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 3112 from 3112.

Solution:

Method I.

613 – 3112

= (6 - 3) + (13 – 112)

= 3 + (13 – 112)

= 3 + (1×43×4 – 1×112×1)

(L.C.M. of 12 and 3 = 12)

= 3 + 412 – 112

= 3 + 4112

= 3 + 313

= 3 + 14

= 314


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:

613 – 3112

(6×3)+13(3×12)+112

= 193 – 3712

19×43×4 – 37×112×1,

(L.C.M. of 3 and 12 = 12)

= 7612 – 3712

= 763712

3912

134

= 314


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 1512 from 338

Solution:

We first convert the mixed numbers into improper fractions.

1512 = 1×12+512 = 1712

338 = 3×8+38 = 278

Now, 278 - 1712 = 27×38×3 - 17×212×2

LCM of 8 and 12 is 24

8124 - 3424 = 813424

            = 4724

            = 12324

Hence, 338 - 1512 = 12324

Subtraction of Mixed Fractions


Word Problems on Subtraction of Mixed Fractions:

3. Ron used 314 litres of paint from a tin of 512 l, to color the walls of his room. What fraction of paint is still left in the tin?

Answer: 94 litres


4. Sam has a cloth of length 16 m. He took 1314 m of cloth from it to make curtains for the house. How much cloth is still left with him for further use?

Answer: 234 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 1615 km. What fraction of forest has been destroyed in the last 10 years? What measures can be taken to protect these forests?

Answer: 1645 km


6. A drum full of rice weighs 8412 kg. If the weight of empty drum is 1216 kg, find the weight of the rice.

Answers: 7213 kg

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