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ACCUPLACER Study Guide for MAT 030
1. Fractions
Vocabulary
Numerator: The top part of a fraction – tells us how many equal pieces we have.
Denominator: The bottom part of the fraction – tells us how many equal pieces are in the whole.
Example:
We have 3 equal pieces. The whole pie had 4 equal
pieces. So we have
of a pie!
Proper Fractions: When the numerator is smaller than the denominator
Examples:
1 3
7 9
10 17
Improper Fractions: When the numerator is bigger than or equal to the denominator
Examples:
3 2
9 4
11 11
Mixed Number: The sum of a whole number and a proper fraction
Examples: 2
1
3 , 4^
7
9 , 8^
1 2
Common Denominator: A number that can be divided evenly by all denominators in the
problem
Example: A common denominator of the fractions
1 3
3 4
5 2
is 12.
1 3
4 12
3 4
9 12
5 2
30 12
Note: 24 is also a common denominator of the fractions. In this case, 12 is called the least common denominator.
Changing Mixed Numbers into Improper Fractions
Example: Change 2
3 4 into an improper fraction.
- Multiply the whole number by the denominator of the fraction.
- Add this to the numerator of the fraction.
- This result is the numerator of the improper fraction. The denominator stays the same.
1. 2 × 4 = 8
- Answer:
11 4
Changing an Improper Fraction Into a Mixed Number
Example: Change
14 3
into a mixed number
- Long divide the numerator by the denominator.
- The quotient becomes the whole number and the remainder becomes the numerator of the fraction. The new denominator is the same as that of the original improper fraction.
3 14 2. 4
2 3
Reducing Fractions to Lowest Terms
Example: Reduce
48 64
to lowest terms
- Divide both the numerator and denominator by a common factor.
- Repeat until the numerator and denominator have no more common factors.
Example:
48 64
÷
8 8
=
6 8
6 8
÷
2 2
=
3 4
NOTE: To multiply/divide/add/subtract mixed numbers, you must first change them into improper fractions!
Example 1:
Add 3
1
2 + 2^
2 3
- Change both mixed numbers to improper fractions, and find a common denominator.
- Add and reduce
Practice Problems:
6
5 +^
2
3^2.^2
1
2 + 4^
2
3^3.^2
4
7 × 4^
2
3^4.^
4
5 ÷^
2 7
2
3 + 4 + 2^
1
2 6.^
5
3 −^
6
7 7.^
2
3 −^
1 6
8. Which of the following is not equivalent to
3 5
a. 3050 b. 159 c. 10060 d.^3660 e. 208
Answers:
28
15 or^1
13
15^2.^
43
6 or^7
1
6^3.^12^4.^
14
5 or^2
4 5
49
6 or^8
1
6^6.^
17
21^7.^
1
2^8. e
2. Decimals
Adding and Subtracting Decimals
Example 1 : Add 28.5 + 2.64 + 105.3 Example 2: Subtract 230.43 − 25.
To add/subtract decimals, we line up the decimal points, then add/subtract
Example 1: Example 2:
Multiplying Decimals
Example 1: Multiply 1.57 × 32.1 Example 2: Multiply 4.1 ×.
To multiply decimals, you don’t have to line up the decimals. Just multiply the two numbers as you would without any decimals. Then count the number of digits to the right of all decimals in the problem. This number is the same as the number of digits to the right of the decimal in your answer!
Example 1: Example 2:
X 32.1 X.
Dividing a Decimal By a Whole Number
Example: Divide 2.701 ÷ 73
To divide a decimal, put a decimal directly above the position of the decimal in the problem. Divide like normal filling in any gaps with zeros.
3. Word Problems
A good percentage of accuplacer math problems are word problems. It’s important to know that you’re probably more likely to see a problem phrased
“You have 3 pizzas. Bill eats 1
1 4 pizzas and Tom eats^
2 3 of a pizza. How much pizza is left?”
than you are to see the same problem worded
“Find 3 − 1
1 4 −^
2 3_._^ ”
Solving word problems just takes a lot of practice, focus, and critical thinking. Many students like to use a list of “key words” to help them translate words into math. Here is a chart of some key words:
Addition (+) Subtraction (-) Multiplication (∙) Division (÷) Equality (=)
Sum Difference Of Quotient Equals
Plus Minus Times Divide Is equal to
Added to Subtracted from Multiply Shared equally among
Is/was
More than Less Than Twice Per Yields
Increased by Decreased by Product Divided by Amounts to
Total Less Double/triple Divided into gives
Of course, these key words won’t help in every problem, so we have to think hard about what each problem gives us and what it is asking for. Let’s try some out!
- A 127.42 acre area of rain forest is beginning to be cut down. So far, 82.5 acres have been removed. How many acres of this area of rain forest are left?
- Heather is collecting money for a charity bike ride. So far, she’s been given donations of $12.50, $9.25, and $44. $10 of this money goes to fund the event and the rest goes to charity. How much of her collected money will go to charity?
- The number of people that hiked Mt. Evans in 2006 was 2/3 the number of people that hiked Mt Evans in 2005. 12,000 people hiked Mt. Evans in 2005. How many people hiked Mt. Evans in 2006?
- Chuck gets paid an hourly rate of $7.15/hr. If he works 4.3 hours, how much is he paid?
- Terry purchaces 2 packages of ground beef. One package weighs 2 13 pounds. The other weighs 1
4 5 pounds. How many pounds of ground beef did Terry buy?
- Marty’s Indian Head penny is made of copper and nickel only. If 325 of the coin is nickel, what fraction of the coin is copper?
Answers:
- 2 13 + 1 45 = 73 + 95 = 3515 + 2715 = 6215 𝑝𝑜𝑢𝑛𝑑𝑠 or 4 152 𝑝𝑜𝑢𝑛𝑑𝑠
5 32 =^
32 32 −^
5 32 =^
27 32 of the coin is copper.
