



Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
A study guide for the accuplacer mat 060 exam, focusing on converting decimals to and from percents, basic percentage word problems, order of operations, and substitution. It also includes practice problems and answers.
Typology: Exams
1 / 7
This page cannot be seen from the preview
Don't miss anything!
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%
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% =.
Example: Convert 58 to a percent.
Divide the denominator into the numerator to get a decimal. Convert this to a percent.
Example: Convert 85% to a fraction
Put the percentage over 100 and reduce to lowest terms.
85 100 รท
Example: What is 21% of 350?
Multiply the decimal form of the percentage by the value.
. 21 ร 350 = 73.
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
Write as a percentage
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:
42 โ 52 (4โ5)^2
Answers:
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
5 ๐ฅโ๐ง ๐ฅ๐ฆ 4.^3 ๐ฆ
Answers:
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:
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
Answers: