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Rates, Ratios, & Mixture Problems (1.1/1.2)
Rates & Proportions (1.3)
Using Tables & Unit Rate (1.4)
Using Proportions (1.5)
Real World Unit Rate (1.6)
100
Is this an example of a rate or ratio? 120 miles / 3 hours
Rate
100
Define proportion.
A proportion is an equation that states that two ratios are equal.
100
Asharia is delivering newspapers. In 2 hours she delivers 40 newspapers. Newspapers 40 80 Hours 1 2 5 Complete the table.
20 newspapers/1 hour 80 newspapers/ 4 hours 100 newspapers/ 5 hours
100
What are the three ways to solve proportions?
scaling method, find the unit rate, or cross multiply
100
Calculate the unit rate: A bottle of 260 vitamins cost $11.75.
The unit rate is $0.05 per vitamin or about 22 vitamins per dollar.
200
Scale up to solve for x: (5 white daisies)/(8 orange daisies) = (X white daisies)/(32 orange daisies)
X = 20 white daisies
200
Scale up or down to determine the unknown quantity: (12 in )/(1 foot) = (36 in )/(X )
x = 3 feet
200
Rich is making fruit salad. The recipe calls for 6 cups of sliced peaches to 4 cups of halved grapes. Peaches (c) 6 Grapes (c) 1 2 3 4 Complete the table.
1.5 cups peaches/ 1 cup grapes 3 cups peaches/ 2 cup grapes 4.5 cups peaches/ 3 cup grapes
200
Solve for the variable & round to the nearest hundredth. 23/48 = 50/x
x= 104.3478... Round this. x = 104.35 (Answer)
200
Calculate the unit rate: A box of 400 business cards costs $16.25.
The unit rate is $0.04 per card or about 25 cards per dollar.
300
Scale down to determine the unit rate: (81 yards of fabric)/(9 dresses) = (X yards of fabric)/(X dress)
The unit rate is 9 yards of fabric / 1 dress
300
Scale up or down to determine the unknown quantity: (48 oz )/(3 lb) = (16 oz )/(X )
x = 1 lb
300
Determine the unit rate to solve. Brittany made 15 pairs of earrings in 3 hours. How many pairs of earrings could she make in 5 hours?
In 5 hours, Brittany can make 25 pairs of earrings.
300
Millie found out that 5 granola bars contain 700 calories. How many granola bars would it take to consume 280 calories?
2 granola bars
300
Estimate the unit rate to determine which is the better buy. Explain your reasoning. Round to the hundredths place. 13 vitamins for $1.23 or 30 vitamins for $2.50
It is better to buy 30 vitamins for $2.50. It is $0.08 per vitamin compared to $0.09 per vitamin for the other deal.
400
Lisa and Todd are making lemonade. Lisa's recipe calls for 5 parts lemon juice to 3 parts sugar syrup. Todd's recipe calls for 7 parts lemon juice to 5 parts sugar syrup. Which recipe has the stronger lemon flavor & why? Use ratios to answer this.
Lisa's recipe has the stronger lemon flavor because 15/24 > 14/24.
400
Use a rate and multiply to determine each measurement conversion: How many ounces are in 4 pounds?
64 oz
400
Use the unit rate to help you solve. Sam ran 4.5 miles in 1 hour and 30 minutes. How long did it take Sam to run 0.5 miles?
It took Sam 10 minutes to run 0.5 miles.
400
You are making lemonade to sell at the track meet. According to the recipe, you need 14 ounces of lemon juice for every 210 ounces of sugar water. You have 18 ounces of lemon juice. How many ounces of sugar water do you need?
270 ounces of sugar water
400
Estimate the unit rate to determine which is the better buy. Explain your reasoning. Round to the hundredths place. 26.7 ounces for $8.52 or 35.2 ounces for $13.55
It is better to buy the 26.7 ounces for $8.52, which is about $0.32 per ounce verses the other deal which came out to about $0.39 per ounce.
500
Dan makes snack mix to take with him on vacation. His favorite snack mix is 4 parts raisins and 5 parts peanuts. He wants to take 36 cups of snack mix. How many cups of raisins and peanuts does he need? # of cups in one part of the recipe: # of cups of raisins: # of cups of peanuts:
# of cups in one part of the recipe: (36 cups )/(9 total parts) = (4 cups)/(1 part) # of cups of raisins: (4 cups)/(1 part) = (X cups )/(4 parts) X = 16 cups raisins # of cups of peanuts: (4 cups)/(1 part) = (X cups )/(5 parts) X = 20 cups raisins
500
Convert the rate of 10 yards per 5 minutes to feet per hour.
360 feet per 1 hour
500
Jerry's grandma reminds him that he can burn calories from helping out around the house. General housecleaning can burn 470 calories every 2 hours. A) Complete the table. Time (hours) 1 2 3 4 5 Calories burned 470 B) What is the unit rate for this situation? C) How many calories can Jerry burn in 3.5 hours of housework without any breaks?
A) 1 hour/235 calories burned 3 hours/705 calories burned 4 hours/940 calories burned 5 hours/1175 calories burned B)235 calories per 1 hour C) Jerry can burn 822.5 calories if he does 3.5 hours of housework.
500
Malak is trying to decide which activity she wants to participate in today. She asks for the current number of people who have signed up for each activity. Activity Number of sign ups Snorkeling 20 Shuffle Board 6 Board Games 10 Beach Volleyball 24 a) How many guests have already signed up for activities? b) If a total of 90 guests are expected to sign up for activities, how many guests can the events coordinator expect to sign up for snorkeling?
a) 60 guests b) The events coordinator can expect 30 guests to sign up for snorkeling.
500
Erik and his mom need to purchase sleepers for his baby sister to wear. They can buy a 3-pack for $10.99 or a 2-pack for $7.99. Use unit rate to help Erik decide which package is the better buy. Explain your reasoning.
They should buy the 3-pack of sleepers because it has a lower unit rate of about $3.66 per sleeper. The other deal came out to be about $4.00 per sleeper.