Compare Quantities using Ratios
What is the definition of a ratio?
A ratio is a way to show a relationship or compare two numbers/quantities.
There are 3 bags of popcorn divided equally among 2 friends. How much of a bag does each student get?
2/3 bags of popcorn
Write an equivalent ratio for the following:
12:4
3:1, 6:2, 24:8, 36:12, 48:16, 60:20, or 72:24
What types of models can we use to solve unit price, constant speed, and converting measurement math problems? (name at least 2 for the 100 points)
tables
double number lines
bar models
what is 55% written as a fraction?
55/100
There are 17 boys and 32 girls. What is the ratio of girls to boys 3 different ways?
32:17
32 to 17
32/17
How could you model 5 students sharing 4 bags of popcorn equally? How much will each student get?
You could draw a picture showing 5 divided by 4.
Each students gets 4/5 of a bag of popcorn
Adrianna can read 7 pages in 10 minutes. At this rate, how many pages can she read in 25 minutes.
17.5 pages
All the comic books in the store are the same price. Vera buys 3 comic books for $7.50. How much does 1 comic book cost?
$2.50
There are 50 pages in Jordans coloring book. Jordan finished 30% of the pages. How many more pages does she have left to do?
Jordan has 35 pages left
Ben has a collection of 15 coins in quarters and dimes. There are 7 quarters and 8 dimes. Is the ratio of quarters to dimes the same as the ratio of dimes to quarters?
No, the order matters when you are writing ratios.
What is the definition of a unit rate? Give an example
The number in a rate that is being compared to 1.
ex: 35 miles per 1 hour
ex: walks 40 hours in 1 week
Which recipe uses a different ratio of cups of raisins to cereal than the rest?
a) Kate uses 3 cups of raisins for every 8 cups of cereal.
b) Mario uses 4 cups of raisins for every 12 cups of cereal.
c) Sato uses 6 cups of raisins for every 16 cups of cereal.
d) Den uses 9 cups of raisins for every 24 cups of cereal.
b
Hugos friends bought used books at the yard sale. Sonia paid $2.25, John paid $6.00 and Keisha paid $3.75. How many books did each friend buy?
Sonia bought 3 books, John bought 8 books, and Keisha bought 5 books.
Students sold 80% of their candy bars. They sold 48 candy bars in all. How many candy bars do they need to sell to sell 100%?
60 candy bars
Jordan is painting his kitchen. To get the color he wants, he mixes 2 parts red paint for every 5 parts yellow paint.
Write the ratio or parts red paint to parts yellow paint in 3 different forms.
2 to 5
2:5
2/5
2 for every 5
There are 50 campers at a day camp and 10 couselors. Write a ratio of campers to counselors as a fraction. Explain how to use equivalent fractios to write a related rate and unit rate. What does the unit rate tell you?
50/10
You can set up two fractions to find the unit rate and related rate
50/10 ?/1
See how the two fractions are related. The unit rate tells us that there are 5 campers to every 1 counselor.
Rosa earns $10 for every 3 hours that she works. Ralph earns $7 for every 2 hours that he works. Who earns more per hour? How much more does this person earn after 12 hours of work.
Ralph earns more per hour. After 12 hours, Ralph earns $2 more than Rosa
Alyssa and Caleb both drove 210 miles to the beach in separate cars. They left at the same time. They both drove at a constant speed. Alyssa drove 105 miles in 3.5 hours. Caleb drove 168 miles in 4 hours. Who arrived earlier? How much earlier?
Caleb arrived 2 hours before Alyssa
Josh got a 45/50 on his math test. Jasmine got a 30/40 on his test. What did they each score out of 100%? Who received a higher grade?
Josh= 90%
Jasmine = 75%
Josh received a higher score.
Piper is making iced tea. The recipe calls for 3 scoops of iced tea mix for every 5 scoops of water. Draw a diagram or model to show this ratio, and write the ratio of iced tea mix to water 3 different ways.
iced tea [] [] []
water [] [] [] [] []
3/5
3 to 5
3 : 5
3 for every 5
part a) what models can you use to find unit rate?
part b) you buy 3 tickets for $48 dollars. How much is 1 ticket?
part c) on another night, you buy 2 tickets for $36. How much is 1 ticket?
part d) If your brother collected $96 to buy 6 tickets, which night can he go to the show? Part b or c?
a) you can use a picture model or a double number line
b) $16 for 1 ticket
c) $18 for 1 ticket
d) you can buy tickets for part b
Gloria rides a bike 8 miles in 40 minutes. Nanette rides a bike 5 miles in 30 minutes. If they continue to ride at those speeds, who will be the farthest in 1 hour? How much farther?
In 1 hour, Gloria will travel 12 miles and Nanette will travel 10 miles. Gloria will travel 2 miles farther
Clair is measuring ingredients for recipes. She knows that there are 12 cups in 6 pints. She also knows that 4 quarts equals 16 cups. Which has more cups, 5 pints or 3 quarts? How many more cups?
There are 2 more cups in 3 quarts than there are in 5 pints.
Andreis grandfather offered to give him a gift of 35% of the amount of money he saved in one year. Andrei saved $140. How much did his grandfather give him as a gift?