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

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Factoring - Simplifying Fractions with Factors - Composite to Bracketed Factors
1
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 (7)
b A LaTex expression showing (2 multiplied by 5) multiplied by (3 multiplied by 7) over (3 multiplied by 5) multiplied by (7)
c 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)
d 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)
e 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)
f A LaTex expression showing (5) multiplied by (3 multiplied by 7) over (3 multiplied by 5 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 3 multiplied by 45 over 9 multiplied by 9
a A LaTex expression showing (11) multiplied by (3 multiplied by 3 multiplied by 5) over (3 multiplied by 3) multiplied by (3 multiplied by 7)
b A LaTex expression showing (3) multiplied by (3 multiplied by 5) over (3 multiplied by 3) multiplied by (7)
c A LaTex expression showing (13) multiplied by (3 multiplied by 3 multiplied by 5) over (3 multiplied by 3) multiplied by (2 multiplied by 3)
d A LaTex expression showing (3) multiplied by (3 multiplied by 13 multiplied by 5) over (11 multiplied by 3) multiplied by (3 multiplied by 3)
e A LaTex expression showing (11) multiplied by (3 multiplied by 5) over (3) multiplied by (3 multiplied by 3)
f A LaTex expression showing (3) multiplied by (3 multiplied by 3 multiplied by 5) over (3 multiplied by 3) 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 50 multiplied by 3 over 25 multiplied by 9
a A LaTex expression showing (2 multiplied by 5 multiplied by 5) multiplied by (3) over (5 multiplied by 5 multiplied by 5) multiplied by (3)
b A LaTex expression showing (2 multiplied by 5 multiplied by 5) multiplied by (3) over (5 multiplied by 5) multiplied by (3 multiplied by 3)
c A LaTex expression showing (2 multiplied by 5 multiplied by 5) multiplied by (3) over (5 multiplied by 5 multiplied by 5) multiplied by (3 multiplied by 3)
d A LaTex expression showing (11 multiplied by 5 multiplied by 5) multiplied by (3) over (5 multiplied by 5 multiplied by 5) multiplied by (3)
e A LaTex expression showing (2 multiplied by 5 multiplied by 5) multiplied by (3) over (5) multiplied by (3 multiplied by 3)
f A LaTex expression showing (2 multiplied by 5 multiplied by 5 multiplied by 5) multiplied by (3 multiplied by 3) over (2 multiplied by 5 multiplied by 5) multiplied by (7 multiplied by 2)
4
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 35 multiplied by 10
a A LaTex expression showing (2 multiplied by 3 multiplied by 7) multiplied by (5) over (5 multiplied by 7) multiplied by (2 multiplied by 5)
b A LaTex expression showing (3 multiplied by 7) multiplied by (5) over (5 multiplied by 7) multiplied by (2 multiplied by 5)
c A LaTex expression showing (2 multiplied by 2 multiplied by 3 multiplied by 7) multiplied by (5) over (5 multiplied by 7 multiplied by 7) multiplied by (2 multiplied by 5)
d A LaTex expression showing (2 multiplied by 3) multiplied by (5) over (5 multiplied by 7) multiplied by (2 multiplied by 5 multiplied by 5)
e A LaTex expression showing (3 multiplied by 7) multiplied by (5) over (7 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 5)
f A LaTex expression showing (3 multiplied by 5) multiplied by (5) over (5 multiplied by 7) multiplied by (2 multiplied by 5 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 4 multiplied by 10 over 30 multiplied by 2
a A LaTex expression showing (2 multiplied by 2) multiplied by (2 multiplied by 5) over (2 multiplied by 3 multiplied by 7) multiplied by (7)
b A LaTex expression showing (2 multiplied by 2 multiplied by 2) multiplied by (2 multiplied by 5) over (2 multiplied by 2 multiplied by 3 multiplied by 5 multiplied by 5) multiplied by (2)
c A LaTex expression showing (2 multiplied by 2) multiplied by (11 multiplied by 5) over (2 multiplied by 2 multiplied by 3 multiplied by 5) multiplied by (2)
d A LaTex expression showing (2 multiplied by 2) multiplied by (2 multiplied by 5) over (2 multiplied by 3 multiplied by 5) multiplied by (2)
e A LaTex expression showing (2 multiplied by 2) multiplied by (2 multiplied by 5) over (2 multiplied by 3 multiplied by 7) multiplied by (2 multiplied by 2)
f A LaTex expression showing (5) multiplied by (5) over (2 multiplied by 2 multiplied by 3 multiplied by 5) multiplied by (2)
6
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 36 over 5 multiplied by 18
a A LaTex expression showing (2 multiplied by 2 multiplied by 3 multiplied by 3) over (5) multiplied by (2 multiplied by 3 multiplied by 3)
b A LaTex expression showing (2 multiplied by 7 multiplied by 3 multiplied by 3) over (5) multiplied by (5 multiplied by 3)
c A LaTex expression showing (2 multiplied by 3 multiplied by 3 multiplied by 3) over (5) multiplied by (2 multiplied by 3 multiplied by 3)
d A LaTex expression showing (2 multiplied by 2 multiplied by 5 multiplied by 3) over (5) multiplied by (11 multiplied by 3)
7
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 (3) over (3 multiplied by 3 multiplied by 5) multiplied by (3)
b 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)
c A LaTex expression showing (2) multiplied by (3 multiplied by 5) over (3 multiplied by 5) multiplied by (3)
d 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)
e 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)
8
Use factorization to factor each number and show what factors in this fraction can be cancelled out
A LaTex expression showing 70 multiplied by 2 over 14 multiplied by 4
a A LaTex expression showing (5) multiplied by (2) over (2 multiplied by 7) multiplied by (11 multiplied by 2)
b A LaTex expression showing (2 multiplied by 5 multiplied by 7) multiplied by (2) over (2 multiplied by 7) multiplied by (2 multiplied by 2)
c A LaTex expression showing (2 multiplied by 5 multiplied by 7) multiplied by (5) over (2 multiplied by 7) multiplied by (2 multiplied by 2)
d A LaTex expression showing (2 multiplied by 5 multiplied by 7 multiplied by 7) multiplied by (2) over (2) multiplied by (2 multiplied by 2)
e A LaTex expression showing (2 multiplied by 7) multiplied by (2) over (2 multiplied by 13) multiplied by (2 multiplied by 2)
f A LaTex expression showing (2 multiplied by 5 multiplied by 7) multiplied by (2) over (2 multiplied by 7) multiplied by (2 multiplied by 2 multiplied by 2)