Level 1
Introduction to order of operation
"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.
But, when you see something like ...
7 + (6 × 52 + 3)
... what part should you calculate first?
But, when you see something like ...
7 + (6 × 52 + 3)
... what part should you calculate first?
|
|
PEMDAS
PEMDAS is an acronym that stands for Parenthesis, Exponents, Multiplication, Addition and Subtraction. The order of operation is:
- P is for Parentheses: (), brackets [], braces {} and fraction bars.
- E is for Exponent, including roots.
- M is for Division.
- D is for Multiplication.
- A is for Addition.
- S is for Subtraction.
- Always start by calculating all expressions within parentheses
- Simplify all the exponents such as square roots, squares, cube and cube roots
- Perform the multiplication and the division starting from left to right
- Finally, do the addition and subtraction similarly starting from left to right.
Practice-
Solve
1. 30 ÷ 5 x 2 + 1
Answer- 13
2. 5 + (4 – 2 ) X 2 x 3 ÷ 6 – 1
Answer : 6
3. 3 2 + [6 (11 + 1 – 4)] ÷ 8 x 2
Answer: 21
4. 10 ÷ 2 + 12 ÷ 2 × 3
Answer : 23
5. 20 – [3 x (2 + 4)]
Answer 18
6. (6 – 3) 2 – 2 x 4
Answer: 1
7. 9 – 5 ÷ (8 – 3) x 2 + 6
Answer: 13
Note: sometimes an expression might contain two operations on the same level.
For example, if an expression contains both square and cube, either can be worked out first. Always do the operation from the left to the right following the PEMDAS rule. If you come across an expression with no grouping symbols such as braces, brackets and parentheses, you can make the operation easier by adding your own grouping symbols.
More practice:
1) Solve
4 – 3 [4 – 2 (6 – 3)] ÷ 2
2) Simplify the following expression using PEMDAS:
16 – 3 (8 – 3) 2 ÷ 5
3) Evaluate the following expression using the order of operations:
3 + 6 x (4 + 5) ÷ 3 – 7
4) Evaluate the expression below using PEMDAS.
150 ÷ (6 + 3 x 8) – 5
5) Simplify the following expression;
45 ÷ (8 {5 – 4} – 3)
Solve
1. 30 ÷ 5 x 2 + 1
Answer- 13
2. 5 + (4 – 2 ) X 2 x 3 ÷ 6 – 1
Answer : 6
3. 3 2 + [6 (11 + 1 – 4)] ÷ 8 x 2
Answer: 21
4. 10 ÷ 2 + 12 ÷ 2 × 3
Answer : 23
5. 20 – [3 x (2 + 4)]
Answer 18
6. (6 – 3) 2 – 2 x 4
Answer: 1
7. 9 – 5 ÷ (8 – 3) x 2 + 6
Answer: 13
Note: sometimes an expression might contain two operations on the same level.
For example, if an expression contains both square and cube, either can be worked out first. Always do the operation from the left to the right following the PEMDAS rule. If you come across an expression with no grouping symbols such as braces, brackets and parentheses, you can make the operation easier by adding your own grouping symbols.
More practice:
1) Solve
4 – 3 [4 – 2 (6 – 3)] ÷ 2
2) Simplify the following expression using PEMDAS:
16 – 3 (8 – 3) 2 ÷ 5
3) Evaluate the following expression using the order of operations:
3 + 6 x (4 + 5) ÷ 3 – 7
4) Evaluate the expression below using PEMDAS.
150 ÷ (6 + 3 x 8) – 5
5) Simplify the following expression;
45 ÷ (8 {5 – 4} – 3)
Book : Math Makes Sense
Math Makes Sense : Student book
Your browser does not support viewing this document. Click here to download the document.
Order of operation with decimal
Link to practice
|
|
Your browser does not support viewing this document. Click here to download the document.
Challenge yourself: ( with fraction)
Working with expressions having fractions are solved by first simplifying the numerator followed by the denominator. The next step is to simplify the numerator and denominator if possible.
Practice Questions1) Simplify the expression;
2 + 3 /2 (5 – 1)
Working with expressions having fractions are solved by first simplifying the numerator followed by the denominator. The next step is to simplify the numerator and denominator if possible.
Practice Questions1) Simplify the expression;
2 + 3 /2 (5 – 1)
Order of Operation with Exponents
Practice :
Order of Operation with integers:
Practice:
2 2 – 3 × (10 – 6)
Answer: - 8
2 2 – 3 × (10 – 6)
Answer: - 8
Worksheets : Click the link
Order of Operation with Algebraic expression
1) By using PEMDAS, simplify the following algebraic expression:
14 z + 5 [6 – (2 z + 3)]
2) Simplify the algebraic expression below;
– {2 y – [ 3 – (4 – 3 y)] + 6 y
14 z + 5 [6 – (2 z + 3)]
2) Simplify the algebraic expression below;
– {2 y – [ 3 – (4 – 3 y)] + 6 y