Equivalent Fractions
Equivalent fractions are the fractions having the same value.
We have,
^{2}/_{4} = ^{(1 × 2)}/_{(2 × 2)}
^{3}/_{6} = ^{(1 × 3)}/_{(2 × 3)}
^{4}/_{8} = ^{(1 × 4)}/_{(2 × 4)}
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.
Thus, an equivalent fraction of a given fraction can be obtained by multiplying its numerator and denominator by the same number (other than zero).
^{2}/_{4} = ^{(2÷ 2)}/_{(4 ÷ 2)} = ^{1}/_{2}
^{3}/_{6} = ^{(3÷ 3)}/_{(6 ÷ 3)} = ^{1}/_{2}
^{4}/_{8} = ^{(4 ÷ 4)}/_{(8 ÷ 4)} = ^{1}/_{2}
We observe that if we divide the numerators and denominators of
^{2}/
_{4},
^{3}/
_{6} and
^{4}/
_{8} each by their common factor 2, we get an equivalent fraction
^{1}/
_{2}.
Thus, an equivalent fraction of a given fraction can be obtained by dividing its numerator and denominator by their common factor (other than 1), if ant.
Note:
(i) Multiplying its numerator (top) and denominator (bottom) by the same number (other than 0).
(ii) Dividing its numerator (top) and denominator (bottom) by their common factor (other than 1).
For Example:
1. Write three equivalent fraction of
^{3}/
_{5}.
Equivalent fractions of
^{3}/
_{5} are:
^{(3 × 2)}/_{(5× 2)} = ^{6}/_{10},
^{(3 × 3)}/_{(5 × 3)} = ^{9}/_{15},
^{(3 × 4)}/_{(5 × 4)} = ^{12}/_{20}
Therefore, equivalent fractions of
^{3}/
_{5} are
^{6}/
_{10},
^{9}/
_{15} and
^{12}/
_{20}.
2. Write three equivalent fraction of
^{2}/
_{3}.
Equivalent fractions of
^{2}/
_{3} are:
^{(2× 2)}/_{(3× 2)} = ^{4}/_{6},
^{(2 × 3)}/_{(3 × 3)} = ^{6}/_{9},
^{(2× 4)}/_{(3× 4)} = ^{8}/_{12}
Therefore, equivalent fractions of
^{2}/
_{3} are
^{4}/
_{6},
^{6}/
_{9} and
^{8}/
_{12}.
3. Write three equivalent fraction of
^{1}/
_{4}.
Equivalent fractions of
^{1}/
_{4} are:
^{(1× 2)}/_{(4× 2)} = ^{2}/_{8},
^{(1 × 3)}/_{(4 × 3)} = ^{3}/_{12},
^{(1× 4)}/_{(4× 4)} = ^{4}/_{16}
Therefore, equivalent fractions of
^{1}/
_{4} are
^{2}/
_{8},
^{3}/
_{12} and
^{4}/
_{16}.
4. Write three equivalent fraction of
^{2}/
_{15}.
Equivalent fractions of
^{2}/
_{15} are:
^{(2× 2)}/_{(15 × 2)} = ^{4}/_{30},
^{(2 × 3)}/_{(15 × 3)} = ^{6}/_{45},
^{(2× 4)}/_{(15 × 4)} = ^{8}/_{60}
Therefore, equivalent fractions of
^{2}/
_{15} are
^{4}/
_{30},
^{6}/
_{45} and
^{8}/
_{60}.
5. Write three equivalent fraction of
^{3}/
_{10}.
Equivalent fractions of
^{3}/
_{10} are:
^{(3× 2)}/_{(10× 2)} = ^{6}/_{20},
^{(3 × 3)}/_{(10 × 3)} = ^{9}/_{30},
^{(3× 4)}/_{(10× 4)} = ^{12}/_{40}
Therefore, equivalent fractions of
^{3}/
_{10} are
^{6}/
_{20},
^{9}/
_{30} and
^{12}/
_{40}.
● Fraction
Representations of Fractions on a Number Line
Fraction as Division
Types of Fractions
Conversion of Mixed Fractions into Improper Fractions
Conversion of Improper Fractions into Mixed Fractions
Equivalent Fractions
Interesting Fact about Equivalent Fractions
Fractions in Lowest Terms
Like and Unlike Fractions
Comparing Like Fractions
Comparing Unlike Fractions
Addition and Subtraction of Like Fractions
Addition and Subtraction of Unlike Fractions
Inserting a Fraction between Two Given Fractions
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