This subtopic would deal with numerical expressions involving fractional numbers. Likewise we learnt numerical expressions with whole numbers following the **BODMAS** rule in the same way we will do numerical expressions involving fractional numbers.

We know, BODMAS stands for

**B** implies **Brackets**

**O** implies **Of**

**D** implies **Division**

**M** implies **Multiplication**

**A** implies **Addition**

**S** implies **Subtraction**

**Here are few examples illustrating numerical expressions involving fractional numbers:**

**1.** 1/7 × 4/7 ÷ 1/49 + 2/7

**Solution:**

1/7 × 4/7 ÷ 1/49 + 2/7

= 1/7 × 4/7 × 49 + 2/7

= 1/7 × 28 + 2/7

= 4 + 2/7

= 30/7

= 4 2/7

**Explanation:**

First do division that is 4/7 ÷ 1/49 to get 28. Then do the multiplication that is 1/7 × 28 to get 4. And finally addition that is 4 + 2/7 to get 30/7. Then 30/7 is in improper fraction hence it should be changed into mixed fraction.

**2.** 5/3 + 8/9 × 9/5 + 2/3 × 0

**Solution:**

3/5 + 8/9 × 9/5 + 2/3 × 0

= 3/5 + 8/5 + 0

= 11/5

= 2 1/5

**Explanation:**

In the first step 8/9 × 9/5 to get 8/5 and 2/3 × 0 to get 0. Then we need to do the addition that is 3/5 + 8/5 to get 11/5. 11/5 is in improper fraction and hence we need to divide it to change it into mixed fraction.

**3.** 72 ÷ 8/9 × 64/27 ÷32/7 ̶ 2/5

**Solution:**

72 ÷ 8/9 × 64/27 ÷ 32/7 - 2/5

= 72 × 9/8 × 64/27 × 7/32 - 2/5

= 81 × 14/27 - 2/5

= 3 × 14 – 2/5

= 42 – 2/5

= 208/5

= 41

**Explanation:**

First carry out both the division i.e. 72 ÷ 8/9 and 64/27 ÷ 32/7 to get 81 and 14/27 respectively. Then 81 and 14/27 is multiplied to get 42. And lastly 2/5 is subtracted from 42 to get the answer 208/5. Since 208/5 is in improper fraction we need to divide it get the answer in mixed fraction. The final answer is 41

**4.** 49/7 × 81/343 + 4/7 × 0 – 5/7

**Solution:**

49/7 × 81/343 + 4/7 × 0 – 5/7

= 81/49 + 4/7 × 0 – 5/7

= 81/49 + 0 – 5/7

= 81/49 – 5/7

= 46/49

**Explanation:**

First do the multiplication (i.e. 49/7 × 81/343 to get 81/49). Then 4/7 is multiplied by 0 to get 0. Then finally 81/49 is subtracted from 5/7 to get 46/49. 46/49 is in proper fraction and hence cannot be changed into mixed fraction and 46/49 is the final answer.

**NOTE:**

In numerical simplifications involving fraction the final answer should be presented either in proper fraction or in mixed fraction or if the answer comes in whole number then we will leave it in whole number. We cannot leave any answer in improper fraction it should be changed into mixed fraction by long division as shown in the examples above.

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