Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

ACCUPLACER Study Guide: Percents and Basic Math Operations, Exams of Algebra

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

Pre 2010

Uploaded on 08/19/2009

koofers-user-7oc
koofers-user-7oc ๐Ÿ‡บ๐Ÿ‡ธ

10 documents

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Page 1 of 7
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% = .9
Convert from a Fraction to a Percent
Example: Convert 5
8 to a percent.
Divide the denominator into the numerator to get a decimal. Convert this to a percent.
.625
8 5.000 .625 62.5%๏‚ฎ๏€ฝ
Convert a Percent to a Fraction
Example: Convert 85% to a fraction
Put the percentage over 100 and reduce to lowest terms.
85
100 รท5
5=17
20
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 =73.5
pf3
pf4
pf5

Partial preview of the text

Download ACCUPLACER Study Guide: Percents and Basic Math Operations and more Exams Algebra in PDF only on Docsity!

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 โ€œisโ€ changes into an equals sign. The word โ€œofโ€ means multiply. โ€œWhatโ€ changes into a variable (Iโ€™ll use โ€œaโ€).

๐‘–๐‘  โ†’ = , ๐‘œ๐‘“ โ†’ ร— , ๐‘ค๐‘•๐‘Ž๐‘ก โ†’ ๐‘Ž

Example 1:

9 is what percent of 45? โ†’ 9 = ๐‘Ž ร— 45

Now solve for โ€œaโ€ by dividing both sides by 45: 459 = ๐‘Ž

Now reduce and divide to get a decimal value for โ€œaโ€โ€ฆ ๐‘Ž =.

Now convert this decimal to a percent for the final answer ๐‘Ž = 20%

Example 2:

30% of what number is 66? โ†’ 30% ร— ๐‘Ž = 66

Convert this decimal to a fraction: 10030 ร— ๐‘Ž = 66

Reduce: 103 ร— ๐‘Ž = 66

Solve for a (multiply by 10, then divide by 3) 3 ร— ๐‘Ž = 66 ร— 10

๐‘Ž = 6603 = 220

Practice problems:

Write as a percentage

  1. 0.12 2. 25 3. 1.15 4. What is 11% of $3000?
  2. 60 is what percent of 12000? 6. 28 is 40% of what number?

Answers:

(๐Ÿ๐Ÿ^ โˆ’ ๐Ÿ)

Now add/subtract

๐Ÿ๐Ÿ‘ (๐Ÿ๐Ÿ^ โˆ’ ๐Ÿ)

Now letโ€™s work inside the parentheses in the denominatorโ€ฆ no parentheses, we have an exponent:

๐Ÿ๐Ÿ‘ (๐Ÿ’ โˆ’ ๐Ÿ)

Thereโ€™s no multiplication or division, so we just have to add/subtract:

๐Ÿ๐Ÿ‘ ๐Ÿ‘

This is an improper fraction which can be converted to a mixed number:

๐Ÿ’

Practice problems:

  1. 5 + 1 4 โˆ’ 2 โˆ’ 3 2. 3 โˆ™ 72 3. 49 รท 7 โˆ’ 2 โˆ™ 3

42 โˆ’ 52 (4โˆ’5)^2

Answers:

  1. 9 2. 147 3. 1

III. Substitution

Example: Find ๐‘ฅ๐‘ฆ๐‘ง โˆ’ ๐‘ง^2 if ๐‘ฅ = 2, ๐‘ฆ = โˆ’1, ๐‘ง = โˆ’ 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.

๐‘ฅ๐‘ฆ๐‘ง โˆ’ 4 ๐‘ง^2 = 2 โˆ’ 1 โˆ’ 3 โˆ’ 4 โˆ’ 3 2 = 2 โˆ’ 1 โˆ’ 3 โˆ’ 4 9 = 6 โˆ’ 36 = โˆ’ 30

Practice Problems:

Find the following if ๐‘ฅ = 1, ๐‘ฆ = โˆ’2, ๐‘ง = 4

  1. 2 ๐‘ฅ โˆ’ 3 ๐‘ฆ 2. ๐‘ฆ(๐‘ฅ โˆ’ 2 ๐‘ง) 3.

5 ๐‘ฅโˆ’๐‘ง ๐‘ฅ๐‘ฆ 4.^3 ๐‘ฆ

Answers:

  1. 8 2. 14 3. โˆ’ 12 4. 7

IV. Linear equations with one variable

Example 1: Solve for x. 6 ๐‘ฅ โˆ’ 48 = 6 Example 2: Solve for x. 4 ๐‘ฅ โˆ’ 2 1 + ๐‘ฅ = 4

The basic steps are:

  1. Distribute to get rid of any parentheses.
  2. Add and subtract to get all terms with an x on one side of the equation and everything else on the other side.
  3. Multiply or divide to solve for x

Example 1: Example 2:

๐Ÿ”๐’™ โˆ’ ๐Ÿ’๐Ÿ– = ๐Ÿ” ๐Ÿ’๐’™ โˆ’ ๐Ÿ ๐Ÿ + ๐’™ = ๐Ÿ’

Add 48 to both sides Distribute the -

๐Ÿ”๐’™ โˆ’ ๐Ÿ’๐Ÿ– + ๐Ÿ’๐Ÿ– = ๐Ÿ” + ๐Ÿ’๐Ÿ– ๐Ÿ’๐’™ โˆ’ ๐Ÿ โˆ’ ๐Ÿ๐’™ = ๐Ÿ’

๐Ÿ”๐’™ = ๐Ÿ“๐Ÿ’ Add 2 to both sides

Divide both sides by 6 ๐Ÿ’๐’™ โˆ’ ๐Ÿ โˆ’ ๐Ÿ๐’™ + ๐Ÿ = ๐Ÿ’ + ๐Ÿ

๐Ÿ”๐’™/๐Ÿ” = ๐Ÿ“๐Ÿ’/๐Ÿ” Combine like terms

๐’™ = ๐Ÿ— ๐Ÿ๐’™ = ๐Ÿ”

Divide both sides by 2

๐’™ = ๐Ÿ‘

  1. The sides of a rectangle are 2.4 cm and 1.1 cm. Find the area of the rectangle.
  2. The area of a rectangle is 23.7 feet. If the length of the rectangle is 4.2 feet, find its width.

Answers:

  1. 30% of the number of lefties is 120: 10030 โˆ™ ๐‘ฅ = 120 โ†’ ๐‘ฅ = 400 ๐‘™๐‘’๐‘“๐‘ก๐‘–๐‘’๐‘ 
  2. We want 20% of 55: 10020 โˆ™ 55 = 11 ๐‘”๐‘Ž๐‘š๐‘’๐‘ 
  3. The total increase is 667 โˆ’ 599 = 68 ๐‘Ž๐‘๐‘๐‘–๐‘‘๐‘’๐‘›๐‘ก๐‘ . What percent of 599 is 68? ๐‘ฅ โˆ™ 599 = 68 โ†’ ๐‘ฅ =
  1. You get 55011 = 50 jelly beans per dollar. So you can get 50 โˆ™ 20 = 1000 jelly beans.
  2. 14 of the total plants is 5212 plants. So there are 5212 โˆ™ 4 = 20848 total plants.
  3. 2.4 1.1 = 2.64 ๐‘๐‘š^2 (centimeters squared)
  4. 23.74.2 = 5.64 ft