Mathematical expressions involving operations and brackets

Mathematical expressions involving operations and brackets

An expression consisting of brackets and all four basic mathematical operations which are division, multiplication, addition, and subtraction is evaluated or simplified by using a complete order of the BODMAS rule.

Calculations are done as follows:

1. Open Brackets by solving the terms inside it. Multiply the number outside the bracket with the answer obtained.
2. Divide
3. Multiply
4. Add
5. Subtract

Example 1

Find the value of $3 × 8 + (20 − 6) ÷ 2$.

Solution

Using the BODMAS rule, follow the steps:

Start by opening brackets: $3 × 8 + (20 − 6) ÷ 2 = 3 × 8 + 14 ÷ 2$

Divide: $3 × 8 + 14 ÷ 2 = 3 × 8 + 7$

Multiply: $3 × 8 + 7 = 24 + 7$

Finish by adding: $24 + 7 = 31$

Therefore, $3 × 8 + (20 − 6) ÷ 2 = 31$.

Example 2

Find the value of $(63.6 + 36.4) ÷ (6/7 − 8) + 58 × 2/3 − 1 1/8$.

Solution

Using the BODMAS rule, follow the steps:

Start by opening brackets: $(63.6 + 36.4) ÷ (6/7 − 8) + 58 × 2/3 − 1 1/8 = 100 ÷ (−50/7) + 58 × 2/3 − 1 1/8$

Divide: $100 ÷ (−50/7) + 58 × 2/3 − 1 1/8 = −14 + 58 × 2/3 − 1 1/8$

Multiply: $−14 + 58 × 2/3 − 1 1/8 = −14 + 116/3 − 1 1/8$

Add: $−14 + 116/3 − 1 1/8 = 116/3 − 121/8$

Finally subtract: $116/3 − 121/8 = 23 \frac{13}{24}$

Therefore, $(63.6 + 36.4) ÷ (6/7 − 8) + 58 × 2/3 − 1 1/8 = 23 \frac{13}{24}$.

Example 3

Find the value of $(258.36 − 110.16) ÷ (61.49 − 24.44) + 0.38 × 4.25 + 3.92$.

Solution

Using the BODMAS rule, follow the steps:

Start by opening brackets: $(258.36 − 110.16) ÷ (61.49 − 24.44) + 0.38 × 4.25 + 3.92 = 148.2 ÷ 37.05 + 0.38 × 4.25 + 3.92$

Divide: $148.2 ÷ 37.05 + 0.38 × 4.25 + 3.92 = 4 + 0.38 × 4.25 + 3.92$

Multiply: $4 + 0.38 × 4.25 + 3.92 = 4 + 1.615 + 3.92$

Finally add: $4 + 1.615 + 3.92 = 9.535$

Therefore, $(258.36 − 110.16) ÷ (61.49 − 24.44) + 0.38 × 4.25 + 3.92 = 9.535$