VARIABLES AND EXPRESSIONS WORKSHEET

Problem 1 to 4 : Give two ways to write each algebraic expression in words.

Problem 1 : 

y + 7

Problem 2 : 

⋅ p

Problem 3 : 

k - 5

Problem 4 : 

÷ 2

Problem 5 : 

Jacob reads 18 pages per hour. Write an expression for the number of pages Jacob reads in x hours. 

Problem 6 : 

John is 3 years younger than Michael, who is m years old.  Write an expression for John's age. 

Problem 7 : 

Neil runs a mile in 14 minutes. Write an expression for the number of miles that Neil runs in y minutes.  

Problem 8 : 

Lily is 7 cm taller than her sister, who is k cm tall. Write an expression for Lily's height in centimeters. 

Problem 9 : 

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

Problem 10 : 

Evaluate the following expression for y = 24 and z = 4. 

y/z

Problem 11 : 

Evaluate the following expression for x = 3 and y = 4. 

x2y + y

Problem 12 : 

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

(x + 2y)2 - 2x

Problem 13 : 

About twenty 15-ounce plastic drink bottles must be recycled to produce 1 square foot of carpet. 

(i) Write an expression for the number of bottles needed to make y square feet of carpet. 

(ii) Find the number of bottles needed to make 50, 120 and 224 square feet of carpet. 

Problem 14 : 

About five 2-meters cloths required to make a garment.

(i) Write an expression for the number of cloths needed to make g garments.  

(ii) Find the number of cloths needed to make 5, 12 and 25 garments. 

Answers

Problem 1 to 4 : Give two ways to write each algebraic expression in words.

Problem 1 : 

y + 7

Answer :

(i) The sum of y and 7

(ii) y increased by 7

Problem 2 : 

⋅ p

Answer :

(i) 3 times p

(ii) The product of 3 and p

Problem 3 : 

k - 5

Answer :

(i) The difference of k and 5

(ii) 5 less than k

Problem 4 : 

÷ 2

Answer :

(i) m divided by 2

(ii) The quotient of m and 5

Problem 5 : 

Jacob reads 18 pages per hour. Write an expression for the number of pages Jacob reads in x hours. 

Answer :

Think : x groups of 18 pages.

18 ⋅ x  or  18x

Problem 6 : 

John is 3 years younger than Michael, who is m years old.  Write an expression for John's age. 

Answer :

m represents Michael's age

Think : "younger than" means " less than".

John's age :

m - 2

Problem 7 : 

Neil runs a mile in 14 minutes. Write an expression for the number of miles that Neil runs in y minutes.  

Answer :

y represents the total time Neil runs

Think : How many groups of 14 are in y ? 

y/14

Problem 8 : 

Lily is 7 cm taller than her sister, who is k cm tall. Write an expression for Lily's height in centimeters. 

Answer :

k represents the height of Lily's sister 

Lily's height in centimeters : 

k + 7

Problem 9 : 

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

x + y

Answer :

=  x + y

Substitute 2 for x and 3 for y. 

=  2 + 3

=  5

Problem 10 : 

Evaluate the following expression for y = 24 and z = 4. 

y/z

Answer :

=  y/z

Substitute 24 for y and 4 for z. 

=  24/4

=  6

Problem 11 : 

Evaluate the following expression for x = 3 and y = 4. 

x2y + y

Answer :

=  x2y + y

Substitute 3 for x and 4 for y. 

=  32(4) + 4

Use PEMDAS. 

=  9(4) + 4

=  36 + 4

=  40

Problem 12 : 

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

(x + 2y)2 - 2x

Answer :

=  (x + 2y)2 - 2x

Substitute 5 for x and 3 for y. 

(5 + 2 ⋅ 3)2 - 2 ⋅ 5

Use PEMDAS. 

=  (5 + 6)2 - 10

=  112 - 10

=  121 - 10

=  111

Problem 13 : 

About twenty 15-ounce plastic drink bottles must be recycled to produce 1 square foot of carpet. 

(i) Write an expression for the number of bottles needed to make y square feet of carpet. 

(ii) Find the number of bottles needed to make 50, 120 and 224 square feet of carpet. 

Answer :

Part (i) :

Twenty bottles required to make 1 square foot of carpet. 

Number of bottles required to make y square feet of carpet :  

20y

Part (ii) :

Evaluate 20y for y = 50, 120 and 224.

20(50)  =  1000

20(120)  =  2400

20(224)  =  4480

To make 50 ft2 of carpet, 1000 bottles are needed.

To make 120 ft2 of carpet, 2400 bottles are needed.

To make 224 ft2 of carpet, 4480 bottles are needed.

Problem 14 : 

About five 2-meters cloths required to make a garment.

(i) Write an expression for the number of cloths needed to make g garments.  

(ii) Find the number of cloths needed to make 5, 12 and 25 garments. 

Answer :

Part (i) :

Five cloths required to make 1 garment.

Number of cloths required to make g garments :

5g

Part (ii) :

Evaluate 5g for g = 5, 12 and 25.

5(5)  =  25

5(12)  =  60

5(25)  =  125

To make 5 garments, 25 cloths are needed.

To make 12 garments, 60 cloths are needed.

To make 25 garments, 125 cloths are needed.

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