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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 3

Evaluate
Expressions

Substitute each given value, then simplify.

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Key Ideas Easy Medium Hard Two Groups
What to Remember

Replace each letter

Write the given value in place of each variable.

Put parentheses around a negative value.

Powers and products first

Evaluate powers, multiplication, and division before you add or subtract.

Then add the amounts

Add or subtract the numbers that are left.

A fraction stays stacked until it becomes a whole number.

Level 1

Easy

Replace x with a positive whole number, then simplify.

Example
Evaluate for x = 3.
2³ + 2x + 1

Replace x with 3.

2³ + 2x + 1

2³ + 2(3) + 1

8 + 6 + 1

15

Answer: 15

1
Evaluate for x = 4.
2² + 3x + 1
Show Answer

Replace x with 4.

2² + 3x + 1

2² + 3(4) + 1

4 + 12 + 1

17

Answer: 17

2
Evaluate for x = 2.
3² + 2x + 5
Show Answer

Replace x with 2.

3² + 2x + 5

3² + 2(2) + 5

9 + 4 + 5

18

Answer: 18

3
Evaluate for x = 5.
2³ + x + 4
Show Answer

Replace x with 5.

2³ + x + 4

2³ + 5 + 4

8 + 5 + 4

17

Answer: 17

4
Evaluate for x = 1.
5² + 2x + 3
Show Answer

Replace x with 1.

5² + 2x + 3

5² + 2(1) + 3

25 + 2 + 3

30

Answer: 30

5
Evaluate for x = 3.
2⁴ + 3x + 2
Show Answer

Replace x with 3.

2⁴ + 3x + 2

2⁴ + 3(3) + 2

16 + 9 + 2

27

Answer: 27

6
Evaluate for x = 4.
4² + x + 6
Show Answer

Replace x with 4.

4² + x + 6

4² + 4 + 6

16 + 4 + 6

26

Answer: 26

7
Evaluate for x = 3.
3¹ + 4x + 2
Show Answer

Replace x with 3.

3¹ + 4x + 2

3¹ + 4(3) + 2

3 + 12 + 2

17

Answer: 17

8
Evaluate for x = 2.
2² + 5x + 7
Show Answer

Replace x with 2.

2² + 5x + 7

2² + 5(2) + 7

4 + 10 + 7

21

Answer: 21

9
Evaluate for x = 5.
6² + 2x + 1
Show Answer

Replace x with 5.

6² + 2x + 1

6² + 2(5) + 1

36 + 10 + 1

47

Answer: 47

10
Evaluate for x = 2.
3³ + x + 4
Show Answer

Replace x with 2.

3³ + x + 4

3³ + 2 + 4

27 + 2 + 4

33

Answer: 33

Level 2

Medium

Two variables. Multiply and divide before you add.

Example
Evaluate for x = 9 and y = 3.
x − y + 4

Replace x with 9 and y with 3.

x − y + 4

9 − 3 + 4

10

Answer: 10

1
Evaluate for a = 5 and b = 9.
a² − b
Show Answer

Replace a with 5 and b with 9.

a² − b

5² − 9

25 − 9

16

Answer: 16

2
Evaluate for x = 8 and y = 3.
7(x − y)
Show Answer

Replace x with 8 and y with 3.

7(x − y)

7(8 − 3)

7(5)

35

Answer: 35

3
Evaluate for y = 2 and x = 6.
yx ÷ 4
Show Answer

Replace y with 2 and x with 6.

yx ÷ 4

2 · 6 ÷ 4

12 ÷ 4

3

Answer: 3

4
Evaluate for m = 11 and n = 6.
m − n ÷ 3
Show Answer

Replace m with 11 and n with 6.

m − n ÷ 3

11 − 6 ÷ 3

11 − 2

9

Answer: 9

5
Evaluate for x = 4 and y = 1.
x − y + 8
Show Answer

Replace x with 4 and y with 1.

x − y + 8

4 − 1 + 8

11

Answer: 11

6
Evaluate for z = 7 and x = 2.
z + x³
Show Answer

Replace z with 7 and x with 2.

z + x³

7 + 2³

7 + 8

15

Answer: 15

7
Evaluate for y = 3 and x = 4.
y + yx
Show Answer

Replace y with 3 and x with 4.

y + yx

3 + 3 · 4

3 + 12

15

Answer: 15

8
Evaluate for q = 20 and p = 6.
q ÷ 5 + p
Show Answer

Replace q with 20 and p with 6.

q ÷ 5 + p

20 ÷ 5 + 6

4 + 6

10

Answer: 10

9
Evaluate for x = 12 and y = 4.
x + 5 − y
Show Answer

Replace x with 12 and y with 4.

x + 5 − y

12 + 5 − 4

13

Answer: 13

10
Evaluate for m = 4 and p = 7.
18 − (m + p)
Show Answer

Replace m with 4 and p with 7.

18 − (m + p)

18 − (4 + 7)

18 − 11

7

Answer: 7

Level 3

Hard

A fraction with three variables, or a negative number times a power.

Example
Evaluate for m = −4, n = 2, and p = 3.
2m − np + 2

Replace m with −4, n with 2, and p with 3.

2m − np + 2

2(−4) − 23 + 2

−8 − 23 + 2

−105

−2

Answer: −2

1
Evaluate for m = 4, n = −4, and p = 8.
3m + np − 4
Show Answer

Replace m with 4, n with −4, and p with 8.

3m + np − 4

3(4) + (−4)8 − 4

12 + (−4)8 − 4

84

2

Answer: 2

2
Evaluate for m = 4, n = −3, and p = 4.
m − 2np + 1
Show Answer

Replace m with 4, n with −3, and p with 4.

m − 2np + 1

4 − 2(−3)4 + 1

4 − (−6)4 + 1

105

2

Answer: 2

3
Evaluate for m = −3, n = 6, and p = −1.
4m + n2p
Show Answer

Replace m with −3, n with 6, and p with −1.

