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

● **Related Concepts**

**Fraction of a Whole Numbers****Representation of a Fraction****Equivalent Fractions****Properties of Equivalent Fractions****Finding Equivalent Fractions****Reducing the Equivalent Fractions****Verification of Equivalent Fractions****Finding a Fraction of a Whole Number****Like and Unlike Fractions****Comparison of Like Fractions****Comparison of Fractions having the same Numerator****Comparison of Unlike Fractions****Fractions in Ascending Order****Fractions in Descending Order****Types of Fractions****Changing Fractions****Conversion of Fractions into Fractions having Same Denominator****Conversion of a Fraction into its Smallest and Simplest Form****Addition of Fractions having the Same Denominator****Addition of Unlike Fractions****Addition of Mixed Fractions****Word Problems on Addition of Mixed Fractions****Worksheet on Word Problems on Addition of Mixed Fractions****Subtraction of Fractions having the Same Denominator****Subtraction of Unlike Fractions****Subtraction of Mixed Fractions****Word Problems on Subtraction of Mixed Fractions****Worksheet on Word Problems on subtraction of Mixed Fractions****Addition and Subtraction of Fractions on the Fraction Number Line****Word Problems on Multiplication of Mixed Fractions****Worksheet on Word Problems on Multiplication of Mixed Fractions****Multiplying Fractions****Dividing Fractions****Word Problems on Division of Mixed Fractions****Worksheet on Word Problems on Division of Mixed Fractions**

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