Mathematical expressions involving three operations

Mathematical expressions involving three operations

An expression involving three operations is simplified or evaluated by performing each operation one after another by following the BODMAS rule.

Example 1

Find the value of $27 × 2 − 4 + 15$.

Solution

Using the BODMAS rule, follow the steps:

Start by multiplying: $27 × 2 − 4 + 15 = 54 − 4 + 15$

Followed by adding positive integers: $54 − 4 + 15 = 54 + 15 − 4 = 69 − 4$

Finally subtract: $69 − 4 = 65$

Therefore, $27 × 2 − 4 + 15 = 65$.

Example 2

Find the value of $320 ÷ 5 + 4/5 × 1/9$.

Solution

Using the BODMAS rule, follow the steps:

Start by dividing: $320 ÷ 5 + 4/5 × 1/9 = 64 + 4/5 × 1/9$

Followed by multiplying: $64 + 4/5 × 1/9 = 64 + 4/45$

Finally add: $64 + 4/45 = 64 4/45$

Therefore, $320 ÷ 5 + 4/5 × 1/9 = 64 4/45$.

Example 3

Find the value of $180 × 4/9 + 19.64 − 26.84$.

Solution

Using the BODMAS rule, follow the steps:

Start by multiplying: $180 × 4/9 + 19.64 − 26.84 = 80 + 19.64 − 26.84$

Followed by adding: $80 + 19.64 − 26.84 = 99.64 − 26.84$

Finally subtract: $99.64 − 26.84 = 72.8$

Therefore, $180 × 4/9 + 19.64 − 26.84 = 72.8$.

Mathematical expressions involving four operations

When an expression involves four operations, the evaluation or simplification is done by considering the order of priority given in the BODMAS rule.

Example 1

Find the value of $36 ÷ 9 + 48 − 10 × 2$.

Solution

Using the BODMAS rule, follow the steps:

Start by dividing: $36 ÷ 9 + 48 − 10 × 2 = 4 + 48 − 10 × 2$

Multiply: $4 + 48 − 10 × 2 = 4 + 48 − 20$

Add: $4 + 48 − 20 = 52 − 20$

Finally subtract: $52 − 20 = 32$

Therefore, $36 ÷ 9 + 48 − 10 × 2 = 32$.

Example 2

Find the value of $6 1/4 × 5 1/2 + 252 ÷ 7 − 1 3/5$.

Solution

Using the BODMAS rule, follow the steps:

Start by dividing: $6 1/4 × 5 1/2 + 252 ÷ 7 − 1 3/5 = 6 1/4 × 5 1/2 + 36 − 1 3/5$

Multiply: $6 1/4 × 5 1/2 + 36 − 1 3/5 = 25/4 × 11/2 + 36 − 1 3/5 = 275/8 + 36 − 1 3/5$

Add: $275/8 + 36 − 1 3/5 = 563/8 − 1 3/5$

Finally subtract: $563/8 − 1 3/5 = 2751/40 = 68 31/40$

Therefore, $6 1/4 × 5 1/2 + 252 ÷ 7 − 1 3/5 = 68 31/40$.

Example 3

Find the value of $32.65 × 8.4 − 1143 ÷ 127 + 51.64$.

Solution

Using the BODMAS rule, follow the steps:

Start by dividing: $32.65 × 8.4 − 1143 ÷ 127 + 51.64 = 32.65 × 8.4 − 9 + 51.64$

Multiply: $32.65 × 8.4 − 9 + 51.64 = 274.26 − 9 + 51.64$

Add: $274.26 − 9 + 51.64 = 274.26 + 51.64 − 9 = 325.9 − 9$

Finally subtract: $325.9 − 9 = 316.9$

Therefore, $32.65 × 8.4 − 1143 ÷ 127 + 51.64 = 316.9$.