1. Ratios, Percents, Simple Equations, and Ratio-Proportion
Chapter 2
Ratios, Percents,
Simple Equations, and Ratio-Proportion
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

2. Ratios
Indicate the relationship of one part of a quantity to the whole
May be in a fraction or separated by a colon
Example:
5 nurses per 35 patients = 5/35 or
5:35 or 1:7
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

3. Percent To remember the value of a given percent Example:
Replace % symbol with “/” for per and “100” for cent
Example:
“20% said ‘yes’ in the survey,” that means 20 per 100 said “yes”
20% may be written as 20/100
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

4. Percent (Continued) You may find it helpful to think of money for %
For example, 25% is 25/100
There are 4 quarters in $1.00 and 25/100 = ¼
One quarter is ¼ of a dollar
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

5. Convert Ratio to Fraction
To express a ratio as a fraction
Number to left of colon becomes the numerator
Number to right of colon becomes the denominator
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

6. Convert Ratio to Fraction (Continued)
The colon in a ratio is equivalent to the division sign in a fraction
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

7. Convert Ratio to Decimal
To change a ratio to a decimal
Convert ratio to a fraction
Divide numerator by denominator
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

8. Convert Percent to Fraction
To change a percent to a fraction
Drop % sign
Place remaining number as the numerator over denominator 100
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

9. Convert Percent to Fraction (Continued)
Reduce fraction to lowest terms
Think: per (/) cent (100)
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

10. Convert Percent to Ratio
To change a percent to a ratio
Convert percent to a fraction in lowest terms
Place numerator to left of colon and denominator to right of colon
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

11. Convert Percent to Decimal
To change a percent to a decimal
Drop % sign
Divide by 100
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

12. Convert Decimal to Percent
To change a decimal to percent
Multiply by 100
Add % sign
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

13. How to Remember These? Think PDL (Percent to Decimal, Left)
You may think of paddle or puddle for PDL
DPR (Decimal to Percent, Right)
How about dipper or diaper for DPR?
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

14. Convert Ratio to Percent
To change a ratio to a percent
First convert ratio to a fraction
Convert resulting fraction to a decimal and then to a percent
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

15. Convert Ratio to Percent (Continued)
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

16. Proportion
Two ratios that are equal or an equation between equal ratios
Math Tip
A proportion is written as two ratios separated by an equal sign or a double colon
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

17. Ratio-Proportion 5 : 10 :: 10 : 20
The above reads 5 is to 10 as 10 is to 20
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

18. Proportion Cross-Products
If two fractions are equivalent, or equal, then their cross-products are also equal
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

19. Solving for X in a Proportion
Simplifying the equation
First cross multiply, then
Divide each side of an equation by same number to produce an equivalent equation
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

20. Percentage of a Quantity
Percentage (part)
= Percent X Whole Quantity
Example: What is 12% of 48?
“Of” in math means multiply
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.

21. Percentage of a Quantity (Continued)
What is 8% of 200?
0.08 × 200 = 16
How much is 4% of 30?
0.04 × 30 = 1.2
© 2013 Delmar Cengage Learning. All Rights Reserved. May not be scanned, copied, duplicated, or posted to a publicly accessible website, in whole or in part.