Exam III Review: Chapters 7-9
What You Need to Know
Chapter 7
 conversions between decimals, fractions and percents
7.1 Decimals and Place Value

place value: writing decimals in expanded form

rounding decimals to a certain place value

ordering of decimals
7.2 Operations with Decimals

addition and subtraction, multiplication and division
(where does the decimal point go?)

recognizing scientific notation
7.3 Ratios and Proportions
 identify ratios given information about a distribution
 solving proportions using cross multiplication
 solving proportion word problems
7.4 Percents
 definition of percent
 finding X% of Y
 solving percent word problems
Chapter 8 Integers

Understanding that integers are the whole numbers with their negatives.

Models for integer addition: measurement model and set model (jar model)

New approach for subtraction.

Knowing rules for integer multiplication.
Chapter 9 Rationals and Reals

understanding that rationals are fractions where the numerator and denominator
can be negative (integers).

understanding that all numbers are real, but that many of them aren’t rational –
they can’t be described by a fraction
Exam III Review: Chapters 7-9
Study Guide Practice Questions
Chapter 7
1.
CONVERSIONS BETWEEN DECIMALS, FRACTIONS AND PERCENTS
Convert from a decimal to a fraction:
Convert from a decimal to a percent:
a) 0.051
d) 0.37
b) 82.19
e) 0.051
c) 0.2 (a longer problem, show work)
f) 250
Convert from a percent to a decimal:
Convert from a percent to a fraction:
g) 89%
j) 11%
h) 110%
k) 10.29%
i) 0.3%
l) 100%
Convert from a fraction to a decimal:
Convert from a fraction to a percent:
m)
32
100
p)
321
100
n)
3
5
q)
2
5
o)
1
6
r)
1
3
7.1 Decimals and Place Value
2. WRITE THESE DECIMALS IN EXPANDED FORM.
a) 0.051
b) 82.19
c) 4.001
3. ROUND THESE DECIMALS TO THE SPECIFIED PLACE VALUE.
a) Round 8.575 to the nearest tenth.
b) Round 8.549 to the nearest hundreth.
c) Round 8.549 to the nearest tenth.
4. ARRANGE THE FOLLOWING NUMBERS IN ORDER FROM SMALLEST TO LARGEST.
a) 0.73, 0.037, 0.37
b) 305.049, 305.094, 305.001
c) 22.01, 23.9, 23.11
5. MODELS OF DECIMALS USING HUNDREDS SQUARES
Assume that one Hundreds Square equals a
whole:
= whole
Model 2.57 using hundreds Square by shading the Hundreds Squares below.
How many tenths are in 2.57? _________
How many hundredths are in 2.57? _________
How many thousandths are in 2.57? _________
7.2 Operations with Decimals
6. COMPUTE THE FOLLOWING, SHOWING YOUR WORK.
a) 48.62 + 5.009
b) 10.33 − 0.72
c) 48.6 × 52.07
d) 2.3  0.4
7.3 Ratios and Proportions
IDENTIFY RATIOS GIVEN INFORMATION ABOUT A DISTRIBUTION
7. Sandra collected 15 bugs from her garden. 8 of them were black beetles, 4 of
them were black spiders and 3 of them were red ants. Ants and beetles are insects,
but spiders are not.
a. What was the ratio of insects to non-insects of the bugs she found?
b. What was the ratio of black bugs to red bugs?
c. What was the ratio of all bugs to spiders?
SOLVING PROPORTIONS USING CROSS MULTIPLICATION
8. Solve the following proportions, showing your intermediate steps:
a.
x 2

35 7
b.
45 30

100 x
SOLVING PROPORTION WORD PROBLEMS
9. If Jack needs 2 ½ pints of cream to make a dessert. How many pints will he need
to make 3 desserts?
10. On a map, 1/3 inch equals 15 miles. The distance between two towns on a map is
3 2/3 inches. How many miles are actually between the two towns?
11. 10,000 silkworms make one pound of silk. If there are 16 ounces in a pound, how
many silkworms are needed to make one ounce of silk?
7.4 Percents
12. What is the definition of a percent?
13. Finding X% of Y.
a. Find 23% of 80.
b. Find 700% of 5.
c. Find 1% of 100.
14. 15 of the people in the survey used ACME brand laundry detergent. If 15% of
people used the ACME brand, how many people were questioned in the survey?
15. Rachel bought a dress that originally cost $125, but was marked down by 60%.
How much did she pay for the dress?
16. Henry won 10 of his last 28 games. What percents of his last 30 games has he
won?
Chapter 8 Integers
UNDERSTANDING THAT INTEGERS ARE THE WHOLE NUMBERS WITH THEIR NEGATIVES.
17. Circle all of the numbers below that are integers.
55
6
5.5
-6
-5
2.2
MODELING ADDITION OF INTEGERS
18. Model the following sums using (i) measurement and (ii) set models for integer
addition.
a. -5 + 4
b. -4 + 5
c. -2 − -3
NEW APPROACH FOR SUBTRACTION
19. Compute the following differences using the ‘add the opposite’ approach for
subtraction.
a. -5 − 4
b. 3 − -2
c. 3 − -3
20. Identify which subtraction approach is being applied to compute 5−3=2.
a. I had 5 apples, John took 3, and then I had 2 left.
b. 3 + ? = 5
c. 5 − 3 = 5+(-3) = 2
KNOWING RULES FOR INTEGER MULTIPLICATION
21. Compute the following products.
a. -5×3
b. -5×-30
c. -1×-2×-3×-4
d. -1×2×-3×4
Chapter 9 Rationals and Reals
UNDERSTANDING THAT RATIONALS ARE FRACTIONS (OF INTEGERS)
22. Circle all of the numbers below that are rational numbers.

6.3
2
2

5
2.2
23. Give examples of 3 real numbers that are not rational.
24. Show how you can use the operation of addition, subtraction, multiplication or
division to make a rational number from an irrational number. You can use other
numbers in your steps.
Example: Multiplication
×0 = 0
Here,  is irrational, but when you multiply it by 0 you get the rational number 0.