Many recycled products are used in a "green built" house, including carpet made from recycled plastic drink bottles. We will be able to determine how many square feet of carpet can be made from a certain number of plastic drink bottles by using variables, constants and expression.
A variable is a letter or symbol used to represent a value that can change.
A constant is a value that does does not change.
A numerical expression may contain only constants and/or operations.
A algebraic expression may contain variables, constants and/or operations.
To be successful in Math, we may have to translate between algebraic expressions and words.
Let us see some of the ways to write mathematical operations with words.
Plus, sum, increased by -----> +
Minus, difference, less than -----> -
Times, product, equal groups of -----> x
Divided by, quotient -----> ÷
Give two ways to write each algebraic expression in words.
Example 1 :
y + 7
Solution :
(i) The sum of y and 7
(ii) y increased by 7
Example 2 :
3 ⋅ p
Solution :
(i) 3 times p
(ii) The product of 3 and p
Example 3 :
k - 5
Solution :
(i) The difference of k and 5
(ii) 5 less than k
Example 4 :
m ÷ 2
Solution :
(i) m divided by 2
(ii) The quotient of m and 5
To translate words into algebraic expressions, look for words that indicate the action that is taking place.
Put together, combine -----> Add
Find how much more or less -----> Subtract
Put together equal groups -----> Multiply
Separate into equal groups -----> Divide
Example 5 :
Jacob reads 18 pages per hour. Write an expression for the number of pages Jacob reads in x hours.
Solution :
Think : x groups of 18 pages.
18 ⋅ x or 18x
Example 6 :
John is 3 years younger than Michael, who is m years old. Write an expression for John's age.
Solution :
m represents Michael's age
Think : "younger than" means " less than".
John's age :
m - 2
Example 7 :
Neil runs a mile in 14 minutes. Write an expression for the number of miles that Neil runs in y minutes.
Solution :
y represents the total time Neil runs
Think : How many groups of 14 are in y ?
y/14
Example 8 :
Lily is 7 cm taller than her sister, who is k cm tall. Write an expression for Lily's height in centimeters.
Solution :
k represents the height of Lily's sister
Lily's height in centimeters :
k + 7
Example 9 :
Evaluate the following expression for x = 2 and y = 3.
x + y
Solution :
= x + y
Substitute 2 for x and 3 for y.
= 2 + 3
= 5
Example 10 :
Evaluate the following expression for y = 24 and z = 4.
y/z
Solution :
= y/z
Substitute 24 for y and 4 for z.
= 24/4
= 6
Example 11 :
Evaluate the following expression for x = 3 and y = 4.
x^{2}y + y
Solution :
= x^{2}y + y
Substitute 3 for x and 4 for y.
= 3^{2}(4) + 4
Use PEMDAS.
= 9(4) + 4
= 36 + 4
= 40
Example 12 :
Evaluate the following expression for x = 5 and y = 3.
(x + 2y)^{2} - 2x
Solution :
= (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
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