Equivalent fractions are the fractions having the same value. Same fraction can be represented in many ways. Let us take the following example.
In picture (i) the shaded part is represented by fraction \(\frac{1}{2}\).
The shaded part in picture (ii) is represented by fraction \(\frac{2}{4}\). In picture (iii) the same part is represented by fraction \(\frac{4}{8}\). SO, the fraction represented by these shaded portions are equal. Such fractions are called equivalent fractions.
We say that \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\)
Hence, for a given fraction there can be many equivalent fractions.
Making Equivalent Fractions:
We have seen in the above example that \(\frac{1}{2}\), \(\frac{2}{4}\) and \(\frac{4}{8}\) are equivalent fractions.
Therefore, \(\frac{1}{2}\) can be written as \(\frac{1}{2}\) = \(\frac{1 × 2}{2 × 2}\) = \(\frac{1 × 3}{2 × 3}\) = \(\frac{1 × 4}{2 × 4}\) and so on.
Hence, an equivalent fraction of any given fraction can be obtained by multiplying its numerator and denominator by the same number.
Same way, when the numerator and denominator of a fraction are divided by the same number, we get its equivalent fractions.
\(\frac{1}{2}\) = \(\frac{1 ÷ 1}{2 ÷ 1}\) = \(\frac{2}{4}\) = \(\frac{2 ÷ 2}{4 ÷ 2}\) = \(\frac{3}{6}\) = \(\frac{3 ÷ 3}{6 ÷ 3}\)
We have,
^{2}/_{4} = ^{(1 × 2)}/_{(2 × 2)}We observe that ^{2}/_{4}, ^{3}/_{6} and ^{4}/_{8} are obtained by multiplying the numerator and denominator of ^{1}/_{2} by 2, 3 and 4 respectively.
^{3}/_{6} = ^{(1 × 3)}/_{(2 × 3)}
^{4}/_{8} = ^{(1 × 4)}/_{(2 × 4)}
^{2}/_{4} = ^{(2÷ 2)}/_{(4 ÷ 2)} = ^{1}/_{2}
^{3}/_{6} = ^{(3÷ 3)}/_{(6 ÷ 3)} = ^{1}/_{2}
^{4}/_{8} = ^{(4 ÷ 4)}/_{(8 ÷ 4)} = ^{1}/_{2}
Note:
^{(3 × 2)}/_{(5× 2)} = ^{6}/_{10},
^{(3 × 3)}/_{(5 × 3)} = ^{9}/_{15},
^{(3 × 4)}/_{(5 × 4)} = ^{12}/_{20}
2. Write next three equivalent fraction of \(\frac{2}{3}\).
We multiply the numerator and the denominator by 2.
We get, \(\frac{2 × 2}{3 × 2}\) = \(\frac{4}{6}\)
Next, we multiply the numerator and the denominator by 3. We get
\(\frac{2 × 3}{3 × 3}\) = \(\frac{6}{9}\).
Next, we multiply the numerator and the denominator by 4. We get
\(\frac{2 × 4}{3 × 4}\) = \(\frac{8}{12}\).
Therefore, equivalent fractions of \(\frac{2}{3}\) are \(\frac{4}{6}\), \(\frac{6}{9}\) and \(\frac{8}{12}\).
^{(1× 2)}/_{(4× 2)} = ^{2}/_{8},
^{(1 × 3)}/_{(4 × 3)} = ^{3}/_{12},
^{(1× 4)}/_{(4× 4)} = ^{4}/_{16}
^{(2× 2)}/_{(15 × 2)} = ^{4}/_{30},
^{(2 × 3)}/_{(15 × 3)} = ^{6}/_{45},
^{(2× 4)}/_{(15 × 4)} = ^{8}/_{60}
^{(3× 2)}/_{(10× 2)} = ^{6}/_{20},
^{(3 × 3)}/_{(10 × 3)} = ^{9}/_{30},
^{(3× 4)}/_{(10× 4)} = ^{12}/_{40}
● Fraction
Representations of Fractions on a Number Line
Conversion of Mixed Fractions into Improper Fractions
Conversion of Improper Fractions into Mixed Fractions
Interesting Fact about Equivalent Fractions
Addition and Subtraction of Like Fractions
Addition and Subtraction of Unlike Fractions
Inserting a Fraction between Two Given Fractions
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