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Reducing Fractions

A fraction is a rational number. It can also be represented as a decimal number. The general form of a fraction is $\frac{a}{b}$ where a is the numerator and b is the denominator. At times the number in the numerator and denominator has common factors which can be cancelled out to have a simpler fraction. This process is known as reducing fractions or simplifying fraction. Reducing fractions makes it easier to perform calculations on two or more fractions.

 Related Calculators Fraction Reducer Calculator Mixed Fraction to Improper Fraction Calculate Fraction

How to Reduce Fractions

The following steps are followed to reduce fractions,
Step 1: First, write the prime factors of the numerator quantity and the denominator quantity.

Step 2: Find the common factors of both the numerator quantity and the denominator quantity.

Step 3: Divide both numerator or denominator by common factors or in other word, cancel out all the common factors.

Solved Examples

Question 1: Reduce $\frac{30}{105}$, using prime factorization.
Solution:

Step 1: Prime factors of 30 = 2 $\times$ 3 $\times$ 5 and

105 = 3 $\times$ 5 $\times$ 7

Step 2:

$\frac{30}{105}$ = $\frac{2\times3\times5}{3\times5\times7}$

Step 3:

$\frac{30}{105}$ = $\frac{2}{7}$

Question 2: Reduce $\frac{42}{33}$, using prime factorization.
Solution:

Step 1: Prime factors of 42 = 2 $\times$ 3 $\times$ 7 and

33 = 3 x 11

Step 2:

$\frac{42}{33}$ = $\frac{2\times3\times7}{3\times11}$

Step 3:

$\frac{42}{33}$ =
$\frac{14}{11}$

Reducing Fractions with Variables

Examples on reducing fractions with variables:

Solved Examples

Question 1: Reduce $\frac{6xy}{42x^2}$ to lowest terms.

Solution:

Step 1: Factor of 6xy = 2 x 3 x $x$ x $y$ and

42 $x^2$ = 2 $\times$ 3 $\times$ 7 $\times$ $x$ $\times$ $x$

Step 2:

$\frac{6xy}{42x^2}$ =
$\frac{2 \times 3 \times x \times y}{2 \times 3 \times 7 \times x \times x}$

Step 3:

$\frac{6xy}{42x^2}$ =
$\frac{y}{7x}$

Question 2: Reduce $\frac{30xy}{98xz}$ to lowest terms.
Solution:

Step 1: Factor of 30 $xy$ = 2 $\times$ 3 $\times$ 5 $\times$ $x$ $\times$ $y$ and

98$xz$ = 2 $\times$ 7 $\times$ 7 $\times$ $x$ $\times$ $z$

Step 2:

$\frac{30xy}{98xz}$ =
$\frac{2 \times 3 \times 5 \times x \times y}{2 \times 7 \times 7 \times x \times z}$

Step 3:

$\frac{30xy}{98xz}$ = $\frac{15y}{49z}$

Practice Problems

Problem 1: Simplify $\frac{268}{124}$.
Problem 2: Can the term $\frac{8xy}{2x}$ be simplified?
Problem 3: Reduce the fraction $\frac{265}{165}$
Problem 4: Find the simplified form of the fraction $\frac{65}{13}$.