How do you read and write equivalent expressions using variables and exponents?
1.3 Write expressions You will translate verbal phrases into expressions How do you write an...
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Warm-Up Exercises 1.3 Write expressions • You will translate verbal phrases into expressions • How do you write an expression to represent a real-world situation
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Transcript of 1.3 Write expressions You will translate verbal phrases into expressions How do you write an...
1.3 Write expressions
• You will translate verbal phrases into expressions
• How do you write an expression to represent a real-world situation
Warm-Up ExercisesEXAMPLE 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
Warm-Up ExercisesGUIDED 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
Warm-Up Exercises
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.
Warm-Up ExercisesEXAMPLE 2 Write an expression
ANSWER
The expression 8 – l represents the length (in feet) of the remaining piece.
Warm-Up Exercises
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
Warm-Up ExercisesEXAMPLE 3 Use a verbal model to write an expression
ANSWER
An expression that represents each person’s share (in dollars) is .a
6
Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3
WHAT IF? In Example 2, suppose that you cut the original ribbon into p pieces of equal length. Write an expression that represents the length (in feet) of each piece.
ANSWER
lp
Warm-Up ExercisesGUIDED PRACTICE for Examples 2 and 3
WHAT IF? In Example 3, suppose that each of the 6 workers contributes an equal amount for an after-work celebration. Write an expression that represents the total amount (in dollars) contributed.
ANSWER
6d, where d represents the amount contributed by each worker.
Warm-Up ExercisesEXAMPLE 4 Find a unit rate
A car travels 120 miles in 2 hours. Find the unit rate in feet per second.
The unit rate is 88 feet per second.
ANSWER
Warm-Up Exercises
SOLUTION
EXAMPLE 5 Solve a multi-step problem
TrainingFor a training program, each day you run a given distance and then walk to cool down. One day you run 2 miles and then walk for 20 minutes at a rate of 0.1 mile per 100 seconds. What total distance do you cover?
STEP 1 Convert your walking rate to miles per minute.
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
Use unit analysis to check that the expression 2 + 0.06m is reasonable.
Because the units are miles, the expression is reasonable.
STEP 2Write a verbal model and then an expression.Let m be the number of minutes you walk.
Warm-Up ExercisesEXAMPLE 5 Solve a multi-step problem
Evaluate the expression when m = 20.
2 + 0.06(20) = 3.2
ANSWER
You cover a total distance of 3.2 miles.
STEP 3
Warm-Up ExercisesGUIDED PRACTICE for Examples 4 and 5
4. WHAT IF? In Example 1, suppose tomorrow you run 3 miles then walk for 15 minutes at a rate of 0.1 mile per 90 seconds. What total distance will you cover?
ANSWER
You will cover a total distance of 4 miles.
Warm-Up ExercisesDaily Homework Quiz
1. Write an expression for the situation: The number of miles left in a 425-mile trip after m miles have been traveled.
ANSWER 425 – m
ANSWER 3 figurines per box
2. Find the unit rate for the rate 18 figurines
6 boxes
Warm-Up ExercisesDaily Homework Quiz
ANSWER 5g + 12, where g is the number of games; $42
3. A video store charges $5 per game rental plus $12 to rent the game system. Write an expression for renting the game system and a number of games. Then find the total cost if you rent 6 games.
• You will translate verbal phrases into expressions
• How do you write an expression to represent a real-world situation
• Certain words and phrases indicate the operation(s) to be used in a real-world situation.
• A verbal model can be used to write an expression that models a real-world situation.
• Use unit analysis to check that the expression is reasonable.
Translate the verbal phrase in the problem into operations and variables, create a verbal model, and then translate the verbal model into an expression.
