We will discuss here how to solve the word problems on subtraction of mixed fractions or subtraction of mixed numbers.

**Let us consider some of the examples.**

**1.** Jack jumped 4 1/7 m in a long jump competition. Shane jumped 3 2/9 m. Who jumped longer and by how many metres?

**Solution:**

Jack jumped = 4 1/7 m = 29/7 m = 261/63 m

Shane jumped = 3 2/9 m = 29/9 m = 203/63 m

Because 261 > 203, so Jack jumped more.

Difference = 261/63 – 203/63

= 261 - 203/63

= 58/63 m

Thus, Jack jumped 58/63 m more than Shane.

**2.** Mary gave 1/8 part of her money to Shelly. What fraction
of money is left with her?

**Solution:**

The fraction of money given to Shelly = 1/8

The remaining fraction of money = 1 - 1/8

= 1/1 - 1/8

= 8/8 - 1/8

= 8 - 1/8

= 7/8

**3.** Sharon spent 4 3/7 hours studying maths and playing tennis.
If she played tennis for 2 ¼ hours, how long did she study?

**Solution:**

Total hours spent for studying and playing = 4 3/7 = (4 × 7) + 3/7 = 31/7

Hours spent for playing tennis = 2 ¼ = 9/4

So, hours spent for studying = 31/7 – 9/4

= 31 × 4/7 × 4 - 9 × 7/4 × 7, (L.C.M. = 28)

= 124/28 - 63/28

= 61/28

= 2 5/28

**4.** Rex had some money. He spent 1/6 of it on Monday, 3/8 on
Thursday and ¼ on Wednesday. What part of money is still left with him?

**Solution:**

Total part of money spent = 1/6 + 3/8 + ¼

= 1 × 4/6 × 4 + 3 × 3/8 × 3 + 1 × 6/4 × 6, (L.C.M. of 6, 8 and 4 = 24)

= 4/24 + 9/24 + 6/24

= 19/24

The part of money left with him = 1 – 19/24

= 1/1 - 19/24

= 24/24 - 19/24

= 24 - 19/24

= 5/24

**Related Concept**

● Representation of a Fraction

● Properties of Equivalent Fractions

● Comparison of Like Fractions

● Comparison of Fractions having the same Numerator

● 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

● Subtraction of Fractions having the Same Denominator

● Addition and Subtraction of Fractions on the Fraction Number Line

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