1
Ratio language
Describe how two quantities are related using words, a colon, or fraction notation.
Worked examples + 20 practice questions
Grade 6 Ratios and Rates Practice Guide
Build a clear understanding of ratio language, equivalent ratios, rates, unit rates, percentages, and measurement conversions—then check progress with a complete practice set.
Covers the major Grade 6 ratio and rate expectations in the Common Core State Standards for Mathematics. State and district requirements may differ.
What students should master
Six connected ratio and rate skills
The ideas build from comparison to representation, calculation, and application.
2
Equivalent ratios
Scale both quantities by the same factor and recognize the same relationship in different forms.
3
Rates and unit rates
Compare quantities with different units and calculate the amount for one unit.
4
Representations
Use tables, tape diagrams, double number lines, equations, and graphs.
5
Percent reasoning
Interpret percent as a rate per 100 and solve percent-of-a-quantity problems.
6
Unit conversions
Use ratio reasoning to convert measurements while preserving the original quantity.
Concept 1
A ratio compares two quantities
The order of the quantities matters. Always name what each number represents.
Example: red and blue counters
A bag contains 6 red counters and 4 blue counters.
- Red to blue: 6 to 4, 6:4, or 6/4.
- Blue to red: 4 to 6, 4:6, or 4/6.
- Red to total: 6 to 10, 6:10, or 6/10.
Key distinction: A part-to-part ratio compares two groups. A part-to-whole ratio compares one group with the total.
Visual model
6 red : 4 blue = 3 red : 2 blue
Concept 2
Equivalent ratios describe the same relationship
Multiply or divide both quantities by the same nonzero number.
Scaling up
A paint mix uses 2 cups of blue paint for every 3 cups of white paint.
2:34:66:98:12
Each new pair is produced by multiplying both quantities by the same factor.
Simplifying
The ratio 18:24 can be divided by 6.
18 ÷ 6:24 ÷ 6= 3:4
The simplified ratio 3:4 represents the same relationship as 18:24.
| Blue paint | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| White paint | 3 | 6 | 9 | 12 |
Concept 3
A rate compares quantities with different units
A unit rate tells how much of the first quantity corresponds to one unit of the second quantity.
180 miles in 3 hours
180 ÷ 3 = 60 miles per hour
$15 for 5 notebooks
$15 ÷ 5 = $3 per notebook
6 cups for 8 servings
6 ÷ 8 = 0.75 cup per serving
Comparing two rates
Store A sells 8 granola bars for $6. Store B sells 12 granola bars for $8.40.
Store A$6 ÷ 8 = $0.75 per barUnit price: $0.75
Store B$8.40 ÷ 12 = $0.70 per barUnit price: $0.70
Better price: Store B, because $0.70 per bar is less than $0.75 per bar.
Concept 4
Represent the same ratio in more than one way
Strong ratio reasoning includes the ability to move among words, tables, diagrams, double number lines, equations, and graphs.
Ratio table
Three movie tickets cost $27.
| Tickets | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Cost ($) | 9 | 18 | 27 | 36 |
Double number line
The aligned positions show the same ticket-to-cost relationship.
01234
$0$9$18$27$36
Equation
Let c represent total cost and t represent the number of tickets.
c = 9t
The constant 9 is the unit rate: $9 per ticket.
Coordinate graph
Equivalent ratio pairs can be graphed as ordered pairs: (1, 9), (2, 18), (3, 27), and (4, 36).
Concept 5
Use ratio reasoning for percentages and conversions
A percent is a rate per 100. A conversion factor is a ratio equal to 1 that changes the unit without changing the quantity.
Percent of a quantity
Find 30% of 80.
30% = 30/100 = 0.300.30 × 80 = 24Answer: 24
Measurement conversion
Convert 5 feet to inches.
1 foot = 12 inches5 × 12 = 60Answer: 60 inches
Check the direction of the conversion. Multiplying by 12 changes feet to inches. Dividing by 12 changes inches to feet.
Six worked examples
Follow the reasoning step by step
Each example shows a different type of Grade 6 ratio or rate problem.
