Subtraction of Mixed Fractions

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\(\frac{23}{24}\)

Subtraction of Mixed Fractions


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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