Course 3

1-2 Algebraic Expressions

Course 1

1-2 Algebraic Expressions

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 3

1-2 Algebraic Expressions

Warm UpEvaluate each expression for the given values of the variables.

Which operation symbol goes with each word?

2318

1

+

4. Sum

5. Product

6. Quotient7. Difference

1. 9y 13 for y = 42. 6n + 2p for n = 2 and p = 3

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

Course 3

1-2 Algebraic Expressions

Problem of the Day

Find a pair of numbers that fits the description. Their product is 221 and their sum is 30.

13, 17

Course 3

1-2 Algebraic Expressions

Learn to translate between algebraic expressions and word phrases.

Course 3

1-2 Algebraic Expressions

• a number plus 5• add 5 to a number• 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• 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• product of 3 and a number

• a number divided by 7• 7 divided into a number• quotient of a number and 7

++

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Word Phrases Expression

n + 5

x 11

3m

or a 7a7

Course 3

1-2 Algebraic Expressions

Write an algebraic expression for each word phrase.

Additional Examples 1: Translating Word Phrases into Math Expressions

A. 9 less than a number w 9 less than a number ww – 9w – 9

B. 3 increased by the difference of p and 53 increased by the difference of p and 53 + (p – 5)3 + p – 5

Course 3

1-2 Algebraic Expressions

Write an algebraic expression for each word phrase.

Check It Out: Example 1

A. the sum of a number h and 88 minus 4 the sum of h and 88 minus 4h + 88 – 4h + 88 – 4

B. the quotient of a number f and 6quotient of f and 6f 6

f6

Course 3

1-2 Algebraic Expressions

Write a word phrase for the algebraic expression 9 – 3c.

Additional Example 2: Translating Math Expressions into Word Phrases

9 – 3c

9 – 3 • c

9 minus the product of 3 and c

9 minus the product of 3 and c.

Course 3

1-2 Algebraic Expressions

Check It Out: Example 2

Write a word phrase for the algebraic expression 7 + 19b.

7 + 19b

7 + 19 • b

7 plus the product of 19 and b

7 plus the product of 19 and b.

Course 3

1-2 Algebraic Expressions

To solve a word problem, you must first interpret the action you need to perform and then choose the correct operation for that action.

Separate into equal groups

Multiply

How many more? How many less?

Combine

Combine equal groups

Separate

Add

Subtract

Divide

Action Operation Possible Question Clues

How many all together?

How many all together?

How many equal groups?

Course 3

1-2 Algebraic Expressions

A restaurant leased its banquet hall for a function. The cost was $10 per person. Write an algebraic expression to evaluate what the cost would be if 20, 21, 22, or 23 people attended the function

Additional Example 3: Writing and Evaluating Expressions in Word Problems

$10 dollars • n Combine n equal amounts of $10. $10n In dollars

20 $10 • 20 $20021 $10 • 21 $21022 $10 • 22 $22023 $10 • 23 $230

n $10 • n CostEvaluate for n = 20, 21, 22, and 23.

Course 3

1-2 Algebraic Expressions

Gasoline costs $1.99 per n gallons. What will the cost be for 10, 12, 14, and 15 gallons?

Check It Out: Example 3

$1.99 • n Combine n equal amounts of $1.99. $1.99n In dollars

10 $1.99 • 10 $19.9012 $1.99 • 12 $23.8814 $1.99 • 14 $27.8615 $1.99 • 15 $29.85

n $1.99 • n Cost

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

Course 3

1-2 Algebraic Expressions

Write a word problem that can be evaluated by the algebraic expression 27 + t, and evaluate the expression for t = 1.76.

Additional Example 4: Writing a Word Problem from a Math Expression

Possible Answer:

Amed 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 + t

27 + 1.76 = 28.76 Substitute 1.76 for t.

The total cost of the sweater was $28.76.

Course 3

1-2 Algebraic Expressions

Write a word problem that can be evaluated by the algebraic expression 43 - d, and evaluate the expression for d = 10.24.

Check It Out: Example 4

Possible Answer: Tina bought a new jacket for $43 minus a store credit. If the store credit was $10.24 , what was the total cost of the jacket?

43 + d

43 – 10.24 = 33.24 Substitute 10.24 for t.

The total cost of the jacket was $33.24.

Course 3

1-2 Algebraic Expressions

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 to evaluate the word 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

x11