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ACCUPLACER Study Guide for MAT 060
I. Percents
Changing Decimals to Percents
Move the decimal point two places to the right and attach a percent sign.
Example 1:. 35 = 35% Example 2:. 04 = 4% Example 3:. 7 = 70%
Changing a Percent to a Decimal
Move the decimal point two places to the left and get rid of the percent sign.
Example 1: 32% = .32 Example 2: 3% = .03 Example 3: 90% =.
Convert from a Fraction to a Percent
Example: Convert 58 to a percent.
Divide the denominator into the numerator to get a decimal. Convert this to a percent.
Convert a Percent to a Fraction
Example: Convert 85% to a fraction
Put the percentage over 100 and reduce to lowest terms.
85 100 รท
Finding the Percent of a Value
Example: What is 21% of 350?
Multiply the decimal form of the percentage by the value.
. 21 ร 350 = 73.
Basic Percentage Word Problems
Example 1: 9 is what percent of 45?
Example 2: 30% of what number is 66?
We change the sentence into an equation using key words. The word โisโ changes into an equals sign. The word โofโ means multiply. โWhatโ changes into a variable (Iโll use โaโ).
๐๐ โ = , ๐๐ โ ร , ๐ค๐๐๐ก โ ๐
Example 1:
9 is what percent of 45? โ 9 = ๐ ร 45
Now solve for โaโ by dividing both sides by 45: 459 = ๐
Now reduce and divide to get a decimal value for โaโโฆ ๐ =.
Now convert this decimal to a percent for the final answer ๐ = 20%
Example 2:
30% of what number is 66? โ 30% ร ๐ = 66
Convert this decimal to a fraction: 10030 ร ๐ = 66
Reduce: 103 ร ๐ = 66
Solve for a (multiply by 10, then divide by 3) 3 ร ๐ = 66 ร 10
๐ = 6603 = 220
Practice problems:
Write as a percentage
- 0.12 2. 25 3. 1.15 4. What is 11% of $3000?
- 60 is what percent of 12000? 6. 28 is 40% of what number?
Answers:
(๐๐^ โ ๐)
Now add/subtract
๐๐ (๐๐^ โ ๐)
Now letโs work inside the parentheses in the denominatorโฆ no parentheses, we have an exponent:
๐๐ (๐ โ ๐)
Thereโs no multiplication or division, so we just have to add/subtract:
๐๐ ๐
This is an improper fraction which can be converted to a mixed number:
๐
Practice problems:
- 5 + 1 4 โ 2 โ 3 2. 3 โ 72 3. 49 รท 7 โ 2 โ 3
42 โ 52 (4โ5)^2
Answers:
- 9 2. 147 3. 1
III. Substitution
Example: Find ๐ฅ๐ฆ๐ง โ ๐ง^2 if ๐ฅ = 2, ๐ฆ = โ1, ๐ง = โ 3
Simply plug in the given values for x, y and z where they appear in the expression. Use order of operations to simplify. Make sure to use parentheses when plugging values in.
๐ฅ๐ฆ๐ง โ 4 ๐ง^2 = 2 โ 1 โ 3 โ 4 โ 3 2 = 2 โ 1 โ 3 โ 4 9 = 6 โ 36 = โ 30
Practice Problems:
Find the following if ๐ฅ = 1, ๐ฆ = โ2, ๐ง = 4
- 2 ๐ฅ โ 3 ๐ฆ 2. ๐ฆ(๐ฅ โ 2 ๐ง) 3.
5 ๐ฅโ๐ง ๐ฅ๐ฆ 4.^3 ๐ฆ
Answers:
- 8 2. 14 3. โ 12 4. 7
IV. Linear equations with one variable
Example 1: Solve for x. 6 ๐ฅ โ 48 = 6 Example 2: Solve for x. 4 ๐ฅ โ 2 1 + ๐ฅ = 4
The basic steps are:
- Distribute to get rid of any parentheses.
- Add and subtract to get all terms with an x on one side of the equation and everything else on the other side.
- Multiply or divide to solve for x
Example 1: Example 2:
๐๐ โ ๐๐ = ๐ ๐๐ โ ๐ ๐ + ๐ = ๐
Add 48 to both sides Distribute the -
๐๐ โ ๐๐ + ๐๐ = ๐ + ๐๐ ๐๐ โ ๐ โ ๐๐ = ๐
๐๐ = ๐๐ Add 2 to both sides
Divide both sides by 6 ๐๐ โ ๐ โ ๐๐ + ๐ = ๐ + ๐
๐๐/๐ = ๐๐/๐ Combine like terms
๐ = ๐ ๐๐ = ๐
Divide both sides by 2
๐ = ๐
- The sides of a rectangle are 2.4 cm and 1.1 cm. Find the area of the rectangle.
- The area of a rectangle is 23.7 feet. If the length of the rectangle is 4.2 feet, find its width.
Answers:
- 30% of the number of lefties is 120: 10030 โ ๐ฅ = 120 โ ๐ฅ = 400 ๐๐๐๐ก๐๐๐
- We want 20% of 55: 10020 โ 55 = 11 ๐๐๐๐๐
- The total increase is 667 โ 599 = 68 ๐๐๐๐๐๐๐๐ก๐ . What percent of 599 is 68? ๐ฅ โ 599 = 68 โ ๐ฅ =
- You get 55011 = 50 jelly beans per dollar. So you can get 50 โ 20 = 1000 jelly beans.
- 14 of the total plants is 5212 plants. So there are 5212 โ 4 = 20848 total plants.
- 2.4 1.1 = 2.64 ๐๐^2 (centimeters squared)
- 23.74.2 = 5.64 ft
