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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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 - Practice' Learn online: app.mobius.academy/math/units/factoring_multiplication_division_fractions_practice/
1
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 28 multiplied by 14 multiplied by 3 over 4 multiplied by 21 multiplied by 35
a A LaTex expression showing (2 multiplied by 2 multiplied by 7) multiplied by (2 multiplied by 7) multiplied by (3) over (2 multiplied by 2) multiplied by (13 multiplied by 3) multiplied by (5 multiplied by 7)
b A LaTex expression showing (13 multiplied by 2 multiplied by 7) multiplied by (3 multiplied by 7) multiplied by (3) over (2 multiplied by 2) multiplied by (11 multiplied by 7) multiplied by (5 multiplied by 7)
c A LaTex expression showing (2 multiplied by 7) multiplied by (2 multiplied by 7 multiplied by 7) multiplied by (3) over (2 multiplied by 2) multiplied by (3 multiplied by 3 multiplied by 7) multiplied by (5 multiplied by 7 multiplied by 7)
d A LaTex expression showing (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 7) multiplied by (3) over (2 multiplied by 2) multiplied by (3 multiplied by 7) multiplied by (5 multiplied by 11)
e A LaTex expression showing (2 multiplied by 2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 7) multiplied by (3) over (2 multiplied by 2) multiplied by (3 multiplied by 7) multiplied by (5 multiplied by 7)
f A LaTex expression showing (2 multiplied by 2 multiplied by 7) multiplied by (2 multiplied by 7) multiplied by (3) over (2 multiplied by 2) multiplied by (3 multiplied by 7) multiplied by (5 multiplied by 7)
2
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 27 multiplied by 20 over 30 multiplied by 5 multiplied by 9
a A LaTex expression showing (2 multiplied by 3 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 5 multiplied by 5) over (2 multiplied by 3 multiplied by 5 multiplied by 5) multiplied by (5) multiplied by (3 multiplied by 3)
b A LaTex expression showing (3 multiplied by 3 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 2) over (2 multiplied by 3 multiplied by 5) multiplied by (5) multiplied by (3 multiplied by 3 multiplied by 3)
c A LaTex expression showing (3 multiplied by 2) multiplied by (2 multiplied by 2 multiplied by 5) over (2 multiplied by 3 multiplied by 3 multiplied by 7) multiplied by (3) multiplied by (3 multiplied by 3 multiplied by 3)
d A LaTex expression showing (3 multiplied by 3 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 5) over (2 multiplied by 3 multiplied by 5) multiplied by (5) multiplied by (3 multiplied by 3)
e A LaTex expression showing (3 multiplied by 5 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 5) over (2 multiplied by 3 multiplied by 7) multiplied by (5) multiplied by (3 multiplied by 3)
f A LaTex expression showing (3 multiplied by 3) multiplied by (5 multiplied by 2 multiplied by 7) over (2 multiplied by 3 multiplied by 5 multiplied by 5) multiplied by (5) multiplied by (3 multiplied by 3)
3
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 2) multiplied by (5)
c 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)
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 7) multiplied by (5)
e 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)
4
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 35 multiplied by 7 multiplied by 30 over 25 multiplied by 5 multiplied by 42
a A LaTex expression showing (5 multiplied by 7) multiplied by (7) multiplied by (2 multiplied by 3 multiplied by 5) over (5 multiplied by 5) multiplied by (11) multiplied by (2 multiplied by 3 multiplied by 3)
b A LaTex expression showing (5 multiplied by 7) multiplied by (7) multiplied by (2 multiplied by 3 multiplied by 5) over (5 multiplied by 5) multiplied by (5) multiplied by (2 multiplied by 3 multiplied by 7)
c A LaTex expression showing (5 multiplied by 7) multiplied by (7) multiplied by (2 multiplied by 5) over (2) multiplied by (5 multiplied by 5) multiplied by (5)
d A LaTex expression showing (2 multiplied by 7) multiplied by (11) multiplied by (13 multiplied by 3 multiplied by 5 multiplied by 5) over (13 multiplied by 11) multiplied by (5) multiplied by (3 multiplied by 7)
e A LaTex expression showing (5 multiplied by 3) multiplied by (7) multiplied by (2 multiplied by 3 multiplied by 5) over (5 multiplied by 5 multiplied by 5) multiplied by (5) multiplied by (2 multiplied by 3 multiplied by 7)
