Chapter 7: Proportional Reasoning
7.3Solving Percent Problems
7.3.1.Definition of percent
7.3.1.1.Definition of percent: a percent is a ratio with a denominator of 100
7.3.1.2.represented by the symbol %
7.3.1.3.100% means or ALL of the amount
7.3.1.4.Twice the amount would be or 200% of the amount
7.3.1.5.Three times the amount would be or 300%; etc.
7.3.1.6.One circle or one grid represents 100%
7.3.1.6.1.– to show less than 100% shade in the fractional amount of the circle or grid equivalent to the desired percent
7.3.1.6.1.1. then shade of the circle
7.3.1.6.1.2. then shade of the grid
7.3.1.6.2.– to show a percent larger than 100% shade in one whole circle or grid for each multiple of 100% and then the fractional amount of another circle or grid equivalent to the desired percent
7.3.1.6.2.1. then shade of the circles
7.3.1.6.2.2. then shade of the grid
7.3.2.Connecting percents, ratios, and decimals
7.3.2.1.Converting a percent to a decimal – divide the percent by 100 and drop the percent sign
7.3.2.1.1.
7.3.2.1.2.
7.3.2.1.3.
7.3.2.1.4.
7.3.2.2.Converting a percent to a fraction – place the percent over 100, drop the percent sign, then simplify the fraction
7.3.2.2.1.
7.3.2.2.2.
7.3.2.2.3.
7.3.2.2.4.
7.3.2.3.Converting a fraction to a decimal or percent – write an equivalent fraction with a denominator of 100
7.3.2.3.1.
7.3.2.3.2.
7.3.2.3.3.
7.3.2.3.4.
7.3.2.3.5.
7.3.2.3.6.
7.3.3.Types of percent problems
7.3.3.1.Three (3) basic types
7.3.3.2.A% x B = C
7.3.3.2.1.Finding a percent of a number – know A% and B
7.3.3.2.1.1.Nkenze sees a dress in a store that regularly sells for $65 in the 20% off rack. How much will she save if she buys the dress on sale?
7.3.3.2.1.2.
7.3.3.2.1.3.Nkenze will save $13 if she buys the dress on sale.
7.3.3.2.2.Finding a number when a percent of it is known – know A% and C
7.3.3.2.2.1.Kevin determined that he had traveled 240 miles, which he estimated as being 40% of the trip. If his estimate is correct, how long is the trip?
7.3.3.2.2.2.
7.3.3.2.2.3.Kevin’s trip is 600 miles long.
7.3.3.2.3.Finding the percent that one number is of another – know B and C
7.3.3.2.3.1.Beth learned that 72 of her 150-member senior class went to college. What percent of her senior class went to college?
7.3.3.2.3.2.
7.3.3.2.3.3.48% Beth’s senior class attended college.
7.3.4.Solving percent problems
7.3.4.1.Finding a percent of a number
7.3.4.1.1.1.Nkenze sees a dress in a store that regularly sells for $65 in the 20% off rack. How much will she save if she buys the dress on sale?
7.3.4.1.1.2.
7.3.4.1.2.Nkenze will save $13 if she buys the dress on sale.
7.3.4.2.Finding a number when a percent of it is known – know A% and C
7.3.4.2.1.Kevin determined that he had traveled 240 miles, which he estimated as being 40% of the trip. If his estimate is correct, how long is the trip?
7.3.4.2.2.
7.3.4.2.3.Kevin’s trip is 600 miles long.
7.3.4.3.Finding the percent that one number is of another – know B and C
7.3.4.3.1.Beth learned that 72 of her 150-member senior class went to college. What percent of her senior class went to college?
7.3.4.3.2.
7.3.4.3.3.48% Beth’s senior class attended college.
7.3.5.Percent increase or decrease
7.3.5.1.Increase or decrease relative to the original situation
7.3.5.2.Procedure for finding the percent increase or decrease:Step 1 – Determine the amount of increase or decrease; Step 2 – Divide this amount by the original amount; and Step 3 – Convert this fraction or decimal to a percent
7.3.5.3.See examples p. 407
7.3.6.Estimating the percent of a number
7.3.6.1.helpful for leaving tips in restaurants
7.3.6.2.figuring out discounts on sale items
7.3.6.3.rounding usually provides reasonable estimate
7.3.6.4.See example p. 409
7.3.7.Problems and Exercises p. 410
7.3.7.1.Home work: 1, 4, 5, 7, 9, 12, 14, 19, 20, 25, 26, 29-31, 33, 35, 37