We will learn how to solve subtraction of mixed fractions or subtraction of mixed numbers.
There are two methods to subtract the mixed fractions.
1. Subtract 3\(\frac{1}{12}\) from 3\(\frac{1}{12}\).
Solution:
Method I.
6\(\frac{1}{3}\) – 3\(\frac{1}{12}\) = (6 - 3) + (\(\frac{1}{3}\) – \(\frac{1}{12}\)) = 3 + (\(\frac{1}{3}\) – \(\frac{1}{12}\)) = 3 + (\(\frac{1 × 4}{3 × 4}\) – \(\frac{1 × 1}{12 × 1}\)) (L.C.M. of 12 and 3 = 12) = 3 + \(\frac{4}{12}\) – \(\frac{1}{12}\) = 3 + \(\frac{4 - 1}{12}\) = 3 + \(\frac{3}{13}\) = 3 + \(\frac{1}{4}\) = 3\(\frac{1}{4}\) |
Step I: Subtract the whole numbers.
Step II: To subtract the fractions we convert them into like fractions. Step III: Add the differences of whole numbers and like fractions. |
Method II:
6\(\frac{1}{3}\) – 3\(\frac{1}{12}\)
= \(\frac{(6 × 3) + 1}{3}\) + \(\frac{(3 × 12) + 1}{12}\) = \(\frac{19}{3}\) – \(\frac{37}{12}\) = \(\frac{19 × 4}{3 × 4}\) – \(\frac{37 × 1}{12 × 1}\), (L.C.M. of 3 and 12 = 12) = \(\frac{76}{12}\) – \(\frac{37}{12}\) = \(\frac{76 - 37}{12}\) = \(\frac{39}{12}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\) |
Step I: Change the mixed numbers into improper fractions. Step II: Make the fractions like fraction to have a common denominator. Step III: Subtract and express the fraction in the simplest form. |
2. Subtract 1\(\frac{5}{12}\) from 3\(\frac{3}{8}\)
Solution:
We first convert the mixed numbers into improper fractions.
1\(\frac{5}{12}\) = \(\frac{1 × 12 + 5}{12}\) = \(\frac{17}{12}\)
3\(\frac{3}{8}\) = \(\frac{3 × 8 + 3}{8}\) = \(\frac{27}{8}\)
Now, \(\frac{27}{8}\) - \(\frac{17}{12}\) = \(\frac{27 × 3}{8 × 3}\) - \(\frac{17 × 2}{12 × 2}\)
LCM of 8 and 12 is 24
\(\frac{81}{24}\) - \(\frac{34}{24}\) = \(\frac{81 - 34}{24}\)
= \(\frac{47}{24}\)
= 1\(\frac{23}{24}\)
Hence, 3\(\frac{3}{8}\) - 1\(\frac{5}{12}\) = 1\(\frac{23}{24}\)
Word Problems on Subtraction of Mixed Fractions:
3. Ron used 3\(\frac{1}{4}\) litres of paint from a tin of 5\(\frac{1}{2}\) l, to color the walls of his room. What fraction of paint is still left in the tin?
Answer: \(\frac{9}{4}\) litres
4. Sam has a cloth of length 16 m. He took 13\(\frac{1}{4}\) m of cloth from it to make curtains for the house. How much cloth is still left with him for further use?
Answer: 2\(\frac{3}{4}\) m
5. Ten years ago a forest was spread up to a distance of 33 km. Due to forest fires and industrial set up now it is spread upto a distance of 16\(\frac{1}{5}\) km. What fraction of forest has been destroyed in the last 10 years? What measures can be taken to protect these forests?
Answer: 16\(\frac{4}{5}\) km
6. A drum full of rice weighs 84\(\frac{1}{2}\) kg. If the weight of empty drum is 12\(\frac{1}{6}\) kg, find the weight of the rice.
Answers: 72\(\frac{1}{3}\) kg
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