Warm-Up Questions1. A student scored 96% on a test with 50 questions. How many questions were missed?2. Ramon spent 40% of his savings on new shoes. He has saved $275. How much were the shoes?3. In a survey, people were asked to name their favorite sport. 30 said Baseball, 42 football, and 8 soccer. What percent like baseball best?4. Minimum wage in the CNMI has increased from $4.60 to $5.55 in the past two years. What is the percent increase?5. You are 15 years old and have lived 18% of your life. At what age will you die?
Ratios, Proportions, & RatesA Ratio is a comparison of two numbers by division. Ratios canbe expressed by: 4:3, or 4 to 3, or 4/3.A Proportion is an equation that two ratios are equal. Todetermine if ratios are equal, cross-multiply and check forequality. 2/5 and 6/15 are proportional ratios.A Rate is the comparison (ratio) of two different units ofmeasure. Ex: miles per hour, gallons an hour, dollars a poundWe have used the Percent Proportion to solve percent problems,but there are other problems which do not involve percents.
Solving Proportions Example 1: Ben runs 4 miles in 45 minutes. If he only has 30 minutes, how far can he run? Set up a proportion and solve: 4 (miles) = x (miles) 45 (min.) 30 (min.)Example 2: Jill can jump rope 420 times in 2.5 minutes. At thisrate, how many can she do in 30 minutes?Set up a proportion and solve: 402(jumps) = x (jumps) 2.5 (min.) 30 (min.)
Proportions and Similar Figures. You can use proportions to find dimensions of objects that are difficult to measure directly…In the Figure below, ABC ~ (is similar) DFE. Find DE. C E Set up the 18 cm proportion: 21 cm x 15 = 21 D F 10 x 10 cm A B 15 cm
Example 1: Writing Ratios in Simplest FormWrite the ratio 15 bikes to 9 skateboards in simplestform. bikes = 15 Write the ratioskateboards 9 as a fraction. 15 ÷ 3 = = 5 Simplify. 9÷3 3 The ratio of bikes to skateboards is 5 , 5:3, or 5 to 3. 3
Example 1: Using RatiosThe ratio of the number of bones in a human’s ears to thenumber of bones in the skull is 3:11. There are 22 bones inthe skull. How many bones are in the ears? Write a ratio comparing bones in ears to bones in skull. Write a proportion. Let x be the number of bones in ears. Since x is divided by 22, multiply both sides of the equation by 22. There are 6 bones in the ears.
The ratio of games lost to games won for a baseball teamis 2:3. The team has won 18 games. How many gamesdid the team lose? Write a ratio comparing games lost to games won. Write a proportion. Let x be the number of games lost. Since x is divided by 18, multiply both sides of the equation by 18. The team lost 12 games.
The ratio of left handed to right handed students atNorth High is 2:21. North High has an enrollment of1058 students. How many left handers are at theschool?
Solving Rate ProblemsA rate is a ratio of two quantities with different units, such asRates are usually written as unit rates. A unit rate is a rate with asecond quantity of 1 unit, such as or 17 mi/gal. You canconvert any rate to a unit rate.
(1) Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.(2) Explain what this ratio tell us.
Rate Problems: Example 1Cory earns $52.50 in 7 hours. Find the unit rate. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is $7.50.
Converting Rates of Different UnitsA cheetah can run at a rate of 60 miles per hour in shortbursts. What is this speed in feet per minute? Step 1 Convert the speed to feet per hour. Step 2 Convert the speed to feet per minute. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The speed is 5280 feetfeet per hour. 316,800 per minute.
Example 2A cyclist travels 56 miles in 4 hours. What is the cyclist’s speedin feet per second? Round your answer to the nearest tenth,and show that your answer is reasonable. Step 1 Convert the speed to feet per hour. Change to miles in 1 hour. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the second quantity. The speed is 73,920 feet per hour.
(1) You have 150 different shirts. The ratio ofblue to black shirts is 20 . How many blackshirts do you have? 30