Worksheet · Ratios & Rates · 1 of 10
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Ratio Language
Look first. Count second. Order matters.
1.The garden has tulips (T) and daisies (D). Write the ratio of tulips to daisies three ways.
T
T
T
T
D
D
D
:
to
as a fraction:
2.Fill in the sentence frames for the garden above.
For every tulips, there are daisies.
The ratio of daisies to tulips is to .
The ratio of tulips to all flowers is : .
3.A fruit bowl holds 5 apples and 2 bananas. Write each ratio.
apples to bananas
bananas to apples
apples to all fruit
A ratio is a comparison. The numbers only mean something in order.
Worksheet · Ratios & Rates · 2 of 10
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Two Kinds of Ratios
Before you write a ratio, decide: is the second number a part or the whole?
1.A class has 12 sixth graders and 8 fifth graders. Label each ratio PP (part to part) or PW (part to whole), then write it.
sixth graders to fifth graders ratio
fifth graders to the whole class ratio
sixth graders to the whole class ratio
2.A team's ratio of wins to losses is 5 : 3. They played 8 games, no ties. Answer, then explain which ratio type you used.
Wins out of all games:
What fraction of the games did they win?
Because:
3.Tom says the ratio 5 : 3 above means the team won 5/3 of their games. What did Tom mix up?
Only part to whole ratios can act like fractions of the total.
Worksheet · Ratios & Rates · 3 of 10
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Equivalent Ratios
Multiply or divide both numbers by the same amount. Always both.
1.Grow each ratio. The multiplier is given.
3 : 4 ×2 → :
5 : 2 ×3 → :
1 : 6 ×10 → :
2.Shrink each ratio to its simplest form.
10 : 15 → :
12 : 4 → :
18 : 24 → :
3.Circle every ratio equivalent to 2 : 5. Show a check for one of your circles in the work space.
4 : 10
5 : 2
6 : 15
3 : 6
20 : 50
Equivalent ratios tell the same story with different numbers.
Worksheet · Ratios & Rates · 4 of 10
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Tape Diagrams
The tapes are drawn. Your job: find what one box is worth, then count.
1.Red to blue marbles is 2 : 3. There are 30 marbles in all.
red
blue
boxes in all:
one box = 30 ÷ =
red = blue =
2.Ana and Ben split $35 in the ratio 4 : 1.
Ana
Ben
one box =
Ana gets
Ben gets
Total ÷ total boxes = one box. Everything else is counting.
Worksheet · Ratios & Rates · 5 of 10
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Drawing Tape Diagrams
One box per part. Same size boxes. Label both tapes.
1.Granola uses oats to nuts in the ratio 5 : 2. A batch has 21 cups in all. Draw the tape, then find the cups of oats.
cups of oats =
2.A playlist has pop to rock songs in the ratio 3 : 4. There are 12 rock songs. Draw the tape, then find the total number of songs.
total songs =
Problem 2 gives a part, not the total. The tape shows you which boxes you know.
Worksheet · Ratios & Rates · 6 of 10
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Double Number Lines
Fill the missing tick labels. The lines must grow together.
1.A printer prints 6 pages every 2 minutes. Label every tick.
2.Use your finished lines. Answer without a calculator.
Pages printed in 6 minutes:
Minutes to print 30 pages:
Pages in 1 minute (the unit rate):
Zeros line up. Partners line up. That is the whole diagram.
Worksheet · Ratios & Rates · 7 of 10
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Ratio Tables
Every column must tell the same story. Write the multiplier you used above each column.
1.Trail mix: 3 cups of peanuts for every 2 cups of raisins.
| peanuts | 3 | 6 | 15 | ||
| raisins | 2 | 6 | 20 |
2.A car travels 120 miles on 4 gallons of gas.
| miles | 120 | 300 | ||
| gallons | 4 | 1 | 6 |
miles on 1 gallon =
3.Which column in problem 2 was the most useful to find first? Why?
The 1 column unlocks every other column.
Worksheet · Ratios & Rates · 8 of 10
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Ratios on the Coordinate Plane
Each column of a ratio table is a point (x, y). Plot them all.
1.Lemonade: 1 lemon per 2 cups of water. Finish the table.
| lemons (x) | 1 | 2 | 3 | 4 |
| water (y) | 2 |
3.What do you notice about your four points?
2.Plot each (x, y) pair.
Equivalent ratios land in a straight line through (0, 0). Every time.
Worksheet · Ratios & Rates · 9 of 10
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Unit Rates
Scale down until one side reads 1. Then the rate does the work.
1.Write each as a unit rate.
$18 for 3 pounds
per pound 180 miles in 3 hours
per hour 84 pages in 7 days
per day
per pound 180 miles in 3 hours
per hour 84 pages in 7 days
per day
2.Better buy. Store A: 6 juice boxes for $4.80. Store B: 8 juice boxes for $6.00. Find both unit prices, then circle the better buy.
Store A: each
Store B: each
A B
3.A recipe needs 2 cups of flour for 5 pancakes. How much flour for 20 pancakes? Use any tool from this packet.
flour = cups
"Per" always means for each 1.
Worksheet · Ratios & Rates · 10 of 10
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Choosing a Strategy
Tape diagram, double number line, ratio table, or unit rate. You pick. You defend.
1.Tickets cost $36 for 4 people. How much for 7 people? Solve with any tool, and name the tool you chose.
tool:
cost =
2.Find the flaw. Jade says: "Green to purple is 2 : 3. There are 10 green, so there are 11 purple, because 10 is 8 more than 2, and 3 + 8 = 11." Fix her thinking and find the real answer.
purple =
Ratios grow by multiplying, never by adding the same number to both sides.