Equivalent Fractions
What are called equivalent fractions?
A given fraction and various fractions obtained by multiplying (or dividing) its numerator and denominator both by the same non-zero number, are called equivalent fractions.
In other-words:
If two or more fraction have the same value, then they are called the equivalent or equal fractions
The value of the fraction does not change if both the numerator and the denominator are multiplied by the same natural number.
(i)
^{(3 × 2)}/
_{(4 × 2)} =
^{6}/
_{8},
^{(3 × 3)}/
_{(4 × 3) } =
^{9}/
_{12},
^{(3 × 4)}/
_{(4 × 4) } =
^{12}/
_{16} etc. are equivalent fractions equivalent to the fraction
^{3}/
_{4}.
(ii)
^{1}/
_{3} =
^{(1 × 3)}/
_{(3 × 3)} =
^{3}/
_{9};
^{1}/
_{3} =
^{(1 × 6)}/
_{(3 × 6)} =
^{6}/
_{18};
^{1}/
_{3} =
^{(1 × 9)}/
_{(3 × 9)} =
^{9}/
_{27} and so on.
So,
^{1}/
_{3},
^{3}/
_{9},
^{6}/
_{18},
^{9}/
_{27}, etc., are equivalent fractions.
(iii)
^{45}/
_{27} =
^{(45 ÷ 3)}/
_{(27 ÷ 3)} =
^{15}/
_{9};
^{45}/
_{27} =
^{(45 ÷ 9)}/
_{(27 ÷ 9)} = 5/3
So,
^{45}/
_{27},
^{15}/
_{9},
^{5}/
_{3}, etc., are equivalent fractions.
We have,
^{8}/
_{28} =
^{(8 ÷ 4)}/
_{(28 ÷ 4)} =
^{2}/
_{7} ,
^{10}/
_{35} =
^{( 10 ÷ 5)}/
_{(35 ÷ 5)} =
^{2}/
_{7}
^{8}/
_{28} and
^{10}/
_{35} are equivalent fractions equivalent to the fraction
^{2}/
_{7}
If
^{a}/
_{b} and
^{c}/
_{d} are two equivalent fractions, then
a × d = b × c
i.e.,
^{a}/
_{b} =
^{c}/
_{d} ⇔ a × d = b × c
● Fractions
Fractions
Types of Fractions
Equivalent Fractions
Like and Unlike Fractions
Conversion of Fractions
Fraction in Lowest Terms
Addition and Subtraction of Fractions
Multiplication of Fractions
Division of Fractions
● Fractions - Worksheets
Worksheet on Fractions
Worksheet on Multiplication of Fractions
Worksheet on Division of Fractions
7th Grade Math Problems
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