EVALUATE VARIABLE EXPRESSIONS INVOLVING INTEGERS

Example 1 :

Evaluate the expression for x = 2.

5 + x

Solution :

= 5 + x

Substitute x = 2.

= 5 + 2

= 7

Example 2 :

Evaluate the expression for x = -1.

-x + 5

Solution :

Substitute x = -1.

= -x + 5

= -(-1) + 5

= 1 + 5

= 6

Example 3 :

Evaluate the expression for p = 3.

p - 6

Solution :

= p - 6

Substitute p = 3.

= 3 - 6

= -3

Example 4 :

Evaluate the expression for r = -2.

-r + 5

Solution :

= -r + 5

Substitute r = -2.

= -(-2) + 5

= 2 + 5

= 7

Example 5 :

Evaluate the expression for m = 0.

m - 5

Solution :

= m - 5

Substitute m = 0.

 = 0 - 5

  = -5

Example 6 :

Evaluate the expression for t = -4.

5t - 3

Solution :

= 5t - 3

Substitute t = -4.

= 5(-4) - 3

  = -20 - 3

= -23

Example 7 :

Evaluate the expression for x = 5 and y = 6.

x + y - 9

Solution :

= x + y - 9

Substitute x = 5 and y = 6.

= 5(-4) - 3

  = -20 - 3

= -23

Example 8 :

Evaluate the expression for x = 2 and y = -3.

3x + 2y

Solution :

= 3x + 2y

Substitute x = 2 and y = -3.

= 3(2) + 2(-3)

= 6 - 6

= 0

Example 9 :

Evaluate the expression for m = -1 and n = -2.

-2m + 3n + 5

Solution :

= -2m + 3n + 5

Substitute m = -1 and n = -2.

= -2(-1) + 3(-2) + 5

= 2 - 5 + 5

= 2

Example 10 :

Evaluate the expression for p = 5 and q = 7.

(5/p) + (7/q)

Solution :

= (5/p) + (7/q)

Substitute p = 5 and q = 7.

= (5/5) + (7/7)

= 1 + 1

= 2

Example 11 :

Evaluate the expression for x = 5, y = 8 and z = 6.

(y² + z) ÷ x

Solution :

= (y² + x) ÷ x

Substitute x = 5, y = 8 and z = 6.

= (8² + 6) ÷ 5

= (64 + 6) ÷ 5

= 70 ÷ 5

= 14

Example 12 :

Evaluate the expression for p = 6, q = 5 and r = 4.

(pq - 28)² ÷ r

Solution :

(pq - 28)² ÷ r

Substitute p = 6, q = 5 and r = 4.

= [(6)(5) - 28]² ÷ 4

= (30 - 28)² ÷ 4

= 2² ÷ 4

= 4 ÷ 4

= 1

Example 13 :

Shay bought 4 packs of markers for $6 each and a box of colored chalk for $11. What was the total cost of the markers and chalk Shay bought?

a) $35   b)  $17    c) $50     d)  $68

Solution :

Number of packs of markers she has purchased = 4

Cost of each box of marker = $6

Cost of markers pack = 4(6)

= $24

Cost of box of colored chalk = $11

Total cost = 24 + 11

= $35

So, the total cost of markers and chalks is $35.

Example 14 :

There are 64 fourth graders and 86 fifth graders signed up for activities on field day. All the students will be grouped into 6 teams, with the same number of students on each team.

Solution :

Number of fourth graders = 64

Number of fifth graders = 86

Total number of students = 64 + 86

= 150

Number of teams = 6

Each group consists of = 150/6

= 25

So, in each group 25 students will be there.

Example 15 :

An artist poured 6.09 kilograms of orange sand and 14.26 kilograms of blue sand into a mixing container for a project. What was the total amount of sand the artist poured into the container in kilograms?

a) 21.16 kg     b)  14.95 kg     c) 20.25 kg    d)  20.35 kg

Solution :

Quantity of orange sand = 6.09 kg

Quantity of blue sand = 14.26 kg

Total amount of sand = 6.09 + 14.26

= 20.35 kg

Example 16 :

Rajesh bought 2 salads for $3.65 each and a sandwich for $4.35. He gave the clerk $15.00 to pay for the items. How much change should Rajesh have received in dollars and cents?

Solution :

Cost of 2 salads = 2(3.65) ==> $7.3

Cost of sandwich = $4.35

Amount given = $15

Change = 15 - (7.3 + 4.35)

= 15 - 11.65

= 3.35

So, the amount he receive as change is $3.35.

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