Factoring - Simplifying Fractions with Factors - Composite to Bracketed Factors (Level 2)

In this math topic, learners practice factoring numbers and simplifying fractions by identifying and canceling out common factors between the numerator and the denominator. The problems involve transforming composite numbers into their prime factorized form within fractions, then identifying like factors that can be cancelled to simplify the expressions. This set of exercises aims to strengthen skills in multiplication, division, and understanding of factors in the context of fractions.

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

21×4×105×6×20\frac{21 \times 4 \times 10}{5 \times 6 \times 20}

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 2)'. 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 2 multiplied by 28 multiplied by 9 over 3 multiplied by 70 multiplied by 6
a A LaTex expression showing (13) multiplied by (2 multiplied by 2 multiplied by 11) multiplied by (3 multiplied by 3) over (3) multiplied by (2 multiplied by 5 multiplied by 7) multiplied by (2 multiplied by 3)
b A LaTex expression showing (5) multiplied by (2 multiplied by 5 multiplied by 7) multiplied by (11 multiplied by 3) over (3) multiplied by (13 multiplied by 5 multiplied by 7) multiplied by (2 multiplied by 13)
c A LaTex expression showing (2) multiplied by (2 multiplied by 3) multiplied by (3) over (3) multiplied by (13 multiplied by 5 multiplied by 7) multiplied by (2 multiplied by 3)
d A LaTex expression showing (13) multiplied by (2 multiplied by 2 multiplied by 5) multiplied by (3 multiplied by 2) over (3) multiplied by (2 multiplied by 5) multiplied by (2 multiplied by 3)
e A LaTex expression showing (2) multiplied by (2 multiplied by 2 multiplied by 7) multiplied by (5 multiplied by 3 multiplied by 3) over (3) multiplied by (2 multiplied by 2 multiplied by 13) multiplied by (2 multiplied by 3 multiplied by 3)
f A LaTex expression showing (2) multiplied by (2 multiplied by 2 multiplied by 7) multiplied by (3 multiplied by 3) over (3) multiplied by (2 multiplied by 5 multiplied by 7) multiplied by (2 multiplied by 3)
2
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 21 multiplied by 10 multiplied by 4 over 30 multiplied by 20
a A LaTex expression showing (3 multiplied by 7) multiplied by (2 multiplied by 5) multiplied by (2 multiplied by 2) over (2 multiplied by 3 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 5)
b A LaTex expression showing (3 multiplied by 7) multiplied by (2 multiplied by 5) multiplied by (2 multiplied by 2) over (2 multiplied by 3 multiplied by 5) multiplied by (2 multiplied by 2)
c A LaTex expression showing (3 multiplied by 7) multiplied by (2) multiplied by (2 multiplied by 2 multiplied by 2) over (2 multiplied by 3 multiplied by 5) multiplied by (2 multiplied by 5)
d A LaTex expression showing (3 multiplied by 7) multiplied by (5) multiplied by (2 multiplied by 2) over (2 multiplied by 3 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 5 multiplied by 5)
e A LaTex expression showing (3 multiplied by 7) multiplied by (2 multiplied by 5 multiplied by 5) multiplied by (2 multiplied by 2) over (2 multiplied by 2 multiplied by 7 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 5)
f A LaTex expression showing (3 multiplied by 7) multiplied by (3) multiplied by (2) over (2 multiplied by 3 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 2)
3
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 2 multiplied by 4 multiplied by 30 over 5 multiplied by 14 multiplied by 12
a A LaTex expression showing (2) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 3 multiplied by 5) over (5) multiplied by (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 3 multiplied by 3)
b A LaTex expression showing (5) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 3 multiplied by 3 multiplied by 5) over (5) multiplied by (5 multiplied by 7) multiplied by (2 multiplied by 13 multiplied by 3)
c A LaTex expression showing (13) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 3 multiplied by 3) over (5) multiplied by (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 3)
d A LaTex expression showing (2) multiplied by (2) multiplied by (2 multiplied by 3 multiplied by 5) over (5) multiplied by (2) multiplied by (7 multiplied by 2 multiplied by 3)
e A LaTex expression showing (2) multiplied by (5 multiplied by 2) multiplied by (3 multiplied by 5) over (5) multiplied by (2 multiplied by 7) multiplied by (5 multiplied by 2 multiplied by 3 multiplied by 3)
f A LaTex expression showing (2) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 3 multiplied by 5) over (5) multiplied by (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 3)
4
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 7 multiplied by 15 multiplied by 12 over 14 multiplied by 42 multiplied by 5
a A LaTex expression showing (7 multiplied by 7) multiplied by (5) multiplied by (2 multiplied by 2 multiplied by 3) over (13 multiplied by 7) multiplied by (2 multiplied by 3 multiplied by 7) multiplied by (5)
