## Key Concepts

- Evaluate expressions

## Evaluate expressions

How can we evaluate the expression?

To avoid getting more than one answer, we use the order of operations given below.

**Braces**{ }: Symbols that are used to group certain parts of a mathematical expression.

**Brackets **[ ]: Symbols that are used to group certain parts of a mathematical expression.

**Numerical Expressions**: A numerical expression is mathematical combination of numbers, operations, and grouping symbols.

**Order of Operations**: It shows the steps used to evaluate a numerical expression:

- Simplify the expressions inside grouping symbols.

- Evaluate all powers.

- Do all multiplications and/or divisions from left to right.

- Do all additions and/or subtractions from left to right.

**Parentheses**( ): Symbols that are used to group certain parts of a mathematical expression.

**Example 1:**

Explain the steps involved in evaluating the expression

[(6 x 2) – 2] + 6 ÷ 2 x 4.

**Solution:**

**Step1**: First do the operations inside the parentheses.

[(6 x 2) – 2] + 6 ÷ 2 x 4

[12 – 2] + 6 ÷ 2 x 4

Then evaluate the terms inside the brackets.

[12 – 2] + 6 ÷ 2 x 4

10 + 6 ÷ 2 x 4

**Step2:** Next multiply and divide in order from left to right.

10 + 6 ÷ 2 x 4

10 + 3 x 4

10 + 12

**Step3: **Finally, add in order from left to right.

10 + 12 =22

**So, the value of the expression is 22.**[Text Wrapping Break]**Example2:**

Find the value of 15 + 20−8+(6÷2).

**Solution:**

**Step 1**: First do the operations inside the parentheses.

15 + 20−8+(6÷2)

15 + 20−8+3

15 + 20−11

**Step 2: **Subtract from left to right.

15 + 20−11

15 + 9

**Step 3: **Finally, add in order from left to right.

15 + 9 = 24

So the value of the expression is 24.

**Example 3:**

Jordan is working on the expression 25 – [4 + {26 – (28 – 8}]. What is the value of Jordan’s expression?

**Solution:**

**Step 1: **Subtract 8 from 28 and remove the parenthesis.

= 25 – [4 + {26 – (28 – 8}]

= 25 – [4 + {26 – 20}]

**Step 2:** Subtract 20 from 26 and remove the curly brackets.

= 25 – [4 + {26 – 20}]

= 25 – [4 + 6]

**Step 3: **Add 4 and 6 and remove the brackets.

= 25 – [4 + 6]

= 25 – 10

**Step 4: **Subtract 10 from 25.

= 25 – 10

= 15

So, the value of expression is 15.

**Example 4:**

Find the value of [12 + {7 – (8 ÷ 2)}] × 3

**Step1**: First do the operations inside the parentheses.

[12 + {7 – (8 ÷ 2)}] × 3

= [12 + {7 – 4}] × 3

= [12 + 3] × 3

**Step 2: **Add 12 and 3 and remove the brackets.

= [12 + 3] × 3

= 15 × 3

**Step3: **Next, multiply and order from left to right.

= 15 × 3

= 45

So, the value of expression is 45.

## Exercise

Use the order of operations to evaluate the following expressions:

- [(5×2)-2]+4 = 2 x 5
- [(6×3)-6]+5 = 5 x 3
- 8x (20+5)
- 3+ (4×12)
- [4x(S-1)] +50
- 4x (26+7)
- (8 + 9) x (11×10)
- 150-30 + 2 x 4
- 14 x (12+2) = 5

14 x ______ **÷** 5

- 23 = (12-4) x6

### Concept map

### What have we learned

- Understanding the numerical expressions.
- Understanding braces, brackets, parentheses to evaluate expressions.
- Understanding how to use order of operations.
- How to evaluate the expressions.

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