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.
x^{2}y + 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.
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.
x^{2}y + y
Answer :
= x^{2}y + y
Substitute 3 for x and 4 for y.
= 3^{2}(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
= 11^{2} - 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 ft^{2} of carpet, 1000 bottles are needed.
To make 120 ft^{2} of carpet, 2400 bottles are needed.
To make 224 ft^{2} 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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