translating words into symbols - mcclenahan
TRANSCRIPT
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Translating Words into Symbols
August 19, 2011
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Translating Words into Symbols
Objective The student will be able to translate phrases into variable expressions.
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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.
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Vocabulary
Addition
The sum of 8 and x 8 + x
A number increased by 7 n + 7
5 more than a number n + 5
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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
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Vocabulary
Multiplication
The product of 4 and a number
4n
7 times a number 7n
One third of a number 1
3𝑥
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Vocabulary
Division
The quotient of a number and 8
𝑛
8
A number divided by 10 𝑛
10
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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
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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
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More Vocabulary
Shorter
Then, the length of a board 7 cm shorter:
𝑙 − 7
Suppose the length of a board is l cm.
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More Vocabulary
Longer
Then, the length of a board 6 cm longer:
𝑙 + 6
Suppose the length of a board is l cm.
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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
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Example
Find the area of a rectangle with length 10 and width w.
Area = length width
Area = 10 w
Area = 10𝑤
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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
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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
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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
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Class work
Oral Exercises
P 16: 1-20
Homework
p 16: 1-41 odd, p 18: 42-52 even, p 18: Mixed Review