Here we will discuss numerical expressions involving decimal numbers. we know that in numerical expressions we have to perform various operations like addition, subtraction, multiplication and division in one sum following the **BODMAS** rule. This **BODMAS** stands for **brackets**, **of**, **division**, **multiplication**, **addition** and **subtraction**.

**Here are few examples shown following the BODMAS rule:**

**1.** 1.2 ÷ 0.6 of 3.5 × 2.1 – 1.1 + 0.25

**Solution:**

1.2 ÷ 0.6 + 3.6 × 2.1 – 1.1 + 0.25

= 2 + 3.6 × 2.1 – 1.1 + 0.25

= 2 + 7.56 – 1.1 + 0.25

= 9.56 – 1.1 + 0.25

= 9.56 + 0.25 – 1.1

= 9.81 – 1.1

= 8.71

**Explanation:**

We will first divide (i.e. 1.2/0.6) leaving the other operations as it is. Then we will multiply i.e. 3.6 multiplied by 2.1. Then we have are left with addition and subtraction. So we will first do addition and then subtraction.

**2.** 4.5 + 5.6 ÷ 0.8 + 7.56 – 2.53

**Solution:**

4.5 + 5.6 ÷ 0.8 + 7.56 – 2.53

= 4.5 + 7 + 7.56 – 2.53

= 19.06 – 2.53

= 16.53

**Explanation:**

We will first divide (i.e.5.6/0.8 to get 7) then we will do addition (I.e. 4.5 + 7 + 7.56 to get 19.06) and lastly subtraction (i.e. 19.06 – 2.53 to get 16.53) according to the **BODMAS** rule.

**3.** 2.2 × 5.4 + 6.36 – 7.10 × 0 + 3.56

**Solution:**

2.2 × 5.4 + 6.36 – 7.10 × 0 + 3.56

= 11.88 + 6.36 – 0 + 3.56

= 11.88 + 6.36 + 3.56 – 0

= 21.80 – 0

= 21.80

**Explanation:**

First 2.2 multiplied by 5.4 and 7.10 multiplied by 0. After getting the answer of two multiplications we are left with only addition and subtraction. For addition we will arrange the numbers that are to be added together and then add them and finally with that result we subtracted 0 from it.

**4.** 8.5 ÷ 0.5 + 6.58 – 5.54 × 0.62 + 23.25

**Solution:**

8.5 ÷ 0.05 + 6.58 – 5.54 × 0.62 + 23.25

= 170 + 6.58 – 5.54 × 0.62 + 23.25

= 170 + 6.58 – 3.4348 + 23.25

= 170 + 6.58 + 23.25 – 3.4348

= 199.83 – 3.4348

= 196.3952

**Explanation:**

At first 8.5 is divided by 0.05 to get 170 and then perform the multiplication (i.e. 5.54 multiplied by 0.62) and then will be left with addition and then subtraction according to **BODMAS**.

**5.** 7.8 + 3.6 – 2.3 × 0 + 4.9 of 7 ÷ 5.6

**Solution:**

7.8 + 3.6 – 2.3 × 0 + 4.9 of 7 ÷ 5.6

= 7.8 + 3.6 – 2.3 × 0 + 34.3 ÷ 5.6

= 7.8 + 3.6 – 2.3 × 0 + 6.125

= 7.8 + 3.6 – 0 + 6.125

= 7.8 + 3.6 + 6.125

= 17.525

**Explanation:**

Firstly 4.9 of 7 is done ‘of’ actually multiplication. Then the result 34.3 is divided by 5.6 9.8 to get 6.125 and in the next step 2.3 is multiplied by 0 to get 0 and at the end all the three (7.8, 3.6, 2) are added to get the final result.

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