7th Grade Math · Unit 3
Use the order of operations to simplify a numerical expression.
Multiply and divide first
Add and subtract after you multiply and divide.
6 + 4 × 3 means 6 + 12.
Left to right
Multiply and divide from left to right. Then add or subtract.
20 ÷ 4 × 2 means 5 × 2.
Brackets and bars
Work inside brackets or absolute value bars before you multiply.
Absolute value is the distance from zero, so it is never negative.
Powers and square roots
Evaluate a power or a square root before you add.
A power multiplies the base by itself. A square root asks which number times itself gives the inside.
Multiply or divide before you add or subtract.
Multiply before you add.
2 × 5 = 10
8 + 10 = 18
Answer: 18
Multiply before you add.
3 × 4 = 12
6 + 12 = 18
Answer: 18
Multiply before you add.
4 × 2 = 8
9 + 8 = 17
Answer: 17
Multiply before you add.
7 × 3 = 21
5 + 21 = 26
Answer: 26
Multiply before you add.
5 × 2 = 10
12 + 10 = 22
Answer: 22
Multiply before you subtract.
4 × 5 = 20
30 − 20 = 10
Answer: 10
Multiply before you subtract.
3 × 4 = 12
18 − 12 = 6
Answer: 6
Multiply before you subtract.
6 × 7 = 42
50 − 42 = 8
Answer: 8
Multiply and divide from left to right. Then add.
12 ÷ 3 = 4
4 × 2 = 8
7 + 8 = 15
Answer: 15
Multiply and divide from left to right. Then add.
20 ÷ 5 = 4
4 × 3 = 12
4 + 12 = 16
Answer: 16
Multiply and divide from left to right. Then add.
18 ÷ 6 = 3
3 × 4 = 12
9 + 12 = 21
Answer: 21
Brackets, powers, and square roots come before the other operations.
Work inside the brackets first.
6 + 3 = 9
9 × 4 = 36
Answer: 36
Work inside the brackets first.
8 + 2 = 10
10 × 5 = 50
Answer: 50
Work inside the brackets first.
9 + 4 = 13
13 × 3 = 39
Answer: 39
Work inside the brackets first.
15 − 6 = 9
9 × 2 = 18
Answer: 18
Work inside the brackets first.
4 − 10 = −6
−6 × 3 = −18
Answer: −18
Evaluate the power first.
2³ = 8
8 + 5 = 13
Answer: 13
Evaluate the power first.
3² = 9
9 + 7 = 16
Answer: 16
Evaluate the power first.
7¹ = 7
7 + 6 = 13
Answer: 13
16 is a perfect square.
= 4
4 + 3 = 7
Answer: 7
49 is a perfect square.
= 7
7 + 2 = 9
Answer: 9
81 is a perfect square.
= 9
9 + 4 = 13
Answer: 13
Use a power inside brackets, absolute value, or a square root.
Work inside the absolute value bars first.
12 − 4 = 8
|8| = 8
8 + 3 = 11
Answer: 11
Evaluate the power inside the brackets.
2³ = 8
8 + 1 = 9
9 × 4 = 36
Answer: 36
Evaluate the power inside the brackets.
3² = 9
9 + 2 = 11
11 × 5 = 55
Answer: 55
Evaluate the power inside the brackets.
2² = 4
4 − 7 = −3
−3 × 4 = −12
Answer: −12
Work inside the absolute value bars first.
3 − 10 = −7
|−7| = 7
7 + 2 = 9
Answer: 9
Work inside the absolute value bars first.
4 − 15 = −11
|−11| = 11
11 + 1 = 12
Answer: 12
Work inside the absolute value bars first.
8 − 3 = 5
|5| = 5
5 + 5 = 10
Answer: 10
Work inside the absolute value bars, and evaluate the power.
6 − 1 = 5
|5| = 5
2³ = 8
5 × 8 = 40
Answer: 40
Work inside the absolute value bars, and evaluate the power.
2 − 11 = −9
|−9| = 9
4² = 16
9 × 16 = 144
Answer: 144
= 5
3² = 9
5 + 9 = 14
Answer: 14
= 7
2⁴ = 16
7 + 16 = 23
Answer: 23
Need help with this skill?
Book a Session with Amy