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Ratio, Rate & Proportions

Ratio, Rate & Proportions. L.O: Define a ratio, a rate and a proportion SOL 7.?:. Definition of Ratio :. A ratio compares two quantities. The order in which you write a ratio it is important. hearts to stars. hearts. 3. =. stars. 5. Ratios.

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Ratio, Rate & Proportions

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  1. Ratio, Rate & Proportions L.O: Define a ratio, a rate and a proportion SOL 7.?:

  2. Definition of Ratio : A ratio compares two quantities The order in which you write a ratio it is important hearts to stars hearts 3 = stars 5

  3. Ratios It can be written in three different ways: Stars to hearts stars 5 5 to 3 5 : 3 = hearts 3

  4. Practice: The heights of three mountains in the world are illustrated by the following squares Everest(Him) Aconcagua (Arg) Kilimanjaro (Afr) 5. Ratio between Mt. Kilimanjaro and Mt. Everest: 1. Ratio between Mt. Everest and Mt. Aconcagua: 2. Ratio between Mt. Everest and Mt. Kilimanjaro: 3. Ratio between Mt. Aconcagua and Mt. Kilimanjaro: 4. Ratio between Mt. Aconcagua and Mt. Everest: Mt. Everest Mt. Everest Mt. Kilimanjaro Mt. Aconcagua Mt. Aconcagua 3 2 4 3 4 2 to 4 4 to 3 4 to 2 3 to 4 3 to 2 4 : 2 3 : 4 4 : 3 3 : 2 2 : 4 = = = = = Mt. Aconcagua Mt. Kilimanjaro Mt. Everest Mt. Kilimanjaro Mt. Everest 2 2 4 3 4

  5. Ratios need to be written in simplest form Equal Ratios • When two ratios name the same number, they are equal. It’s like writing an equivalent fraction. 20 to 30 10 to 15 2 to 3 2 : 3 20 : 30 10 : 15 10 20 2 2 2 = = 15 30 3 3 3

  6. RATES A rate is a ratio that compares quantities that are measured in different units. This car travels at a certain speed. Speed is an example of a rate. Speed can be measured in many different ways. This car can travel 120 miles in 2 hours.

  7. One key word that often identifies a rate is PER. Miles per gallon, Points per free throw, Dollars per pizza, Sticks of gum per pack RATES A rate is a ratio that compares quantities that are measured in different units. Rates are often written in fraction form. 120 miles in 2 hours is a rate. It can be written as….. 120 Miles hours 2

  8. EXAMPLES Step 1: highlight the units 1). Mr. M run four miles around the track in 45 minutes Step 2: Write the units as a fraction Step 3: Substitute the values 4 Miles = 45 Minutes

  9. EXAMPLES Step 1: highlight the units 2). Mrs. B can drive her car 225 miles per every 10 gallons of gas. Step 2: Write the units as a fraction Step 3: Substitute the values 225 Miles = 10 Gallons

  10. Time for practice 1). Tom loses 4 pounds every three weeks he is on a diet. 2). Mary can drive 140 miles in 3 hours. 3). Six pounds of grass seed covers 150 square feet. 4). Mrs. F scores 28 points in 3 basketball games. Centimeters 25.4 Pounds Points Miles Pounds 28 4 140 6 5). There are 25.4 centimeters in ten inches. = = = = = 10 150 3 3 3 inches B. Games Hours Weeks Sq. Ft

  11. UNIT RATES A unit rate compares a quantity to one unit of another quantity. A average person can walk at a rate of 9 miles in 2 hours. Its speed is a unit rate of 4.5 miles per 1 hour or simply 4.5 miles per hour. 2 Miles Hours 9 4.5 Miles Hour = = 4.5 miles/hour 2 2 1

  12. EXAMPLES Step 1: highlight the units 1). Mr. M in 45 minutes run five miles around the track. How long does he takes per mile? Step 2: Write the units as a fraction Step 3: Substitute the values Step 4: Divide numerator by denominator Minutes 45 45  5 = 9 = Miles 5 Step 5: write an answer: He will run a 9 min/mile

  13. EXAMPLES Step 1: highlight the units 2). Mrs. B can drive her car 220 miles per every 10 gallons of gas. How far can she drive with one gallon? Step 2: Write the units as a fraction Step 3: Substitute the values Step 4: Divide numerator by denominator 220 22 Miles 220  10 = = 10 Gallons Step 5: write an answer: She will drive 22 miles/gallon

  14. Time for practice 1). Tom loses 9 pounds every three weeks he is on a diet. How many pounds does he lose per week? 2). Mary can drive 140 miles in 4 hours. How many miles does she drive per hour? 4). Mrs. F scores 28 points in 4 basketball games. How many points does she score per game? 5). There are 25.4 centimeters in ten inches. How many centimeters per inch? 3). 150 square feet of land can be cover with Six pounds of grass seed. How many square feet can you cover with one pound of grass seed? 150  6 = 140  4 = 28  4 = 2.54 9  3 = 3 25.4  10 = 25 35 7 There are 2.54 centimeters /inch You can cover 25 square feet /pound Mrs. F is scoring 7 points /game She is driving 35 miles/hour He is losing 3 pounds/week Centimeters 25.4 Pounds Points Miles Sq. Ft 9 140 28 150 = = = = = 10 3 4 4 inches Pounds 6 B. Games Weeks Hours

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