ratio and proportion
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Ratio and proportion can be expressed in different ways. A ratio compares two numbers using a colon or fraction. A proportion states that two ratios are equal, also using a colon or equal fractions. To solve proportions, use cross multiplication. Word problems can involve finding an unknown value given ratios or proportions related to distances, times, enrollments and other quantities.
ratio and proportion
- 2. Ratio - a comparison of two numbers - can be written in any form: • the two numbers in a ratio are separated by colon (:) a:b 2:3 25:56 • as a fraction a 2 25 b 3 56
- 3. • the child to books
- 4. • the bananas to monkeys
- 5. • the number of the apple trees to the number of apples
- 6. Proportion - a statement that two ratios are equal - can be written in any form: • using a colon a:b = c:d 2:6 = 1:3 • two equal fractions a a c 2 1 a = = b d b 6 b 3
- 7. a:b = c:d means extremes Remember: The means is always equal to the extremes.
- 8. - use the cross products 3 12 6 24 3 x 24 = 12 x 6 72 = 72
- 9. Find n in the proportion. 20 60 30 n 20 x n = 60 x 30 20 n = 1800 20 20 n = 90
- 10. Word Problems Jane ran 2 meters in 3 seconds. How long can she take to run 50 meters? 2 50 = 3 n Distance 2xn = 3 x 50 Time Let n be our time. 2n = 150 2 2 n = 75 seconds
- 11. a. In 1995, 120 girls were enrolled in a certain elementary school while 100 boys were enrolled. What was the ratio of girls to boys? Boys to girls? girls to boys 120:100 boys to girls 100:120
- 12. b. In 1996, the ratio of girls to boys enrolled in the same school stayed the same as in 1995. How many girls were enrolled in 1996 when there where 130 boys enrolled? 120 n = 100 130 girls to boys 120:100 100 x n = 120 x 130 Let n be the 100 n = 15600 number of girls. 100 100 n = 156 girls
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