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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 2

Order of Operations
with Negative Numbers

Simplify with the four operations, parentheses, exponents, negative numbers, and absolute value.

Jump to section:

Key Ideas + − × ÷ Parenthesis and Exponents Nested Parenthesis Negative Numbers Absolute Value Quiz
What to Remember

The order

Parentheses first. Then exponents. Then multiplication and division from left to right.

Addition and subtraction come last, from left to right.

Multiplication does not come before division. Do whichever comes first as you read.

Nested parentheses

When one pair sits inside another, do the innermost pair first.

Each pair is written with parentheses ( ).

The exponent stays with its base

3² means 3 × 3.

−4² means the negative of 4². The base is 4.

(−4)² means the base is −4.

Absolute value bars

Work inside the bars first. Then drop the sign.

The bars group the inside the way parentheses do.

Easy 1

+ − × ÷

Multiply and divide from left to right. Then add and subtract from left to right.

Example
Simplify.
6 + 15 ÷ 3 × 2 − 4
6+15÷3×2−4
6+5×2−4
6+10−4
16−4

12

1
Simplify.
12 + 16 ÷ 4 × 6 − 5
Show Answer
12+16÷4×6−5
12+4×6−5
12+24−5
36−5

31

2
Simplify.
8 + 20 ÷ 5 × 3 − 4
Show Answer
8+20÷5×3−4
8+4×3−4
8+12−4
20−4

16

3
Simplify.
6 × 7 + 18 ÷ 3 + 4
Show Answer
6×7+18÷3+4
42+18÷3+4
42+6+4
48+4

52

4
Simplify.
4 × 9 + 24 ÷ 6 + 5
Show Answer
4×9+24÷6+5
36+24÷6+5
36+4+5
40+5

45

5
Simplify.
7 × 5 + 8 − 6 + 11
Show Answer
7×5+8−6+11
35+8−6+11
43−6+11
37+11

48

6
Simplify.
9 × 3 + 12 − 7 + 6
Show Answer
9×3+12−7+6
27+12−7+6
39−7+6
32+6

38

7
Simplify.
8 × 8 − 5 × 9 + 6
Show Answer
8×8−5×9+6
64−5×9+6
64−45+6
19+6

25

8
Simplify.
7 × 6 − 4 × 8 + 9
Show Answer
7×6−4×8+9
42−4×8+9
42−32+9
10+9

19

9
Simplify.
9 − 4 + 3 × 5 × 2
Show Answer
9−4+3×5×2
9−4+15×2
9−4+30
5+30

35

10
Simplify.
12 − 5 + 2 × 6 × 4
Show Answer
12−5+2×6×4
12−5+12×4
12−5+48
7+48

55

Easy 2

Parenthesis and Exponents

Parentheses first. Then exponents.

Example
Simplify.
(5 + 1)² + (10 − 16 ÷ 8)
(5+1)²+(10−16÷8)
6²+(10−16÷8)
6²+(10−2)
6²+8
36+8

