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Back to the Basics: Percents, Proportions and Ratios

Back to the Basics: Percents, Proportions and Ratios. Percent. Putting Things over 100. Basic Types of Percent Problems. 3 basic types: 1) find the part; 2) find the whole; 3) find the percent;

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Back to the Basics: Percents, Proportions and Ratios

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  1. Back to the Basics: Percents, Proportions and Ratios

  2. Percent Putting Things over 100

  3. Basic Types of Percent Problems • 3 basic types: 1) find the part; 2) find the whole; 3) find the percent; • For example a class consists of 20 students(the whole) 5 of which are absent(the part), and the percent absent(unknown); • ‘Is’ in top half of circle, and ‘Of’ is in bottom right half; % in bottom left section;

  4. Find the Part(ie. “Is”): • P=percent*whole • Find 20% of 60? Change percent to a decimal; • .20*60= 12 • What is 20% of 60? • 20% of 60 is what number?

  5. Find the Whole( ie. “Of”) • Whole= part/ percent • 16 is 20% of what number? 16 is the part and 20 is the percent; Change percent to decimal and divide; 16/.20=80; • 42% of what number is 294? 42 is the percent and 294 is the part; Change percent to decimal and divide; 294/.42=700;

  6. Find the percent(ie. %) • Percent= part/whole; • What percent of 16 is 10? Solution: 10 is part and 16 is whole, divide, and change answer to percent; 10/16=.625= 62.5% • What percent of 5 is 2? Solution: 2 is part and 5 is whole; 2/5=.40= 40%;

  7. You Try! • What percent of 60 is 40? • What is 15% of 60? • 18% of what number is 200?

  8. Percent Increase/Decrease • A coat that originally cost $150 was reduced to 120. What was the percent reduction( ie. percent is unknown)? • 1)Find amount of reduction • 2)Place reduction($30) in“part” section • 3) Place $150 (starting point) in whole section • 4) $30/$150= .20 • 5) Multiply by hundred .20(100)=20% reduction;

  9. You Try! • An adjunct professor making $30,000 per year gets a tenured track position where she makes $50,000 annually; What is the percent increase in her salary?

  10. Proportions • Proportions are built from ratios. A "ratio" is just a comparison between two different things. For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the ratio of men to women is 15 to 20.

  11. Proportions cont…. • Let's return to the 15 men and 20 women in our original group. I had expressed the ratio as a fraction, namely, 15/20. This fraction reduces to 3/4. This means you express the ratio of men to women as 3/4, 3 : 4, or "3 to 4". • This points out something important about ratios: the numbers used in the ratio might not be absolute measured values. The ratio "15 to 20" refers to the absolute numbers of men and women, respectively, in the group of thirty-five people.

  12. Proportions cont…. • Notice that, in the expression "the ratio of men to women", "men" came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been "the ratio of women to men", then the numbers would have been "20 to 15". • Expressing the ratio of men to women as "15 to 20" is expressing the ratio in words

  13. Proportions cont…. • The simplified or reduced ratio "3 to 4" tells you only that, for every three men, there are four women. The simplified ratio also tells you that, in any representative set of seven people (3 + 4 = 7) three will be men. In other words, the men comprise 3/7 of the people in group. These relationships and reasoning are what you use to solve many word problems: • In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course?

  14. Ratios • Consider Hispanics and non-Hispanics in Sociology classes. Their ratio is 2 Hispanics to 3 non-Hispanics. Suppose that there are 192 Hispanics. How many non-Hispanics are there?

  15. You Try! • the ratio of ducks to geese is 16 to 9. How many of the 300 birds are geese? • Ratio of blue marbles to red marbles is 2:3. How many of the 80 marbles are red? • Ratio of blue marbles to red marbles to green marbles are 2:3:4. How many of the 81 marbles are green?

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