Worked example 1
Find a ratio equivalent to 3:7 whose first number is 21.
Ask the small question first: “3 times what gives me 21?” Answer: 7. So multiply both numbers by 7: 3 × 7 = 21 and 7 × 7 = 49. The equivalent ratio is 21:49.
Answer: 21:49
Grade 6 Math · Topic 03
Equivalent Ratios
Two ratios are equivalent when they describe the same comparison using different numbers. Doubling a recipe, scaling a drawing, or adjusting a paint mixture all create equivalent ratios. The trick: whatever you do to one number, do to the other.
Lesson alignment: 6.RP.A.3 · Take your time. You can return to this lesson whenever you need it.
Explore visually
See equivalent ratios three ways
Keep the ratio values fixed as you switch among bars, a table, and a double number line. Look for the same multiplier and matching values in every view.
Think first: If you multiply both quantities by the same factor, what relationship should stay unchanged? Where could you spot it in a bar, a table, and a number line?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Are 6/10 and 9/15 equivalent? Show your check.
Use the cross-product check to compare both ratios: 6 × 15 = 90 and 10 × 9 = 90. The cross-products are equal, so the ratios are equivalent. (You can also simplify both to 3/5.)
Answer: Yes, equivalent.
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- 2:5 = ________ : 20
Check
8
- 3:4 = 15 : ________
Check
20
- 7:9 = ________ : 27
Check
21
- 8:6 = 4 : ________
Check
3
- 5:11 = 25 : ________
Check
55
- 6:10 = ________ : 5
Check
3
- 12:18 = 2 : ________
Check
3
- 9:12 = ________ : 16
Check
12
Try this situation 1
A pancake recipe uses 2 cups of milk for every 3 cups of flour. If you use 12 cups of flour, how much milk do you need?
Show a worked solution
Answer: 8 cups of milk.
Set up equivalent ratios first so the matching parts are clear: 2:3 = ________:12. Since 3 × 4 = 12, multiply the milk side by 4 too: 2 × 4 = 8.
Try this situation 2
Maya paints a wall using 5 parts white for every 2 parts blue. She uses 35 ounces of white paint. How many ounces of blue paint does she need?
Show a worked solution
Answer: 14 ounces.
Start by writing the calculation clearly: 5:2 = 35:________. Since 5 × 7 = 35, multiply the blue side by 7: 2 × 7 = 14.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.