b A LaTex expression showing (7) multiplied by (3 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 3) over (2 multiplied by 7) multiplied by (2 multiplied by 3 multiplied by 7) multiplied by (5)
c A LaTex expression showing (7) multiplied by (3 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 3) over (2 multiplied by 7) multiplied by (2 multiplied by 3 multiplied by 7 multiplied by 7) multiplied by (13)
d A LaTex expression showing (7) multiplied by (3 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 3) over (2 multiplied by 7) multiplied by (2 multiplied by 3 multiplied by 2) multiplied by (5)
e A LaTex expression showing (7) multiplied by (5 multiplied by 5) multiplied by (2 multiplied by 2 multiplied by 2 multiplied by 3) over (11 multiplied by 7) multiplied by (2 multiplied by 3 multiplied by 7) multiplied by (5)
5
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 70 multiplied by 7 multiplied by 15 over 5 multiplied by 30 multiplied by 35
a A LaTex expression showing (2 multiplied by 5 multiplied by 5 multiplied by 7) multiplied by (7) multiplied by (3 multiplied by 3 multiplied by 5) over (5) multiplied by (2 multiplied by 11 multiplied by 5) multiplied by (11 multiplied by 7)
b A LaTex expression showing (2 multiplied by 5 multiplied by 7) multiplied by (3) multiplied by (3 multiplied by 5) over (5 multiplied by 5) multiplied by (2 multiplied by 3 multiplied by 5) multiplied by (5 multiplied by 7)
c A LaTex expression showing (2 multiplied by 3 multiplied by 7) multiplied by (7) multiplied by (3 multiplied by 5) over (5) multiplied by (13 multiplied by 3 multiplied by 5) multiplied by (7)
d A LaTex expression showing (2 multiplied by 5 multiplied by 7) multiplied by (7) multiplied by (3 multiplied by 5) over (5) multiplied by (2 multiplied by 3 multiplied by 5) multiplied by (5 multiplied by 7)
e A LaTex expression showing (2 multiplied by 5 multiplied by 7) multiplied by (11) multiplied by (3 multiplied by 5) over (5) multiplied by (2 multiplied by 3 multiplied by 5) multiplied by (7)
f A LaTex expression showing (7 multiplied by 7 multiplied by 7) multiplied by (7) multiplied by (3 multiplied by 5) over (5) multiplied by (2 multiplied by 3 multiplied by 5) multiplied by (5 multiplied by 7 multiplied by 7)
6
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 18 multiplied by 2 multiplied by 10 over 12 multiplied by 5 multiplied by 4
a A LaTex expression showing (3 multiplied by 3) multiplied by (5) multiplied by (11 multiplied by 5) over (2 multiplied by 2 multiplied by 3) multiplied by (5) multiplied by (2 multiplied by 2)
b A LaTex expression showing (3 multiplied by 3) multiplied by (2) multiplied by (2 multiplied by 5) over (2 multiplied by 2 multiplied by 3) multiplied by (5) multiplied by (2 multiplied by 2)
c A LaTex expression showing (11 multiplied by 11 multiplied by 3) multiplied by (2) multiplied by (2 multiplied by 5) over (2 multiplied by 2 multiplied by 3) multiplied by (5) multiplied by (2 multiplied by 2)
d A LaTex expression showing (2 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 3) multiplied by (2) multiplied by (2 multiplied by 5) over (2 multiplied by 2 multiplied by 3) multiplied by (5) multiplied by (2 multiplied by 2)
e A LaTex expression showing (2 multiplied by 3 multiplied by 3) multiplied by (2) multiplied by (2 multiplied by 5) over (2 multiplied by 2 multiplied by 3) multiplied by (5) multiplied by (2 multiplied by 2)
f A LaTex expression showing (2 multiplied by 3 multiplied by 3) multiplied by (2) multiplied by (2 multiplied by 5) over (2 multiplied by 2 multiplied by 3 multiplied by 3) multiplied by (5) multiplied by (2 multiplied by 2 multiplied by 2)
7
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 21 multiplied by 4 multiplied by 10 over 5 multiplied by 6 multiplied by 20
a A LaTex expression showing (3 multiplied by 7) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 5) over (5 multiplied by 5) multiplied by (2 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 5)
b A LaTex expression showing (3 multiplied by 7) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 2 multiplied by 5) over (11) multiplied by (2 multiplied by 2 multiplied by 3) multiplied by (11 multiplied by 2 multiplied by 5)
c A LaTex expression showing (5 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 2) multiplied by (2 multiplied by 5) over (5) multiplied by (2 multiplied by 3) multiplied by (13 multiplied by 2)
d A LaTex expression showing (3 multiplied by 7) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 5) over (5) multiplied by (2 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 5)
e A LaTex expression showing (3 multiplied by 3) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 5) over (13) multiplied by (2) multiplied by (2 multiplied by 5)
f A LaTex expression showing (3 multiplied by 7 multiplied by 7) multiplied by (2 multiplied by 2) multiplied by (2 multiplied by 11) over (5) multiplied by (2 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 5)