Write and Interpret Numerical Expressions
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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