4m + n2p

4(−3) + 62(−1)

−12 + 6−2

−6−2

3

Answer: 3

4
Evaluate for m = 6, n = −18, and p = 8.
m + np − 2
Show Answer

Replace m with 6, n with −18, and p with 8.

m + np − 2

6 + (−18)8 − 2

−126

−2

Answer: −2

5
Evaluate for m = 3, n = −1, and p = 1.
5m − np + 3
Show Answer

Replace m with 3, n with −1, and p with 1.

5m − np + 3

5(3) − (−1)1 + 3

15 − (−1)1 + 3

164

4

Answer: 4

6
Evaluate for m = −5, n = 2, and p = 2.
2m + np − 6
Show Answer

Replace m with −5, n with 2, and p with 2.

2m + np − 6

2(−5) + 22 − 6

−10 + 22 − 6

−8−4

2

Answer: 2

7
Evaluate for m = −3 and n = 1.
−2(m² + 3n)
Show Answer

Replace m with −3 and n with 1.

−2(m² + 3n)

−2((−3)² + 3(1))

−2(9 + 3)

−2(12)

−24

Answer: −24

8
Evaluate for n = −2 and m = −1.
−4(n² − m)
Show Answer

Replace n with −2 and m with −1.

−4(n² − m)

−4((−2)² − (−1))

−4(4 − (−1))

−4(5)

−20

Answer: −20

9
Evaluate for m = 2 and n = −6.
−5(m² + n)
Show Answer

Replace m with 2 and n with −6.

−5(m² + n)

−5(2² + (−6))

−5(4 + (−6))

−5(−2)

10

Answer: 10

10
Evaluate for p = −1 and m = 4.
−3(p² + 2m)
Show Answer

Replace p with −1 and m with 4.

−3(p² + 2m)

−3((−1)² + 2(4))

−3(1 + 8)

−3(9)

−27

Answer: −27

Level 3

Two Groups

Simplify inside each group, then add.

Example
Evaluate for a = 7, b = 2, and c = 5.
4(a − b) + 3(c − 1)

Replace a with 7, b with 2, and c with 5.

4(a − b) + 3(c − 1)

4(7 − 2) + 3(5 − 1)

4(5) + 3(4)

20 + 12

32

Answer: 32

1
Evaluate for a = 10, b = 4, and c = 6.
2(a − b) + 5(c − 3)
Show Answer

Replace a with 10, b with 4, and c with 6.

2(a − b) + 5(c − 3)

2(10 − 4) + 5(6 − 3)

2(6) + 5(3)

12 + 15

27

Answer: 27

2
Evaluate for a = 5, b = 1, and c = 4.
6(a − b) + 4(c − 2)
Show Answer

Replace a with 5, b with 1, and c with 4.

6(a − b) + 4(c − 2)

6(5 − 1) + 4(4 − 2)

6(4) + 4(2)

24 + 8

32

Answer: 32

3
Evaluate for a = 8, b = 3, and c = 9.
3(a − b) + (c − 5)
Show Answer

Replace a with 8, b with 3, and c with 9.

3(a − b) + (c − 5)

3(8 − 3) + (9 − 5)

3(5) + 4

15 + 4

19

Answer: 19

4
Evaluate for b = 6, a = 2, and c = 3.
5(b − a) + 2(c + 1)
Show Answer

Replace b with 6, a with 2, and c with 3.

5(b − a) + 2(c + 1)

5(6 − 2) + 2(3 + 1)

5(4) + 2(4)

20 + 8

28

Answer: 28

5
Evaluate for a = 6, b = 9, and c = 4.
4(a − 2) + 3(b − c)
Show Answer

Replace a with 6, b with 9, and c with 4.

4(a − 2) + 3(b − c)

4(6 − 2) + 3(9 − 4)

4(4) + 3(5)

16 + 15

31

Answer: 31

6
Evaluate for a = 9, b = 4, and c = 6.
2(a − b) + 7(c − 4)
Show Answer

Replace a with 9, b with 4, and c with 6.

2(a − b) + 7(c − 4)

2(9 − 4) + 7(6 − 4)

2(5) + 7(2)

10 + 14

24

Answer: 24

7
Evaluate for a = 7, b = 2, and c = 4.
8(a − b) + 2(c − 1)
Show Answer

Replace a with 7, b with 2, and c with 4.

8(a − b) + 2(c − 1)

8(7 − 2) + 2(4 − 1)

8(5) + 2(3)

40 + 6

46

Answer: 46

8
Evaluate for a = 9, b = 7, and c = 2.
3(a − 4) + 5(b − c)
Show Answer

Replace a with 9, b with 7, and c with 2.

3(a − 4) + 5(b − c)

3(9 − 4) + 5(7 − 2)

3(5) + 5(5)

15 + 25

40

Answer: 40

9
Evaluate for c = 5, a = 2, and b = 7.
6(c − a) + 2(b − 3)
Show Answer

Replace c with 5, a with 2, and b with 7.

6(c − a) + 2(b − 3)

6(5 − 2) + 2(7 − 3)

6(3) + 2(4)

18 + 8

26

Answer: 26

10
Evaluate for a = 11, b = 6, and c = 8.
4(a − b) + 9(c − 6)
Show Answer

Replace a with 11, b with 6, and c with 8.

4(a − b) + 9(c − 6)

4(11 − 6) + 9(8 − 6)

4(5) + 9(2)

20 + 18

38

Answer: 38

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