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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