44

1
Simplify.
(8 + 22 − 6) ÷ 4 − 2²
Show Answer
(8+22−6)÷4−2²
(30−6)÷4−2²
24÷4−2²
24÷4−4
6−4

2

2
Simplify.
(7 + 15 − 4) ÷ 6 − 3²
Show Answer
(7+15−4)÷6−3²
(22−4)÷6−3²
18÷6−3²
18÷6−9
3−9

−6

3
Simplify.
(9 + 27 − 6) ÷ 5 + 4²
Show Answer
(9+27−6)÷5+4²
(36−6)÷5+4²
30÷5+4²
30÷5+16
6+16

22

4
Simplify.
(12 + 18 − 6) ÷ 8 + 2²
Show Answer
(12+18−6)÷8+2²
(30−6)÷8+2²
24÷8+2²
24÷8+4
3+4

7

5
Simplify.
3 × (4 × 5 + 2²) + 6
Show Answer
3×(4×5+2²)+6
3×(4×5+4)+6
3×(20+4)+6
3×24+6
72+6

78

6
Simplify.
2 × (6 × 3 + 4²) + 5
Show Answer
2×(6×3+4²)+5
2×(6×3+16)+5
2×(18+16)+5
2×34+5
68+5

73

7
Simplify.
(5 + 2)² + (11 − 12 ÷ 3)
Show Answer
(5+2)²+(11−12÷3)
7²+(11−12÷3)
7²+(11−4)
7²+7
49+7

56

8
Simplify.
(4 + 4)² + (15 − 18 ÷ 6)
Show Answer
(4+4)²+(15−18÷6)
8²+(15−18÷6)
8²+(15−3)
8²+12
64+12

76

9
Simplify.
(8 − 3)² − (4 + 10 ÷ 5)
Show Answer
(8−3)²−(4+10÷5)
5²−(4+10÷5)
5²−(4+2)
5²−6
25−6

19

10
Simplify.
5 × (3 × 2 + 3²) − 7
Show Answer
5×(3×2+3²)−7
5×(3×2+9)−7
5×(6+9)−7
5×15−7
75−7

68

Medium

Nested Parenthesis

Start with the innermost parentheses.

Example
Simplify.
(10 + (12 ÷ 3)) + 7
(10+(12÷3))+7
(10+4)+7
14+7

21

1
Simplify.
(16 + (18 ÷ 6)) + 5
Show Answer
(16+(18÷6))+5
(16+3)+5
19+5

24

2
Simplify.
14 + ((9 + 6) + 3)
Show Answer
14+((9+6)+3)
14+(15+3)
14+18

32

3
Simplify.
((12 + 6) × 4) − 8
Show Answer
((12+6)×4)−8
(18×4)−8
72−8

64

4
Simplify.
7 + ((11 + 5) × 3)
Show Answer
7+((11+5)×3)
7+(16×3)
7+48

55

5
Simplify.
(15 + (20 ÷ 4 + 6))
Show Answer
(15+(20÷4+6))
(15+(5+6))
(15+11)

26

6
Simplify.
(11 + (18 ÷ 3 − 2))
Show Answer
(11+(18÷3−2))
(11+(6−2))
(11+4)

15

7
Simplify.
13 + (5 × (8 + 4))
Show Answer
13+(5×(8+4))
13+(5×12)
13+60

73

8
Simplify.
9 + (4 + (17 − 6))
Show Answer
9+(4+(17−6))
9+(4+11)
9+15

24

9
Simplify.
(20 + (24 ÷ 6)) + 3
Show Answer
(20+(24÷6))+3
(20+4)+3
24+3

27

10
Simplify.
((14 + 9) + 6) − 8
Show Answer
((14+9)+6)−8
(23+6)−8
29−8

21

Hard

Negative Numbers

Problems like + − × ÷, Parenthesis and Exponents, and Nested Parenthesis, with negative numbers.

Example
Simplify.
−3² + 4 × (2 − (−1))
−3²+4×(2−(−1))
−3²+4×3
−9+4×3
−9+4×3
−9+12

3

1
Simplify.
6 + (−18) ÷ 3 × 2 − 4
Show Answer
6+(−18)÷3×2−4
6+(−6)×2−4
6+(−12)−4
−6−4

−10

2
Simplify.
(−4) × 6 − 5 × (−3) + 2
Show Answer
(−4)×6−5×(−3)+2
−24−5×(−3)+2
−24−(−15)+2
−9+2

−7

3
Simplify.
8 − (−5) + (−3) × 4 × 2
Show Answer
8−(−5)+(−3)×4×2
8−(−5)+(−12)×2
8−(−5)+(−24)
13+(−24)

−11

4
Simplify.
(12 + (−8) − 2) ÷ 2 − 3²
Show Answer
(12+(−8)−2)÷2−3²
(4−2)÷2−3²
2÷2−3²
2÷2−9
1−9

−8

5
Simplify.
(−5)² + (6 − 15 ÷ (−3))
Show Answer
(−5)²+(6−15÷(−3))
(−5)²+(6−(−5))
(−5)²+11
25+11

36

6
Simplify.
−4² + (9 − 2) × 3
Show Answer
−4²+(9−2)×3
−4²+7×3
−16+7×3
−16+7×3
−16+21

5

7
Simplify.
(10 + ((−12) ÷ 4)) + 6
Show Answer
(10+((−12)÷4))+6
(10+(−3))+6
7+6

13

8
Simplify.
((−3 + 8) × 4) − 5
Show Answer
((−3+8)×4)−5
(5×4)−5
20−5

15

9
Simplify.
7 + (2 × (−6 + 10))
Show Answer
7+(2×(−6+10))
7+(2×4)
7+8

15

10
Simplify.
(4 + ((−18) ÷ 3 + 5))
Show Answer
(4+((−18)÷3+5))
(4+(−6+5))
(4+(−1))

3

Challenge 1

Absolute Value

Work inside the bars first. Then drop the sign.

