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