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1-2

Writing Algebraic Expressions

Warm Up

Problem of the Day

Lesson Presentation

Course 3

Warm Up Evaluate each expression for the given

values of the variables. Which operation

symbol goes with each word?

23

1. 9y ? 13 for y 4

18

2. 6n 2p for n 2 and p 3

1

3. 3x ? y for x 1 and y 2

4. Sum

?

5. Product

?

6. Quotient

?

7. Difference

Problem of the Day Find a pair of numbers that

fits the description. Their product is 221 and

their sum is 30.

13, 17

Learn to write algebraic expressions.

- a number plus 5

- add 5 to a number

n 5

- sum of a number and 5

- 5 more than a number

- a number increased by 5

- a number minus 11

- subtract 11 from a number

x ? 11

- difference of a number and 11

- 11 less than a number

- a number decreased by 11

- 3 times a number

- 3 multiplied by a number

3m

- product of 3 and a number

- a number divided by 7

- 7 divided into a number

- quotient of a number and 7

Additional Examples 1A and 1B Translating Word

Phrases into Math Expressions

Write an algebraic expression for each word

phrase.

A. the product of 8 and a number n

the product of 8 and n

8 n

8n

B. a number w decreased by 9

w decreased by 9

w 9

w 9

Additional Examples 1C and 1D Translating Word

Phrases into Math Expressions

Write an algebraic expression for each word

phrase.

C. 3 increased by the difference of p and 5

3 increased by the difference of p and 5

3 (p 5)

3 (p 5)

D. 24 decreased by the product of 6 and q

24 decreased by the product of 6 and q

24 (6 q)

24 6q

Try This Examples 1A and 1B

Write an algebraic expression for each word

phrase.

A. the sum of a number h and 88

the sum of h and 88

h 88

h 88

B. the quotient of a number f and 6

quotient of f and 6

f ? 6

Try This Examples 1C and 1D

Write an algebraic expression for each word

phrase.

C. add 7 to 3 multiplied by m

add 7 to 3 multiplied by m

7 (3 ? m)

7 3m

D. the difference of 5 and the product of 2 and r

the difference of 5 and the product of 2 and r

5 (2 r)

5 2r

To solve a word problem, you must first interpret

the action you need to perform and then choose

the correct operation for that action.

Combine

Add

How many all together?

Combine equal groups

How many all together?

Multiply

Separate

How many more? How many less?

Subtract

Separate into equal groups

How many equal groups?

Divide

Additional Example 2 Interpreting Which

Operation to Use in Word Problems

A. Jared worked for h hours at the pay rate of 5

each hour. Write an expression to determine how

much money Jared earned.

5h

Multiply 5 by h hours.

B. How much money will he earn if he works a

total of 18 hours?

5 18 90

Evaluate the expression for h 18.

Jared earned 90.

Try This Example 2

A. A taxi-cab driver charges a base fee of 2,

plus an additional 0.25 per mile. Write an

expression to determine the fare.

2 .25m

2 plus .25 per mile.

B. If a passenger needs to travel 12 miles, how

much money will they need to pay?

2 .25(12) 5

Evaluate the expression for m 12.

It will cost 5 to travel 12 miles.

Additional Example 3A Writing and Evaluating

Expressions in Word Problems

Write an algebraic expression to evaluate each

word problem.

A. Ahmed bought a new sweater for 27 plus sales

tax t. If the tax was 1.76, what was the total

cost of the sweater?

27.00 t

Combine 27 with t.

27.00 1.76 28.76

Evaluate for t 1.76.

The total cost of the sweater was 28.76.

Additional Example 3B Writing and Evaluating

Expressions in Word Problems

B. The cost to rent a banquet hall is 240. If

the cost will be shared equally among all of the

people who attend the event, how much will it

cost each person if 12, 15, 16 or 20 people

attend?

240 ? n

Separate the cost into n equal groups.

240 ? n

In dollars

Evaluate for n 12, 15, 16, and 20.

12 240 ? 12 20

15 240 ? 15 16

16 240 ? 16 15

20 240 ? 40 12

Additional Example 3C Writing and Evaluating

Expressions in Word Problems

C. An airplane was flying at an altitude of

20,000 feet when it began its descent at 900P.M.

After ten minutes, it had descended a feet. If

the plane descended 8500 feet during the ten

minutes, what was its altitude at 910?

20,000 f

Separate f feet from 20,000.

20,000 8500 11,500

Evaluate for f 8500.

The planes altitude at 910 was 11,500 feet.

Try This Example 3A

Write an algebraic expression and use it to

evaluate each word problem.

A. Taylor orders one pizza for dinner. The 16

pieces are to be divided equally among p people.

If she divides them equally among 4 people, how

many pieces can each person get?

Separate the pieces into p equal groups.

16 ? p

Evaluate for p 4.

16 ? 4 4

Each person gets 4 pieces.

Try This Example 3B

B. Gasoline costs 1.39 per n gallons. What will

the cost be for 10, 12, 14, and 15 gallons?

1.39 n

Combine n equal amounts of 1.39.

1.39n

In dollars

10 1.39 10 13.90

Evaluate for n 10, 12, 14, and 15.

12 1.39 12 16.68

14 1.39 14 19.46

15 1.39 15 20.85

Try This Example 3C

C. After Kyle took his road trip, his car had

39,857 miles on the odometer. Before the trip,

his odometer read m miles less than 39,857. If he

traveled 739 miles on the trip, what was the

mileage on his car before he started the trip?

39,857 m

Subtract m miles from 39,857.

Evaluate for m 739.

39,857 739 39,118

The mileage on his car before he started the trip

was 39,118 miles.

Lesson Quiz

Write an algebraic expression for each word

phrase. 1. 5 less than a number k 2. a number x

divided by 11 3. 4 times the sum of n and

5 Write an algebraic expression and used it to

solve the problem. 4. Karen buys n raffle

tickets for 0.50 each. If she buys 13 of them,

how much will they cost?

k 5

4(n 5)

0.50n 6.50

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