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Ratio Notes

Ratio Notes A ratio is a comparison of two numbers by division. Each number in a ratio is called a term . Ratios can be written three ways and SHOULD ALWAYS BE SIMPLIFIED. Ex: The ratio 4 to 5 can be written 4 to 5 4:5 4 / 5.

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Ratio Notes

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  1. Ratio Notes • A ratio is a comparison of two numbers by division. Each number in a ratio is called a term. • Ratios can be written three ways and SHOULD ALWAYS BE SIMPLIFIED. • Ex: The ratio 4 to 5 can be written • 4 to 5 • 4:5 • 4/5

  2. Equal Ratios are ratios that name the same number. They have the same simplest form. • To find equal ratios, multiply or divide both the numerator and denominator of a ratio by the same number 4/7 = 8/14 • Ratios are proportional if they simplify to the same ratio. Ex: 8:10 = 12:15 because both simplify to 4:5

  3. Write a ratio in three ways to compare each. • Lions to deer _______________________ • Parrot to swans _______________________ • Swans to lions _______________________ • Deer to parrot ________ • Swans to deer ________ • Deer to swans _______________________

  4. Write each ratio as a fraction in simplest form. • (4 pumpkins, 2 watermelon, 12 bananas) • Watermelon to pumpkins _________ • Pumpkins to bananas _________ • Pumpkins to watermelon _________ • Watermelon to bananas _________ • Bananas to watermelon _________ • Bananas to pumpkins ______________________________

  5. Unit Rates • A Rate is a ratio that compares two quantities measured in different units. • Ex. 150 heartbeats to 2 minutes • A unit rate is the rate for one unit of a given quantity. Always has the denominator of 1. • 150 divided by 2 = 75 The unit rate is 75 heartbeats per minute. • Unit Price – a unit rate that gives the cost per unit.

  6. Finding Unit Rates If you are given the price of many items, but you need the price for one item individually, then you need to know the unit rate. Or if you are given the rate for 20 laps around a track, but you want to know the speed PER LAP – you need to know a unit rate. • You are finding “how many” in 1.

  7. Practice with Unit Rates You want to break these down into the “unit” rate. How many miles in 1 min? How many dollars you make in 1 hour? Etc. *Hint: Divide the first by the second* • 760 miles in 30 min • $42.50 in 8 hours • 450 yards gained in 3 football games • 286 shots made in 20 basketball games

  8. Proportions • A proportion is two equivalent ratios. We say that two ratios are “proportional” to one another. • Use cross products to determine if two ratios are proportional. • You can also use proportions to find a missing value in a problem. • You will actually use cross multiplication here, and an algebra equation to solve for missing values. 4 = X 7 35

  9. 1. There are 54 boys and 48 girls in the Leopard team. What is the ratio of girls to boys? • 2. Tell me if the following ratios form a proportion. Show your work. 315 5 35 • Solve to find the missing value in the following proportion: 4 = X 7 35

  10. EXAMPLES: • Example: You can buy 20 CD’s in a pack for $30.00. How much does each individual CD cost? Proportion: Division:

  11. Find the unit rate for each situation. • $80 for 10 shirts • $20 for 4 toys • $56 for 8 hours • $120 for 5 shirts • $45 for 9 boxes

  12. Write the unit rate as a ratio. Then find an equal ratio. • The cost is $4.25 for 1 item. Find the cost of 4 items. • The cost is $10.10 for 1 item. Find the cost of 10 items. • The cost is $8.50 for 1 item. Find the cost of 4 items. • There are 2.54 cm in 1 inch. How many cm are in 6 inches? • There are 365 days in 1 year. How many days are in 2 years?

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