VARIABLES AND EXPRESSIONS WORKSHEET

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

Problem 1 : 

y + 7

Problem 2 : 

3 ⋅ p

Problem 3 : 

k - 5

Problem 4 : 

m ÷ 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 : 

3 ⋅ 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 : 

m ÷ 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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