Division of a Fractional Number
We will discuss here about division of a fractional number by a fractional number.
Now, let us consider the division \(\frac{2}{3}\) ÷ \(\frac{1}{3}\)
= \(\frac{\frac{2}{3}}{\frac{1}{3}}\)
= \(\frac{2}{3}\) × \(\frac{1}{\frac{1}{3}}\)
= \(\frac{2}{3}\) × \(\frac{3}{1}\)
= \(\frac{2}{3}\) × 3
= \(\frac{6}{3}\)
= 2
Therefore, \(\frac{2}{3}\) ÷ \(\frac{1}{3}\) = \(\frac{2}{3}\) × 3 = 2
Therefore, the rules for the division of a fraction by a fraction is
A Fraction ÷ Another Fraction = First Fraction × Reciprocal of the Second Fraction.
Hence, we conclude that to divide a fractional number by another
fractional number, we multiply the first fractional number by the
multiplicative inverse of the second fraction number.
1. \(\frac{1}{3}\) ÷ \(\frac{2}{5}\)
[First Fraction × Reciprocal of the Second Fraction]
= \(\frac{1}{3}\) × \(\frac{5}{2}\)
= \(\frac{1 × 5}{3 × 2}\)
= \(\frac{5}{6}\)
2. \(\frac{6}{19}\) ÷ \(\frac{12}{38}\)
= \(\frac{6}{19}\) × \(\frac{38}{12}\)
= 1
3. 2\(\frac{1}{7}\) ÷ \(\frac{7}{2}\)
= \(\frac{2 × 7 + 1}{7}\) ÷ \(\frac{7}{2}\)
= \(\frac{15}{7}\) ÷ \(\frac{7}{2}\)
= \(\frac{15}{7}\) × \(\frac{2}{7}\)
= \(\frac{15 × 2}{7 × 7}\)
= \(\frac{30}{49}\)
4. 6 2/3 ÷ 4 1/5
= (6 × 3 + 2)/3 ÷ (4 × 5 + 1)/5
= 20/3 ÷ 21/5
= 20/3 × 5/21
= (20 × 5)/(3 × 21)
= 100/63
5. 12/11 ÷ 144/121
= 12/11 × 121/144
= 11/12
6. 5 1/8 ÷ 8 2/16
= (5 × 8 + 1)/8 ÷ (8 × 16 + 2)/16
= 41/8 ÷ 130/16
= 41/8 × 16/130
= 41/65
● Multiplication is Repeated Addition.
● Multiplication of Fractional Number by a Whole Number.
● Multiplication of a Fraction by Fraction.
● Properties of Multiplication of Fractional Numbers.
● Worksheet on Multiplication on Fraction.
● Division of a Fraction by a Whole Number.
● Division of a Fractional Number.
● Division of a Whole Number by a Fraction.
● Properties of Fractional Division.
● Worksheet on Division of Fractions.
● Simplification of Fractions.
● Worksheet on Simplification of Fractions.
● Worksheet on Word Problems on Fractions.
5th Grade Numbers Page
5th Grade Math Problems
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