1.3 writing expressions part 1
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Transcript of 1.3 writing expressions part 1
Lesson 1.3, For use with pages 14-20
1. Evaluate 2[54 (42 + 2)].
ANSWER 6
ANSWER 3
2. Evaluate when x = 3.5xx + 2
Write Expressions
Section 1.3
P. 15-20
• In this section you will learn how to translate verbal phrases into algebraic expressions.
Vocabulary
• Verbal Model
• Rate
• Unit Rate
Describes a real-world situation using words as labels and using math symbols to relate the words.
A rate is a fraction that compares two quantities of different units
5 pencils for $1.25 is a rate
When the fraction’s denominator is one, it is a unit rate. (per)
25 cents per pencil 25/1
Verbal Phrase
• Addition:• The ______ of 3 and a number n• 3 + n
• The number x _______ 10
• X + 10
Verbal Phrase
• Subtraction:• The __________ of 7 and the number n.• 7 – n• Twelve ______ than a number x.• X – 12
• Order is very important when writing a subtraction expression. Why?
Verbal Phrase
• Multiplication:• Five ______ a number y• 5y• The ________ of 2 and the number x• 2x
• The number always comes BEFORE the variable when a product is indicated.
Verbal Phrase
• Division:• The ________ of 6 and a number w• 6 / w
• Eight ________ into a number y• y / 8Order is important when writing division
expressions. Why?
EXAMPLE 1 Translate verbal phrases into expressions
Verbal Phrase Expression
a. 4 less than the quantity 6 times a number n
b. 3 times the sum of 7 and a number y
c. The difference of 22 and the square of a number m
6n – 4
3(7 + y)
22 – m2
GUIDED PRACTICE for Example 1
1. Translate the phrase “the quotient when the quantity 10 plus a number x is divided by 2” into an expression.
ANSWER
1. Expression 10 + x2
SOLUTION
Cutting A Ribbon
EXAMPLE 2 Write an expression
A piece of ribbon l feet long is cut from a ribbon 8 feet long. Write an expression for the length (in feet) of the remaining piece.
Draw a diagram and use a specific case to help you write the expression.Suppose the piece cut is 2 feet long.
Suppose the piece cut is L feet long.
The remaining piece is(8 – 2) feet long.
The remaining piece is(8 – l) feet long.
EXAMPLE 2 Write an expression
ANSWER
The expression 8 – l represents the length (in feet) of the remaining piece.
Write a verbal model.
SOLUTION
You work with 5 other people at an ice cream stand. All the workers put their tips into a jar and share the amount in the jar equally at the end of the day. Write an expression for each person’s share (in dollars) of the tips.
Tips
EXAMPLE 3 Use a verbal model to write an expression
Translate the verbal model into an algebraic expression. Let a represent the amount (in dollars) in the jar.
STEP 1
STEP 2Amount
in jarNumber
of people
a 6
EXAMPLE 3 Use a verbal model to write an expression
ANSWER
An expression that represents each person’s share (in dollars) is a
6
EXAMPLE 4 Find a unit rate
A car travels 110 miles in 2 hours. Find the unit rate.
110 miles 2 hours = 1 hour
55 miles2 hours 2
110 miles 2 =
The unit rate is 55 miles per hour, or 55 mi/h
ANSWER
• Assignment: P. 18 1-28• Most answers today will be short
answers, with little work