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Translating Words into Symbols
August 19, 2011
Translating Words into Symbols
Objective The student will be able to translate phrases into variable expressions.
Translating Words into Symbols
In order to solve problems using algebra, you must often translate phrases aboutnumbers into expressions containing variables.
As in any translation, you must know the vocabulary.
Vocabulary
Addition
The sum of 8 and x 8 + x
A number increased by 7 n + 7
5 more than a number n + 5
Vocabulary
Subtraction
The difference between a
number and 4 x 4
A number decreased by 8 n 8
5 less than a number n 5
6 minus a number 6 n
Vocabulary
Multiplication
The product of 4 and a number
4n
7 times a number 7n
One third of a number 1
3𝑥
Vocabulary
Division
The quotient of a number and 8
𝑛
8
A number divided by 10 𝑛
10
Example
Translate the following phrase into a variable expression:
3 less than half of x
half of x 1
2𝑥
three less than half of x 1
2𝑥 − 3
Example
Translate the following phrase into a variable expression:
half the difference between x and 3
the difference between x and 3
𝑥 − 3
half the difference between x and 3
1
2𝑥 − 3
More Vocabulary
Shorter
Then, the length of a board 7 cm shorter:
𝑙 − 7
Suppose the length of a board is l cm.
More Vocabulary
Longer
Then, the length of a board 6 cm longer:
𝑙 + 6
Suppose the length of a board is l cm.
Formulas
Formulas are often used in algebra. Formulas are equations that state rulesabout relationships. Here are four useful formulas:
Area of rectangle = length of rectangle width of rectangle 𝐴 = 𝑙𝑤
Perimeter of rectangle = (2 length) + (2 width) 𝑃 = 2𝑙 + 2𝑤
Distance traveled = rate time traveled 𝐷 = 𝑟𝑡
Cost = number of items price per item 𝐶 = 𝑛𝑝
Example
Find the area of a rectangle with length 10 and width w.
Area = length width
Area = 10 w
Area = 10𝑤
Example
Find the perimeter of a rectangle with length 10 and width w.
Perimeter = (2 length) + (2 width)
Perimeter = 2 ∙ 10 + 2 ∙ 𝑤
Perimeter = 20 + 2𝑤
Example
You and your friends buy 2 pizzas at p dollars each and 4 salads at s dollars each. How much do you and your friends spend?
Cost = number price
Total cost = 2𝑝 + 4𝑠
Pizza cost = 2p Salad cost = 4s
You spend 2𝑝 + 4𝑠
Example
You travel (h + ½) hours at 80 km/h. How far do you travel?
Distance = rate time
Distance = 80 ℎ +1
2
You travel 80 ℎ +1
2 km
Class work
Oral Exercises
P 16: 1-20
Homework
p 16: 1-41 odd, p 18: 42-52 even, p 18: Mixed Review