# Evaluate Expressions with Parentheses

# – Grade 5 Math Worksheets

Home | 5th Grade Math Worksheets | **Evaluate Expressions with Parentheses**

**Order of Operations**

We follow the **PEMDAS **rule for solving arithmetic expressions. The hierarchy for solving such expressions is determined as follows:

**Step I:** First of all, we need to perform operations inside parentheses or brackets. There are different types of brackets viz big bracket or square bracket denoted as [ ], curly bracket denoted as { }, round or small bracket denoted as ( ), line bracket denoted as ¯z, where *z* is any number. The expression is evaluated from inside out, starting from line bracket to small bracket to curly bracket and finally to big bracket respectively.

**Step II:** Solving any exponent in the expression.

**Step III:** Multiplication and division to be performed from left to right.

**Step IV:** Addition and subtraction to be performed from left to right.

** Example: **Evaluate {20 + (15 + 5)} – 5

First, we solve the brackets from inside out.

{20 + (15 + 5)} – 5 = {20 + 20} – 5 = 40 – 5 = 35

*Example:* Simplify: 96 ÷ 2 × 24 – 2

Here, we will perform multiplication and division from left to right.

96 ÷ 2 × 24 – 2 = 48 × 24 – 2 = 1152 – 2 = 1150

** Example: **Simplify: 4[127 – 5{113 – 2(15 × 9 ÷ 3)}]

4[127 – 5{113 – 2(15 × 9 ÷ 3)}] = 4[127 – 5{113 – 2(135 ÷ 3)}] = 4[127 – 5{113 – 2(45)}]

= 4[127 – 5{113 – 90}] = 4[127 – 5{23}] = 4[127 – 115] = 4[12] = 48

**Check Point**

**Simplify:**

- (10 × 8) ÷ (20 ÷ 5)
- 12 × 3 ÷ 3 × 4 – 2 + 6
- {(18 + 17) ÷ 5} ÷ 7
- 121 ÷ 11 + 29 – 2 × 10
- 10[2 × {45 + (29 – 18)}]

**Answer Key**

- 12 × 3 ÷ 3 × 4 – 2 + 6 = 36 ÷ 3 × 4 – 2 + 6 = 12 × 4 – 2 + 6 = 48 – 2 + 6 = 46 + 6 = 52
- {(18 + 17) ÷ 5} ÷ 7 = {35 ÷ 5} ÷ 7 = 7 ÷ 7 = 1
- 121 ÷ 11 + 29 – 2 × 10 = 11 + 29 – 2 × 10 = 11 + 29 – 20 = 40 – 20 = 20
- 10[2 × {45 + (29 – 18)}] = 10[2 × {45 + 11}] = 10[2 × 56] = 10[112] = 1120

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