CASA Math Study Sheet
Standard 9: Number and Quantity
 Real Numbers – Both rational and irrational numbers are real
o Rational Numbers – Can be expressed as a fraction of two integers. When divided out,
has a repeating or terminating decimal. Can be ordered on a number line.
 Integers – Numbers without fractions, can be positive or negative
 Whole Numbers – Numbers without fractions, positive
o Irrational Numbers – Cannot be expressed as a fraction of two integers. They have nonterminating and non-repeating decimals.
Write each rational number as a fraction. Represent the fractions on the number line:
1. 0.6
2. .009
3. 1.79
Write each rational number in decimal form. Represent the decimals on the number line:
1. 7/100
2. 59/10
3. 99/1000
Represent each irrational number on the number line:
1. π = 3.141592654…
2.
= 1.414213562…
Plot the following points on the coordinate plane. Then, state in which quadrant the point can be
found.
1. (1.2,-6); Quadrant _______
2. (-3/4, -4); Quadrant ______
3. (-5.4,6); Quadrant _______
4. (3.007, 5.42); Quadrant ______
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CASA Math Study Sheet
Standard 9: Number and Quantity
Use a factor tree to find the prime factors of the following whole numbers.
1. 48
2. 74
3. 81
4
5. 56
6. 21
112
Least Common Multiple (LCM): The smallest multiple that is common to each number.
Find the least common multiple of each set of whole numbers:
1. 2
7
8
2. 3
6
15
3. 7
9
12
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CASA Math Study Sheet
Standard 9: Number and Quantity
Find a common denominator to simplify the expression.
1.
3
2.
11
3.
7
4
12
9
+
1
+ +
5
+
7
10
1
3
4
+ −
6
8
6
1
2
Solve the following multistep equations.
1. 2(v-7) = 4
2.
18
𝑐𝑐
=3
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CASA Math Study Sheet
Standard 9: Number and Quantity
3.
𝑏𝑏+7
3
=3
Write an equation that represents the multi-step word problem and solve.
1. Gina earns $19 per hour. She worked 2 hours on Friday, 7 hours on Saturday, and 7 hours on
Sunday. How much money did Gina earn in all on Friday, Saturday, and Sunday?
2. Garrett bought 5 packs of red bouncy balls, 10 packs of yellow bouncy balls, and 4 packs of
green bouncy balls. There were 5 bouncy balls in each red package, 7 bouncy balls in each
yellow package, and 2 balls in each green. How many bouncy balls did Garrett buy in all?
3. There are 29 bicycles and 23 tricycles in the storage area at Jonah's apartment building. Each
bicycle has 2 wheels and each tricycle has 3 wheels. How many wheels are there in all?
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CASA Math Study Sheet
Standard 9: Number and Quantity
Definitions:
 Ratio – Relationship between two quantities. For example, if a child has six black marbles and
one yellow marble, the ratio of black to yellow marbles is 6 to 1. Can be expressed as:
o 6/1
o 6 to 1
o 6:1
 Percent – The specified amount of parts per every hundred.
 Proportion – A part in relation to a whole. Proportions say that two ratios are equal. From the
marble example above. A second bag of marbles containing 18 black marbles is directly
proportional to the example above. How many yellow marbles does the second bag contain?
o 6/1=18/3
Solve the following word problems relating to percents, ratios, and proportions.
1. Mason used 15 centimeters of tape to wrap 5 presents. How many presents did Mason wrap if
he used 27 centimeters of tape? Assume the relationship is directly proportional.
2. Vera prepared 30 kilograms of dough after working 6 hours. How much dough did Vera prepare
if she worked for 9 hours? Assume the relationship is directly proportional.
3. 2 students are going on a field trip and 35 students are staying at school. What is the ratio of the
number of students who are staying at school to the number of students who are going on the
field trip?
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CASA Math Study Sheet
Standard 9: Number and Quantity
4. A fruit basket contains 12 red apples and 1 green apple. What is the ratio of the number of
green apples to the number of red apples?
5. The supermarket has 38 aisles. 14 of the aisles are empty. What percentage of the aisles are
empty?
6. Zach took a math quiz last week. He got 24 out of 80 problems correct. What percentage did
Zach get incorrect?
7. Elizabeth took a math quiz last week. There were 90 problems on the quiz and Elizabeth
answered 40% of them correctly. How many problems did Elizabeth get correct?
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CASA Math Study Sheet
Standard 9: Number and Quantity
Write an equation to represent the following percent of change word problems and solve.
1. Mr. Santiago purchased a condo several years ago at a selling price of $299,440. Recently it was
appraised at a value 60% higher than that. What is the value of the condo now?
2. Brandy is looking over her credit card statements from the past couple of months. Last month's
balance was $23,110. This month, it was $20,799. What was the percent of decrease in
Brandy's balance?
Write and equation and solve the following sale/discount word problems.
1. The original price of a dog bowl is $8.24. How much will Carter pay if he buys it during the 22%
off sale?
2. Dwayne buys a hockey stick priced at $85.80. If the sales tax is 18%, what will the total cost of
the hockey stick be?
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CASA Math Study Sheet
Standard 9: Number and Quantity
3. Bennigan’s Toy Store is celebrating their 76th anniversary. Everything in the story is 76% off. If
Andrea purchased a toy car for $0.96, what was the original price of the car?
For the following simple interest problems, use the formula i=prt; where i=interest (dollar amount),
p=principal, r=interest rate (percent), and t=amount of time in years.
1. Gwen has $76 in a savings account. The interest rate is 17% per year and is not compounded.
How much money will she have in 2 years?
2. Dina has $90 in a savings account that earns 5% interest per year. The interest is not
compounded. How much interest will she earn in 7 years?
3. Haley has some money in her savings account that earns 10% annually. The interest is not
compounded. If the interest after one year is $4, what was her principal amount?
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