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Written practice
Lesson 15
Using the Distributive Property to
Simplify Expressions
1.
-7(-8 +3)
2. Simplify
5(-3 – 6)
3. Evaluate
10,000
4.
Solve
c=
25
5.
In a shipment of 800 eggs, the 2
probability of an egg breaking is 25 .
How many are likely to be broken in
the shipment?
Justify the answer.
6. The digits 0, 1, 2, 3, 4, 5, 6,
7, 8, 9 are written on cards
that are shuffled and placed
face down in a stack. One
card is selected at random.
What is the probability that
the digit is odd and greater
than 5?
7. There are 10 balls in a bucket
numbered 1, 1, 2, 3, 4, 4, 4, 5,
6, and 6. A single ball is
randomly chosen from the
bucket. What is the probability
of drawing the ball with a
number less than 7? Explain.
8. Simplify the expression
-5(x + 6)
Which is correct?
A. -5 + x - 11
B. -5x +1
C. -5x + 30
D. -5x - 30
9. Find the value of y in the
equation
18 – x = y
If x = -4
10. The water level of the
reservoir in Austin, Texas, was
3 feet below normal. After a
heavy rain storm, the water
level increased to 5 feet above
normal. How much did the rain
storm change the water level?
11. Two students evaluated a
numeric expression. Which
student is correct. Explain the
error.
See next slide.
11. Which student is correct?
Explain.
Student A
Student B
-8(-5 + 14)
=40 – 112
=-72
-8(-5 + 14)
=-13 + 6
=-7
12.
Evaluate the expression
-8(9 – 15)
Using the Distributive Property.
13. The county surveyed a piece of
property and divided it into equal-sized
lots. Use the diagram to write an
expression that requires the Distributive
Property to evaluate it. Evaluate the
expression to find the total number of
lots on the property.
6
4
7
14.
True or false.
m+0=m
Justify your answer using the
properties.
15. Convert 3.4 yd3 to ft3.
16. Travis plans to divide his
collection of baseball cards among
8 grandchildren. He will give each
child the same number of cards.
Each card is worth $14. Write an
expression to represent the value
of each child’s cards. Let c equal
the total number of cards.
17. Kennedy’s teacher asked her to
plan the budget for the class party.
Kennedy began by writing the
expression g = b + 7 to represent
the number of girls equals the
number of boys plus seven. Each
girl will need $6. Write and
simplify an algebraic expression
that uses the Distributive Property
to show the total cost for the girls.
18.
If a number cube is rolled, what
is the probability of it landing on
the number 5 or 6?
19. Two students evaluated the
expression
36  z for z  13
Which student is correct. Explain
the error.
See next slide.
19. Which student is correct?
Explain.
Student A
Student B
36  z

36  13
 49
7
36  z

36  z
 6  13
 19
20. The expression 6 ∙ 2 ∙ 4 would
be simplified from left to right
using the order of operations.
What property would allow this
expression to be simplified from
right to left?
21.
Susan invests the same amount of
money in each of 7 stocks. In one
year, her money increased 8 times.
The value of her investment is
represented by the expression 7x ∙ 8.
Show two methods to simplify the
expression and justify each step
using properties.
22. Rickie is 3 ¾ years older than
Raymond. Raymond is 2 ½ years
younger than Ryan. If Ryan is 14 ¼
years old, how old is Rickie?
23.
Write the procedure for evaluating the
expression
16f 2 g 3 – 4f 8 + 12
For f = 3 and g = 5
24.
Use the number line to model
x – 8 when x = -6.
25. In astronomy, brightness is given
in a value called magnitude. A -2
magnitude star is 2.512 times
brighter than a -1 magnitude star,
a -3 magnitude star is 2.512 times
brighter than a -2 magnitude star,
and so on. If Sirius is magnitude 1.5 and the full moon is
magnitude -12.5, how much
brighter is the full moon?
26. Student A and Student B each
solved the absolute-value problem
as shown below.
Which student is correct. Explain
the error.
See next slide.
26. Which student is correct?
Explain.
Student A
Student B
-|12 – 15|
= -|-3|
= -(3)
= -3
-|12 – 15|
= -|-3|
=(+3)
=3
27. Find the value of y in the
equation when x = -3.
x - |x – 2| = y
28. When simplified, will the
expression 3 +
or negative?
2
3
+ |-5| be positive
29. Thomas spun a game spinner and
recorded the results in the table below.
Outcome
Frequency
Red
3
Blue
5
Yellow
9
Green
8
Use the table to find the experimental
probability of each event. Express each
probability as a fraction and as a percent.
a. Landing on red
b. Landing on green
c. Not landing on green
30. What is the perimeter of a square
with an area of 121 sq in?
x
x
Area = 121 in 2
x
x