WRITING AND EVALUATING EXPRESSIONS WORKSHEET

Questions 1-10 : Write the given verbal phrases as mathematical expressions.

Question 1 :

The sum of five times a number and eight.

Question 2 :

2 times the sum of 7 times a number and 4.

Question 3 :

7 less than 4 times a number.

Question 4 :

One fifth of sum of 3 times a number and 9.

Question 5 :

One seventh of 3 less than 4 times a number.

Question 6 :

5 times of a number is decreased by 8.

Question 7 :

 6 times of a number is increased by 15.

Question 8 :

7 less than 3 times the sum of a number and 6.

Question 9 :

3 times the difference between a number and 8.

Question 10 :

One fourth of 3 times the difference between a number and 6.

Questions 11-12 : Evaluate the given numerical expressions.

Question 11 :

3 + 5 x 7

Question 12 :

8² - 28 ÷ 7

Questions 13-15 : Write the given verbal phrases as numerical expressions and evaluate them.

Question 13 :

"The sum of 3 times 4 and 9"

Question 14 :

"7 times the sum of 5 times 3 and 2"

Question 15 :

"15 is multiplied by 4, the result is divided by 20 and 12 is added to the final answer"

Question 16 :

Evaluate the following expression for x = 3 and y = 5.

3x + 2y

Question 17 :

Evaluate the following expression for m = 5 and n = 2.

m² + 2mn²

Question 18 :

Evaluate the following expression for s = 5.

s² + 7s - 2

Question 19 :

Evaluate the following expression for m = 1/3.

18m² + 3m + 7

Question 20 :

Evaluate the following expression for m = 13.

m² + m - 54

Question 21 :

Evaluate the following expression for x = 3 and y = 5.

x² + y²

Question 22 :

Evaluate the following expression for m = 5 and n = 2.

5m² + 2m²n

Question 23 :

Evaluate the following expression for s = 6.

s² - 3s + 10

Question 24 :

Evaluate the following expression for x = 2 and y = -5.

x² - 3y²

Question 25 :

Evaluate the following expression for m = 3.

(2m² + 5m - 7)/2

Answers

1. Answer :

5x + 8

2. Answer :

2(7x + 4)

3. Answer :

4x - 7

4. Answer :

(3x + 9)/5

5. Answer :

(4x - 3)/7

6. Answer :

5x - 8

7. Answer :

6x + 15

8. Answer :

3(x + 6) - 7

9. Answer :

3(x - 8)

10. Answer :

3(x - 6)/4

11. Answer :

= 3 + 5 x 7

In the numerical expression above, we have two operations : addition and multiplication. According to PEMDAS Rule, we have to do multiplication first, then addition.

= 3 + 15

= 18

12. Answer :

8² - 28 ÷ 7

In the given numerical  expression, we have more than two operations. Using PEMDAS Rule, we can carry out the operations one by one as shown below and evaluate.

13. Answer :

"The sum of 3 times 4 and 9"

= 3x4 + 9

Using PEMDAS Rule,

= 12 + 9

= 21

14. Answer :

"7 times the sum of 5 times 3 and 2"

= 7[5(3) + 2]

Using PEMDAS Rule,

= 7[15 + 2]

= 7 x 17

= 119

15. Answer :

"15 is multiplied by 4, the result is divided by 20 and 12 is added to the final answer"

= [(15 x 4)/20] + 12

Using PEMDAS Rule,

= [60/20] + 12

= 3 + 12

= 15

16. Answer :

3x + 2y

Substitute 3 for x and 5 for y into the given expression.

3x + 2y = 3(3) + 2(5)

= 9 + 10

= 19

m² + 2mn²

17. Answer :

m² + 2mn²

Substitute 5 for m and 2 for n into the given expression.

m² + 2mn² = 5² + 2(5)(2)²

= 25 + 40

= 65

18. Answer :

s² + 7s - 2

Substitute 5 for s into the given expression.

s² + 7s - 2 = 5² + 7(5) - 2

= 25 + 35 - 2

= 58

19. Answer :

18m² + 3m + 7

Substitute 1/3 for m into the given expression.

18m² + 3m + 7 = 18(1/3)² + 3(1/3) + 7

= 2 + 1 + 7

= 10

20. Answer :

m² + m - 54

Substitute 13 for s into the given expression.

m² + m - 54 = 13² + 13 -54

= 169 + 13 - 54

= 128

21. Answer :

x² + y²

Substitute 3 for x and 5 for y into the given expression.

x² + y² = 3² + 5²

= 9 + 25

= 34

22. Answer :

5m² + 2m²n

Substitute 5 for m and 2 for n into the given expression.

5m² + 2m²n = 5(5)² + 2(5)²(2)

= 5(25) + 2(25)(2)

= 125 + 100

= 225

23. Answer :

s² - 3s + 10

Substitute 6 for s into the given expression.

s² - 3s + 10 = 6² - 3(6) + 10

= 36 - 18 + 10

= 28

24. Answer :

x² - 3y²

Substitute 2 for x and -5 for y into the given expression.

x² - 3y²  =  2(2)² - 3(-5)²

=  2(4) - 3(25)

= 8 - 75

= -77

25. Answer :

(2m² + 5m - 7)/2

Substitute 3 for m into the given expression.

(2m² + 5m - 7)/2 = [2(3)² + 5(3) - 7]/2

= [2(9) + 15 - 7]/2

= (18 + 15 - 7)/2

= 26/2

= 13

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