GROUPING SYMBOLS WORKSHEET

Evaluate the following numerical expressions.

Question 1 :

2(5) +  3(4 + 3)

Question 2 :

2[5 + (30 ÷ 6)²]

Question 3 :

[7(2) - 4] + [9 + 8(4)]

Question 4 :

[(4 ⋅ 3)² ⋅ 5]/(9 + 3)

Question 5 :

4(11 + 7) - 9 ⋅ 8

Question 6 :

288 ÷ [3(9 + 3)]

Question 7 :

390 ÷ [5(7 + 6)]

Question 8 :

(4 ⋅ 6² - 4² ⋅ 6) / 4 ⋅ 6

Question 9 :

(2 ⋅ 8² - 2² ⋅ 8)/(2 ⋅ 8)

Question 10 :

12(9 + 5) - 6 ⋅ 3

Question 11 :

Evaluate the expression a = 10, b = 9 and c = 4

a) 2a + 3

b) 4c - 7.8

c)  24/b + 8

d)  bc + 12.3

Question 12 :

The expression 20a + 13c is the cost (in dollars) for a adults and c students to enter a science center.

a. How much does it cost for an adult? a student? Explain your reasoning.

b. Find the total cost for 4 adults and 24 students.

c. You find the cost for a group. Then the numbers of adults and students in the group both double. Does the cost double? Explain your answer using an example.

Question 13 :

A television show has 19 episodes per season. a. Copy and complete the table. Seasons b. Write an expression for the number of episodes in n seasons.

Question 14 :

Write the phrase as an expression. Then evaluate when x = 5 and y = 20.

a) 3 less than the quotient of a number y and 4.

b)  The sum of a number x and 4 all divided by 3.

c)  6 more than the product of 8 and a number x.

d)  The quotient of 40 and the difference of a number y and 16.   

1. Answer :

=  2(5) +  3(4 + 3)

=  2(5) +  3(7)

=  10 +  21

 =  31

2. Answer :

=  2[5 + (30 ÷ 6)²]

=  2[5 + (5)²]

=  2[5 + 25]

=  2[30]

=  60

3. Answer :

=  [7(2) - 4] + [9 + 8(4)]

=  [14 - 4] + [9 + 32]

=  10 + 41

=  51

4. Answer :

=  [(4 ⋅ 3)² ⋅ 5]/(9 + 3)

=  [(7)² ⋅ 5]/(9 + 3)

=  [49 ⋅ 5]/(9 + 3)

=  245/12

5. Answer :

=  4(11 + 7) - 9 ⋅ 8

=  4(18) - 9 ⋅ 8

=  72 - 72

=  0

6. Answer :

=  288 ÷ [3(9 + 3)]

=  288 ÷ [3(12)]

=  288 ÷ [36]

=  8

7. Answer :

=  390 ÷  [5(7 + 6)]

=  390 ÷  [5(13)]

=  390 ÷  [45]

=  78/9

8. Answer :

=  (4 ⋅ 6² - 4² ⋅ 6) / 4 ⋅ 6

=  (4 ⋅ 36 - 16 ⋅ 6) / 4 ⋅ 6

=  (144 - 96) / 24

=  48 / 24

=  2

9. Answer :

=  (2 ⋅ 8² - 2² ⋅ 8)/(2 ⋅ 8)

=  (2 ⋅ 64 -  4 ⋅ 8)/16

=  (128 - 32)/16

=  96/16

=  6

10. Answer :

=  12(9 + 5) - 6 ⋅ 3

=  12(14) - 18

=  168 - 18

=  150

11. Answer :

Evaluate the expression a = 10, b = 9 and c = 4

a) 2a + 3

Applying the value of a, we get

= 2(10) + 3

= 20 + 3

= 23

b) 4c - 7.8

Applying the value of c, we get

= 4(4) - 7.8

= 16 - 7.8

= 8.2

c)  (24/b) + 8

Applying the value of b, we get

= (24/9) + 8

= (8/3) + 8

= (8 + 24)/3

= 32/3

d)  bc + 12.3

Applying b = 9 and c = 4

= 9(4) + 12.3

= 36 + 12.3

= 48.3

12. Answer :

The expression is 20a + 13c

a)  The expression represent cost 

• a - number of adults
• c - number of children

b. When a = 4 and c = 24

= 20(4) + 13(24)

= 80 + 312

= 392

c. When a = 2a and c = 2c, then

= 20(2a) + 13(2c)

= 40a + 26c ------(1)

2(20a + 13c) = 40a + 26c ------(2)

Yes it is doubled

13. Answer :

A television show has 19 episodes per season.

a. completing the table :

b. Let n be the number of seasons. Then number of episodes = 19 n.

14. Answer :

Write the phrase as an expression. Then evaluate when x = 5 and y = 20.

a) 3 less than the quotient of a number y and 4.

The quotient of a number y and 4 = y/4

3 less, then (y/4) - 3

Applying the value of y, we get

= (20/4) - 3

= 5 - 3

= 2

b)  The sum of a number x and 4 all divided by 3.

The sum of number x and 4 = x + 4

divided by 3, then (x + 4)/3

Applying the value of x, we get

= (5 + 4)/3

= 9/3

= 3

c)  6 more than the product of 8 and a number x.

The product of 8 and a number x = 8 + x

6 more than, then (8 + x)/6

Applying the value of x, we get

= (8 + 5)/6

= 13/6

d)  The quotient of 40 and the difference of a number y and 16.   

= (y - 16) / 40

= (20 - 16)/40

= 4/40

= 1/10

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