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Understanding proportion

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Kiran Bahuleyan

The document defines ratio and proportion. A ratio compares two numbers using division and can be written in several forms like a:b or a to b. A proportion states that two ratios are equal, like using the cost of some number of items to determine the cost of a different number of items. Examples show setting up and solving proportions to find unknown values.

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Understanding Proportion
Ratio ?A ratio is the comparison of two numbers by division. ?A classroom has 16 boys and 12 girls. ?Also written as 16 boys, 16:12 or 16 to 12 12 girls ?Generally, ratios are in lowest terms: 16 = 16/4 = 4 12 12/4 3
Ratio, continued ?Ratios can compare two unlike things: ?Joe earned $40 in five hours ?The ratio is 40 dollars or 8 dollars 5 hours 1 hour ?When the denominator is one, this is called a unit rate.
Ratio, continued Let¡¯s look at a classroom: ?Ratios can be part-to-part ?16 boys 15 girls ?Ratios can be part-to-whole ?16 boys 31 students
Ratio, continued ?If a ratio is part-to-whole, you can divide and find a decimal or a percent. ?16 boys 31 students 31/16.00 = .516, or 51.6% are boys
Proportion ?Proportion is a statement that says two ratios are equal. ? In an election, Damon got three votes for each two votes that Shannon got. Damon got 72 votes. How many votes did Shannon get? ? Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x 24 48 n = 48, so Shannon got 48 votes.
Proportion, continued ?Tires cost two for $75. How much will four tires cost? ?# of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150 n = 150, so four tires cost $150
Proportion, continued ?One more way to solve proportions: ?2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24
Proportion, continued ?Now you try! ?Three cans of soup costs $5. How much will 12 cans cost? ?# of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars n = 20, so 12 cans cost $20
Proportion, continued ?Now you try! ?Three cans of soup costs $5. How much will 12 cans cost? ?# of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars n = 20, so 12 cans cost $20

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Understanding proportion

  • 2. Ratio ?A ratio is the comparison of two numbers by division. ?A classroom has 16 boys and 12 girls. ?Also written as 16 boys, 16:12 or 16 to 12 12 girls ?Generally, ratios are in lowest terms: 16 = 16/4 = 4 12 12/4 3
  • 3. Ratio, continued ?Ratios can compare two unlike things: ?Joe earned $40 in five hours ?The ratio is 40 dollars or 8 dollars 5 hours 1 hour ?When the denominator is one, this is called a unit rate.
  • 4. Ratio, continued Let¡¯s look at a classroom: ?Ratios can be part-to-part ?16 boys 15 girls ?Ratios can be part-to-whole ?16 boys 31 students
  • 5. Ratio, continued ?If a ratio is part-to-whole, you can divide and find a decimal or a percent. ?16 boys 31 students 31/16.00 = .516, or 51.6% are boys
  • 6. Proportion ?Proportion is a statement that says two ratios are equal. ? In an election, Damon got three votes for each two votes that Shannon got. Damon got 72 votes. How many votes did Shannon get? ? Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x 24 48 n = 48, so Shannon got 48 votes.
  • 7. Proportion, continued ?Tires cost two for $75. How much will four tires cost? ?# of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150 n = 150, so four tires cost $150
  • 8. Proportion, continued ?One more way to solve proportions: ?2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24
  • 9. Proportion, continued ?Now you try! ?Three cans of soup costs $5. How much will 12 cans cost? ?# of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars n = 20, so 12 cans cost $20
  • 10. Proportion, continued ?Now you try! ?Three cans of soup costs $5. How much will 12 cans cost? ?# of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars n = 20, so 12 cans cost $20