# 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$$\frac{23}{24}$$

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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