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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.

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Fraction Reducer Calculator Mixed Fraction to Improper Fraction
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How to Reduce Fractions

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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

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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

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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 $\frac{65}{13}$.
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