by 2) over (2) multiplied by (2 multiplied by 5 multiplied by 5)
b A LaTex expression showing (2 multiplied by 5) multiplied by (2 multiplied by 2) over (13) multiplied by (2 multiplied by 5 multiplied by 5 multiplied by 5)
c A LaTex expression showing (2 multiplied by 5) multiplied by (7 multiplied by 2 multiplied by 2) over (2) multiplied by (2 multiplied by 2 multiplied by 5 multiplied by 7)
d A LaTex expression showing (2 multiplied by 3) multiplied by (2 multiplied by 2) over (3) multiplied by (5 multiplied by 5)
e A LaTex expression showing (2 multiplied by 5) multiplied by (2 multiplied by 2) over (2) multiplied by (2 multiplied by 5 multiplied by 5)
f A LaTex expression showing (2 multiplied by 5) multiplied by (3 multiplied by 2) over (2) multiplied by (5 multiplied by 5 multiplied by 5)
7
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 75 multiplied by 2 over 42 multiplied by 5
a A LaTex expression showing (3 multiplied by 5 multiplied by 5) multiplied by (2) over (2 multiplied by 3 multiplied by 7) multiplied by (5)
b A LaTex expression showing (3 multiplied by 5) multiplied by (2) over (2 multiplied by 3 multiplied by 5) multiplied by (5)
c A LaTex expression showing (3 multiplied by 5 multiplied by 2) multiplied by (2) over (2 multiplied by 3 multiplied by 7) multiplied by (5)
d A LaTex expression showing (3 multiplied by 5) multiplied by (2 multiplied by 2) over (3 multiplied by 7) multiplied by (5 multiplied by 5)
e A LaTex expression showing (3 multiplied by 5 multiplied by 5) multiplied by (7) over (2 multiplied by 3 multiplied by 7) multiplied by (5)