We will learn division in terms of reciprocal.
Let us divide \(\frac{1}{4}\) into 2 parts. In the following figure A the colored part represents \(\frac{1}{4}\) of the whole figure. Now, we divide each part into two equal parts. The colored part in the figure B represents \(\frac{1}{8/}\).
Therefore, \(\frac{1}{4}\) ÷ 2 is equal to \(\frac{1}{8}\). We know that the reciprocal or the multiplicative inverse of 2 is \(\frac{1}{2}\).
So, if we multiply \(\frac{1}{4}\) by the reciprocal of 2, we get \(\frac{1}{4}\) × \(\frac{1}{2}\) = \(\frac{1}{8}\).
To divide a fraction or a whole number by a fraction or a whole number, we multiply the reciprocal of the divisor.
Solved Examples on Division in Terms of Reciprocal:
1. Divide 15 by \(\frac{3}{7}\)
Solution:
Reciprocal of \(\frac{3}{7}\) is \(\frac{7}{3}\). Thus 15 ÷ \(\frac{3}{7}\) = \(\frac{15}{1}\) × \(\frac{7}{3}\) = \(\frac{105}{3}\) = 35
2. Divide \(\frac{4}{9}\) by 8
Solution:
\(\frac{4}{9}\) ÷ 8 = \(\frac{4}{9}\) ÷ \(\frac{8}{1}\)
= \(\frac{4}{9}\) × \(\frac{1}{8}\)
= \(\frac{4}{72}\)
= \(\frac{1}{18}\)
3. Divide 13\(\frac{3}{5}\) by 13
Solution:
We first convert the mixed number into improper fraction.
13\(\frac{3}{5}\) = \(\frac{13 × 5 + 3}{5}\) = \(\frac{68}{5}\)
Now, \(\frac{68}{5}\) ÷ 13 = \(\frac{68}{5}\) ÷ \(\frac{13}{1}\)
= \(\frac{68}{5}\) × \(\frac{1}{13}\)
= \(\frac{68}{65}\)
= 1\(\frac{3}{65}\)
4. Divide 4\(\frac{1}{2}\) by \(\frac{3}{4}\)
Solution:
We first convert the mixed number into improper fraction.
4\(\frac{1}{2}\) = \(\frac{4 × 2 + 1}{2}\) = \(\frac{9}{2}\)
Now, \(\frac{9}{2}\) ÷ \(\frac{3}{4}\) = \(\frac{9}{2}\) × \(\frac{4}{3}\)
= \(\frac{36}{6}\)
= 6
5. How many pieces measuring \(\frac{5}{6}\) m can be cut from a thread of length 150 m?
Solution:
Length of one piece = \(\frac{5}{6}\) m
Length of the thread = 150 m
Number of pieces = 150 ÷ \(\frac{5}{6}\)
= 150 × \(\frac{6}{5}\)
= 180
Questions and Answers on Division in Terms of Reciprocal:
I. Fill in the blanks:
(i) \(\frac{3}{16}\) ÷ 1
(ii) \(\frac{8}{15}\) ÷ \(\frac{15}{8}\)
(iii) \(\frac{5}{9}\) ÷ \(\frac{1}{9}\)
(iv) \(\frac{3}{10}\) ÷ \(\frac{12}{10}\)
(v) 5 ÷ \(\frac{20}{7}\)
(vi) \(\frac{15}{8}\) ÷ 45
(vii) \(\frac{11}{21}\) ÷ \(\frac{33}{28}\)
(viii) \(\frac{2}{9}\) ÷ \(\frac{16}{27}\)
(ix) \(\frac{5}{2}\) ÷ \(\frac{25}{18}\)
Answers:
(i) \(\frac{3}{16}\)
(ii) \(\frac{64}{225}\)
(iii) 5
(iv) \(\frac{1}{4}\)
(v) \(\frac{7}{4}\)
(vi) \(\frac{1}{24}\)
(vii) \(\frac{4}{9}\)
(viii) \(\frac{3}{8}\)
(ix) \(\frac{9}{5}\)
II. Word Problems on Division in Terms of Reciprocal:
1. 7\(\frac{1}{2}\) liter of milk has to be packed in bottles of \(\frac{3}{4}\) liters. How many bottles are required to fill all the milk?
Answer: 10 bottles
2. 12\(\frac{1}{2}\) m of cloth is required to stitch 1 shirt. How many shirts can be stitched from a cloth of length 75 m?
Answer: 6 shirts
3. A car covers 30\(\frac{5}{6}\) km in 1 hour. How much time will the car take to cover 360 km?
Answer: 11\(\frac{25}{37}\) hours
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