Equivalent fractions are different fractions that represent the same value or proportion of a whole. They can be found by multiplying or dividing both the numerator and the denominator by the same non-zero number.
In this article, we will learn how to solve equivalent fractions.
What are Equivalent Fractions?
Equivalent fractions represent the same value or proportion, even though they have different numerators (top numbers) and denominators (bottom numbers). They describe the same part of a whole or the same ratio between two quantities.
For example, the fractions
How to Determine Equivalent Fractions?
To determine if two fractions are equivalent, you can multiply or divide both the numerator and the denominator of one fraction by the same non-zero number. If the resulting fraction matches the other fraction, then the two are equivalent.
Example 1: Find equivalent fraction of
Solution:
- Start with
\frac{1}{3} .- Multiply both the numerator and denominator by 2:
\frac{1 \times 2}{3 \times 2} = \frac{2}{6}. So,
\frac{1}{3} and\frac{2}{6} are equivalent fractions.
Example 2: Find equivalent fraction of
Solution:
- Consider
\frac{4}{5} .- Multiply both the numerator and the denominator by 3:
\frac{4 \times 3}{5 \times 3} = \frac{12}{15} .So,
\frac{4}{5} and\frac{12}{15} are equivalent fractions.
Equivalent Fractions: Solved Examples
Example 1: Are
Solution:
Simplify
\frac{12}{16} by dividing both by 4:\frac{12 \div 4}{16 \div 4} = \frac{3}{4} So, they are equivalent.
Example 2: Simplify the fraction
Solution:
The GCD of 18 and 27 is 9.
Divide both by 9:
\frac{18 \div 9}{27 \div 9} = \frac{2}{3} .
Example 3: Find an equivalent fraction for
Solution:
Multiply the numerator and denominator by 4:
\frac{4 \times 4}{5 \times 4} = \frac{16}{20} .
Example 4: Are
Solution:
Simplify
\frac{10}{15} by dividing both by 5:\frac{10 \div 5}{15 \div 5} = \frac{2}{3} .So, they are equivalent.
Example 5: Simplify the fraction
Solution:
The GCD of 20 and 30 is 10.
Divide both by 10:
\frac{20 \div 10}{30 \div 10} = \frac{2}{3} .
Example 6: Find an equivalent fraction for
Solution:
Multiply the numerator and denominator by 2:
\frac{7 \times 2}{9 \times 2} = \frac{14}{18} .
Example 7: Are
Solution:
Simplify
\frac{9}{12} by dividing both by 3:\frac{9 \div 3}{12 \div 3} = \frac{3}{4} .So, they are equivalent.
Example 8: Simplify the fraction
Solution:
The GCD of 16 and 24 is 8.
Divide both by 8:
\frac{16 \div 8}{24 \div 8} = \frac{2}{3} .
Example 9: Find an equivalent fraction for
Solution:
Multiply the numerator and denominator by 3:
\frac{5 \times 3}{7 \times 3} = \frac{15}{21} .
Example 10: Are
Solution:
Multiply
\frac{3}{4} by 2:\frac{3 \times 2}{4 \times 2} = \frac{6}{8} .So,
\frac{3}{4} and\frac{6}{8} are equivalent.
Worksheet: Equivalent Fractions
Instructions: Simplify the following fractions and find their equivalent forms.
Q1: Find equivalent fraction of
Q2: Find equivalent fraction of
Q3: Find equivalent fraction of
Q4: Find equivalent fraction of
Q5: Find equivalent fraction of
Q6: Find an equivalent fraction for
Q7: Simplify
Q8: Find an equivalent fraction for
Q9: Are
Q10: Simplify
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