Example 1: Write a ratio
A class has 12 students wearing sneakers and 8 wearing sandals. Write the ratio of sneakers to sandals in simplest form.
- Start with 12:8.
- Divide both quantities by 4.
- 12 ÷ 4 : 8 ÷ 4 = 3:2.
Answer: 3:2
Example 2: Complete an equivalent ratio
Complete 5:7 = 20:__.
- 5 was multiplied by 4 to get 20.
- Multiply 7 by the same factor.
- 7 × 4 = 28.
Answer: 28
Example 3: Find a unit rate
A cyclist travels 42 miles in 3.5 hours. What is the average rate per hour?
- Divide distance by time.
- 42 ÷ 3.5 = 12.
Answer: 12 miles per hour
Example 4: Compare prices
A 6-pack of juice costs $4.50. A 10-pack costs $7.20. Which has the lower unit price?
- 6-pack: $4.50 ÷ 6 = $0.75 each.
- 10-pack: $7.20 ÷ 10 = $0.72 each.
- $0.72 is lower than $0.75.
Answer: The 10-pack
Example 5: Find a percent
A student answered 18 of 24 questions correctly. What percent is correct?
- Write the ratio 18/24.
- 18 ÷ 24 = 0.75.
- 0.75 × 100 = 75%.
Answer: 75%
Example 6: Convert units
A ribbon is 3.5 yards long. How many feet is that?
- 1 yard = 3 feet.
- 3.5 × 3 = 10.5.
Answer: 10.5 feet
Avoid these errors
Common ratio and rate mistakes
Reversing the order
The ratio of cats to dogs is not the same as the ratio of dogs to cats. Label both quantities.
Scaling one quantity only
Equivalent ratios require the same multiplication or division factor for both quantities.
Using the wrong division
To find dollars per item, divide dollars by items—not items by dollars.
Ignoring units
A unit rate should include both units, such as miles per hour or dollars per pound.
Treating percent as a decimal
Thirty percent is 30/100 or 0.30, not 30.
Converting in the wrong direction
Decide whether the new unit should produce a larger or smaller numerical value.
Independent practice
20 Grade 6 ratios and rates questions
Try the questions without opening the answer key. Show units and reasoning where appropriate.
A. Ratios and equivalent ratios
- A basket contains 9 apples and 6 oranges. Write the ratio of apples to oranges in simplest form.
- Write the ratio 4 to 11 in two other forms.
- Complete the equivalent ratio: 3:5 = 18:__.
- Are 8:12 and 14:21 equivalent? Explain briefly.
- A recipe uses 2 cups of rice for 5 servings. How many cups are needed for 20 servings?
B. Rates and unit rates
- A car travels 210 miles in 3.5 hours. Find the average speed.
- Six notebooks cost $10.50. Find the cost per notebook.
- A printer produces 168 pages in 7 minutes. Find the unit rate.
- Store A sells 5 pounds of rice for $8.25. Store B sells 8 pounds for $12.40. Which store has the lower price per pound?
- A faucet fills 15 gallons in 6 minutes. At the same rate, how many gallons will it fill in 10 minutes?
C. Percent and conversions
- Find 25% of 68.
- Thirty-six is what percent of 48?
- A $40 backpack is discounted by 15%. How much is the discount?
- Convert 7.5 feet to inches.
- Convert 96 ounces to pounds. Use 16 ounces = 1 pound.
D. Multi-step applications
- A school bus uses 9 gallons of fuel to travel 126 miles. At the same rate, how far can it travel on 14 gallons?
- A map scale is 1 inch to 24 miles. Two towns are 3.75 inches apart on the map. What is the actual distance?
- A paint mixture uses blue and white paint in the ratio 3:7. If 28 cups of white paint are used, how many cups of blue paint are needed?
- A runner completes 5 laps in 12 minutes. At the same rate, how long will 8 laps take?
- A store buys pencils for $0.18 each and sells them for $0.30 each. What percent of the selling price is the profit?
Finished? Open the answer key only after completing all four sections.
