divide. evaluate power. 27 3 2 2 – 3 = 27 9 2 – 3 example 1 27 9 2 – 3 = 3 2 – 3 3 2 – 3 =...
Post on 14-Dec-2015
225 Views
Preview:
TRANSCRIPT
Divide.
Evaluate power.27 32 2 – 3 = 27 9 2 – 3
EXAMPLE 1
27 9 2 – 3 = 3 2 – 3
3 2 – 3 = 6 – 3 Multiply.
Evaluate expressions
Multiply and divide from left to right.STEP 3
Evaluate the expression 27 32 2 3.–
There are no grouping symbols, so go to Step 2.STEP 1
Evaluate powers.STEP 2
STEP 4Add and subtract from left to right.
6 – 3 = 3
EXAMPLE 1
Subtract.
ANSWER
The value of the expression 27 32 2 – 3 is 3.
Evaluate expressions
GUIDED PRACTICE for Example 1
1. Evaluate the expression 20 – 42
ANSWER
1. 4
2. Evaluate the expression 2 32 + 4
ANSWER
2. 22
3. Evaluate the expression 32 23 + 6
ANSWER
3. 10
GUIDED PRACTICE for Example 1
4. Evaluate the expression 15 + 62 – 4
ANSWER
4. 47
24 – (9 + 1)
= 2[9]
EXAMPLE 2 Evaluate expressions with grouping symbols
Evaluate the expression.
a. 7(13 – 8) == 35
Subtract within parentheses.
Multiply.
b. 24 – (32 + 1) = Evaluate power.
= 24 – 10 Add within parentheses.
= 14 Subtract.
c. 2[30 – (8 + 13)] = Add within parentheses.
Subtract within brackets.
= 18 Multiply.
7(5)
2[30 – 21]
EXAMPLE 3 Evaluate an algebraic expression
Evaluate the expression when x = 4.
9x3(x + 2)
Substitute 4 for x.
Add within parentheses.
1836= Multiply.
= 2 Divide.
= 3(4 + 2) 9 4
3 6 9 4
=
GUIDED PRACTICE for Examples 2 and 3
Evaluate the expression.
5. 4(3 + 9) = 48
6. 3(8 – 22) = 12
7. 2[( 9 + 3) 4 ] = 6
GUIDED PRACTICE for Examples 2 and 3
Evaluate the expression when y = 8.
= 61y2 – 38.
= 312 – y – 19.
= 910y + 1 y + 1
10.
Standardized Test Practice
EXAMPLE 4
Standardized Test Practice
EXAMPLE 4
SOLUTION
Substitute 1.25 for j and 2 for s.
= 12(3.75 + 4) + 30 Multiply withinparentheses.
= 93 + 30 Multiply.
= 123 Add.
The sponsor’s cost is $123.The correct answer is B. .A B C D
ANSWER
= 12(7.75) + 30 Add within parentheses.
= 12(3 1.25 + 2 2) + 3012(3j +2s) + 30
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
GUIDED 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
GUIDED 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.
EXAMPLE 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
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.
EXAMPLE 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.
EXAMPLE 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
top related