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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.