Go to the Answer KeyCheck your work
Practice answer key
Use the answers to identify the exact step that needs review. A wrong answer can come from the ratio setup, scaling, division, units, or calculation.
Question 13:2
9:6 simplifies by dividing both quantities by 3.
Question 24:11 and 4/11
The words, colon, and fraction forms represent the same ordered comparison.
Question 330
3 was multiplied by 6, so 5 must also be multiplied by 6.
Question 4Yes
8/12 = 2/3 and 14/21 = 2/3.
Question 58 cups
20 servings is 4 times 5 servings, so 2 × 4 = 8.
Question 660 miles per hour
210 ÷ 3.5 = 60.
Question 7$1.75 per notebook
$10.50 ÷ 6 = $1.75.
Question 824 pages per minute
168 ÷ 7 = 24.
Question 9Store B
Store A: $1.65/lb. Store B: $1.55/lb.
Question 1025 gallons
15 ÷ 6 = 2.5 gallons per minute; 2.5 × 10 = 25.
Question 1117
0.25 × 68 = 17.
Question 1275%
36 ÷ 48 = 0.75 = 75%.
Question 13$6
0.15 × $40 = $6.
Question 1490 inches
7.5 × 12 = 90.
Question 156 pounds
96 ÷ 16 = 6.
Question 16196 miles
126 ÷ 9 = 14 miles per gallon; 14 × 14 = 196.
Question 1790 miles
3.75 × 24 = 90.
Question 1812 cups
7 parts corresponds to 28, so each part is 4; 3 × 4 = 12.
Question 1919.2 minutes
12 ÷ 5 = 2.4 minutes per lap; 2.4 × 8 = 19.2.
Question 2040%
Profit is $0.12. Then $0.12 ÷ $0.30 = 0.40 = 40%.
Choose the next step
- Missed ratio-language questions: review order, labels, and part-to-part versus part-to-whole.
- Missed equivalent-ratio questions: practice multiplying or dividing both quantities by the same factor.
- Missed unit-rate questions: write the desired units before dividing.
- Missed percent questions: rewrite the percent as a decimal or a fraction over 100.
- Missed application questions: identify the two quantities, units, and constant rate before calculating.
Focused review
A five-session ratios and rates study plan
Ratio language
Write, label, reverse, and simplify ratios.
Equivalent ratios
Use scaling, tables, and missing-value problems.
Unit rates
Calculate and compare speed, price, and productivity.
Percent & conversions
Connect rates per 100 and measurement relationships.
Mixed applications
Solve multi-step problems and explain the representation used.
Need a broader Grade 6 review?
Use the free diagnostic to identify gaps, then practice all major Grade 6 domains with the complete revision pack.
Frequently asked questions
Grade 6 ratios and rates FAQ
What is a ratio in Grade 6 math?
A ratio compares two quantities by division. It can be written with words, a colon, or a fraction, such as 3 to 5, 3:5, or 3/5.
What is the difference between a ratio and a rate?
A ratio compares any two quantities. A rate is a ratio that compares quantities measured in different units, such as miles per hour or dollars per item.
What is a unit rate?
A unit rate is a rate expressed for one unit of the second quantity. For example, 180 miles in 3 hours is 60 miles per 1 hour.
How do students find equivalent ratios?
Multiply or divide both quantities in the ratio by the same nonzero number. Ratio tables, tape diagrams, double number lines, and equations can help show the relationship.
How are percentages connected to ratios?
A percent is a rate per 100. For example, 35 percent means 35 for every 100, which can be written as 35/100.
What should a Grade 6 student practice after learning ratios?
Students should practice explaining ratio language, generating equivalent ratios, finding unit rates, comparing rates, solving percent problems, converting measurement units, and choosing representations for real-world situations.
Standards reference and scope
This guide is organized around the Grade 6 Ratios and Proportional Relationships domain in the Common Core State Standards for Mathematics, including ratio concepts, unit rates, equivalent-ratio representations, real-world rate problems, percentages, and measurement conversions. GradeCove is an independent educational publisher and is not endorsed by the Common Core State Standards Initiative. State, district, school, and curriculum expectations may differ.