Example
Simplify.
|−5| + 2 × (−3)
|−5|+2×(−3)
5+2×(−3)
5+(−6)

−1

1
Simplify.
|−8 + 3| × 2
Show Answer
|−8+3|×2
|−5|×2
5×2

10

2
Simplify.
4 × (|−6| − 10)
Show Answer
4×(|−6|−10)
4×(6−10)
4×(−4)

−16

3
Simplify.
−|12 − 5| + 3²
Show Answer
−|12−5|+3²
−|7|+3²
−7+3²
−7+3²
−7+9

2

4
Simplify.
|−4| × |−5| − 6
Show Answer
|−4|×|−5|−6
4×|−5|−6
4×5−6
20−6

14

5
Simplify.
(−3) × |2 − 9| + 15
Show Answer
(−3)×|2−9|+15
(−3)×|−7|+15
(−3)×7+15
−21+15

−6

6
Simplify.
|−15| ÷ 3 + 2 × (−4)
Show Answer
|−15|÷3+2×(−4)
15÷3+2×(−4)
5+2×(−4)
5+(−8)

−3

7
Simplify.
−|−7 − 2| + 4 × 3
Show Answer
−|−7−2|+4×3
−|−9|+4×3
−9+4×3
−9+4×3
−9+12

3

Quiz

Quiz

Ten problems from + − × ÷, Parenthesis and Exponents, and Nested Parenthesis. Open an answer. It names the section to open for more help.

1
Simplify.
5 + 12 ÷ 4 × 3 − 2
Show Answer
5+12÷4×3−2
5+3×3−2
5+9−2
14−2

12

For more help, go to + − × ÷.

2
Simplify.
(4 + 5)² + (7 − 8 ÷ 2)
Show Answer
(4+5)²+(7−8÷2)
9²+(7−8÷2)
9²+(7−4)
9²+3
81+3

84

For more help, go to Parenthesis and Exponents.

3
Simplify.
(6 + (15 ÷ 3)) + 4
Show Answer
(6+(15÷3))+4
(6+5)+4
11+4

15

For more help, go to Nested Parenthesis.

4
Simplify.
5 × 6 − 3 × 4 + 7
Show Answer
5×6−3×4+7
30−3×4+7
30−12+7
18+7

25

For more help, go to + − × ÷.

5
Simplify.
8 + (3 × (5 + 2))
Show Answer
8+(3×(5+2))
8+(3×7)
8+21

29

For more help, go to Nested Parenthesis.

6
Simplify.
(6 + 14 − 2) ÷ 9 + 3²
Show Answer
(6+14−2)÷9+3²
(20−2)÷9+3²
18÷9+3²
18÷9+9
2+9

11

For more help, go to Parenthesis and Exponents.

7
Simplify.
10 − 3 + 2 × 4 × 3
Show Answer
10−3+2×4×3
10−3+8×3
10−3+24
7+24

31

For more help, go to + − × ÷.

8
Simplify.
((7 + 5) × 3) − 6
Show Answer
((7+5)×3)−6
(12×3)−6
36−6

30

For more help, go to Nested Parenthesis.

9
Simplify.
4 × (2 × 3 + 2²) + 1
Show Answer
4×(2×3+2²)+1
4×(2×3+4)+1
4×(6+4)+1
4×10+1
40+1

41

For more help, go to Parenthesis and Exponents.

10
Simplify.
(9 + (16 ÷ 4 − 1))
Show Answer
(9+(16÷4−1))
(9+(4−1))
(9+3)

12

For more help, go to Nested Parenthesis.

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