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Ratios and Proportions Gr. At 5 Jerry was making two different types of cookies. One recipe 6 needed ¾ C of sugar and the other needed 2/3 C of sugar. How much sugar did he need to make both recipes? Mary ran 3 1/6 miles every week for 4 weeks in order to meet her monthly goal. If the first day of the first week she ran 1 ¾ miles, how many more miles does she still need to run the first week? Write an equation and solve. Two afterschool clubs are having pizza parties. For the Math Club, the teacher will order 3 pizzas for every 5 students. For student council, the teacher will order 5 pizzas for every 8 students. Since you are in both groups, you need to decide which party to attend. How much pizza would you get at each party? If you want to have the most pizza, which party should you attend? “The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every 2 wings there was 1 beak.” “This recipe has a ratio of 3 cups of flour to 4 cups of sugar so there is a ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” “If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were the lawns being mowed?” “Jacks car can go 486 miles on 17 gallons of gas. What is the unit rate of miles per gallon?” “A grocery store sign indicates that bananas are 6 for $1.50, and a sign by the oranges indicates that they are 5 for $3.00. Find the total cost of buying 2 bananas and 2 oranges.” “Jeremy has two 7 foot long boards. He needs to cut pieces that are 15 inches long from the boards. What is the greatest number of 15 inch pieces he can cut from the two boards?” Accelerated
Subtract fractions with unlike denominators.
4 ¼ ‐ 2 1/3 4 3/12 – 2 4/12 3 5/ 12 – 4 4/12 = 1 11/12 Multiply mixed numbers. 3 1/5 x 1 3/8 16/5 x 11/8 = 176/40 = 4 16/40 = 4 2/5 Divide mixed numbers. 6 3/5 / 2 2/10 33/5 / 22/10 = 3 Cheetahs are the fastest land animals. They can chase prey by running at speeds of 60 miles per hour. A cheetah can only maintain top speeds for a short time. If a cheetah runs 1 mile in 60 seconds show how far the cheetah will run in 210 seconds. (3 ½ miles) Create three different drawings showing a number of circles and triangles in which the ratio of circles to triangles is 2:3. `The ratio of red jelly beans to yellow jelly beans in a dish is 2:3. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish. (36 jelly beans) Honors You are having a party and 36 friends have been invited. You surveyed the group and found out that 4/9 of them like Jolly Ranchers and 5/12 of them like Hershey’s Kisses. You want to get the candy liked by most guests. Which candy would you buy and why? Also figure out how many people had no opinion. Show all work and write and explanation. What percent of English words have more consonants than vowels? Carry out an experiment using words from at least two different sources. If a car can travel 300 km on 40 liters of gas, can it travel 450 km on a tank of 50 liters? Suppose a 10” pizza costs $5. Using a proportion based on the diameters of the pizzas, what should a 15” pizza cost? Ratios and Proportions 7 If a person walks ½ mile in each ¼ hour, compute the unit rate Given similar figures, use proportions to find the
8 as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour. Appliances at Discount City Store are on sale for 70% of the original price. Eli has a coupon for an 18% discount on the sale price. If the original priced of a microwave oven is $500, how much will Eli pay for the oven before tax? David is making his own strawberry yogurt. In his mixture, the number of strawberries is proportional to the amount of milk in cups. David uses 4 cups of milk for every 14 strawberries in his mixture. Write an equation to represent the relationship between the number of strawberries and the number of cups of milk David uses. Solving proportions‐ If 5 out of 15 people want water for dinner, how many people would you expect to have water out of 45 people? Using graphs to represent proportionality‐Graph solutions to how much money is earned babysitting for $10/hr. A trainer for a professional football team keeps track of the amount of water players consume throughout practice. The trainer observes that the amount of water consumed is a linear function of the temperature on a given day. The trainer finds that when it is 90 degrees F, the players consume about 220 gallons of water, and when it is 76 degrees F the players consume about 178 gallons of water. Write a linear function to model the relationship between the gallons of water consumed and the temperature. Explain the meaning of the slope in the context of the problem. value of the missing side. If triangle ABC is similar to triangle DEF and line segment AB=12, line segment DE=20, and line segment DF=16, what is the length of line segment AC? Using graphs to determine if given data is proportional. Evaluate equations in the form of y=kx and y=mx+b Given the slope and point on a line, use proportions to write an equation for the line in the y=mx+b form. Slope =3/4 containing point (8,2). Use direct variation equations. How does y=10x+20 differ from y=10x. Use of graphs, tables, examples to explain.