f A LaTex expression showing (5 multiplied by 7) multiplied by (7) multiplied by (5 multiplied by 5 multiplied by 5) over (5 multiplied by 5) multiplied by (5) multiplied by (2 multiplied by 3 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 5 multiplied by 6 multiplied by 12 over 14 multiplied by 36
a A LaTex expression showing (5) multiplied by (2) multiplied by (2 multiplied by 2 multiplied by 3) over (2 multiplied by 7) multiplied by (2 multiplied by 3 multiplied by 3)
b A LaTex expression showing (5) multiplied by (2) multiplied by (11 multiplied by 2 multiplied by 3) over (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 7 multiplied by 3)
c A LaTex expression showing (5) multiplied by (2 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 3) over (2 multiplied by 7) multiplied by (3 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 3)
d A LaTex expression showing (5) multiplied by (2 multiplied by 3) multiplied by (2 multiplied by 2 multiplied by 3) over (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 3 multiplied by 3)
e A LaTex expression showing (5) multiplied by (3) multiplied by (2 multiplied by 2 multiplied by 2 multiplied by 3) over (3 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 2 multiplied by 3 multiplied by 3 multiplied by 7)
f A LaTex expression showing (5) multiplied by (11 multiplied by 13) multiplied by (2 multiplied by 2 multiplied by 3) over (2) multiplied by (2 multiplied by 2 multiplied by 3 multiplied by 3)
6
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 5 multiplied by 42 multiplied by 35 over 21 multiplied by 75 multiplied by 7
a A LaTex expression showing (5) multiplied by (2 multiplied by 2 multiplied by 2) multiplied by (5 multiplied by 7) over (3) multiplied by (3 multiplied by 5 multiplied by 5 multiplied by 5) multiplied by (7 multiplied by 7)
b A LaTex expression showing (5 multiplied by 5) multiplied by (3) multiplied by (2 multiplied by 7) over (3 multiplied by 7) multiplied by (5 multiplied by 5 multiplied by 11) multiplied by (7)
c A LaTex expression showing (5) multiplied by (2 multiplied by 3 multiplied by 7) multiplied by (5 multiplied by 7) over (3 multiplied by 7) multiplied by (3 multiplied by 5 multiplied by 5) multiplied by (7)
d A LaTex expression showing (5) multiplied by (2 multiplied by 7 multiplied by 7) multiplied by (5 multiplied by 7) over (3 multiplied by 3) multiplied by (3 multiplied by 5 multiplied by 5) multiplied by (7)
e A LaTex expression showing (5) multiplied by (13 multiplied by 3 multiplied by 7) multiplied by (5 multiplied by 5 multiplied by 7) over (3 multiplied by 3) multiplied by (3 multiplied by 3 multiplied by 5 multiplied by 5) multiplied by (7)
f A LaTex expression showing (5) multiplied by (2 multiplied by 2 multiplied by 3 multiplied by 7) multiplied by (2 multiplied by 7) over (3 multiplied by 7) multiplied by (5 multiplied by 5 multiplied by 5) multiplied by (7)
7
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 45 multiplied by 63 over 9 multiplied by 49 multiplied by 15
a A LaTex expression showing (3 multiplied by 3 multiplied by 5) multiplied by (3 multiplied by 3 multiplied by 7) over (3 multiplied by 3 multiplied by 3 multiplied by 3) multiplied by (13 multiplied by 7) multiplied by (3 multiplied by 2)
b A LaTex expression showing (3 multiplied by 3 multiplied by 5) multiplied by (3 multiplied by 3 multiplied by 7) over (3 multiplied by 3) multiplied by (7 multiplied by 7) multiplied by (3 multiplied by 5)
c A LaTex expression showing (3 multiplied by 3 multiplied by 3 multiplied by 5) multiplied by (3 multiplied by 7) over (3) multiplied by (7) multiplied by (5 multiplied by 5)
d A LaTex expression showing (3 multiplied by 3 multiplied by 3 multiplied by 11) multiplied by (3 multiplied by 3 multiplied by 7 multiplied by 7) over (3 multiplied by 3) multiplied by (13) multiplied by (3 multiplied by 5)
e A LaTex expression showing (3 multiplied by 3 multiplied by 5) multiplied by (3 multiplied by 3 multiplied by 3 multiplied by 7) over (3) multiplied by (2 multiplied by 7) multiplied by (3 multiplied by 5 multiplied by 5)
f A LaTex expression showing (3 multiplied by 3 multiplied by 5) multiplied by (3 multiplied by 3 multiplied by 7) over (3 multiplied by 3 multiplied by 3) multiplied by (7 multiplied by 7) multiplied by (3)
Factoring - Simplifying Fractions with Factors - Composite to Bracketed Factors (Level 2) - Mobius Math