How to Combine Ratios
Learn how to combine ratios to form a 3-part ratio with clear examples. Let’s get started! 🚀

Video Lesson
Watch and learn the basics

Flashcards
Review key concepts visually
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🛎️ Same Middle Number
- If the middle number is already the same, combine the ratios directly.
- Example: if and , then .
🛎️ Different Middle Numbers
- If the middle numbers are different, make them the same first using the LCM.
- Example: and → make both have .
🛎️ Writing the Combined Ratio
- Once the middle numbers match, write all three parts together as one ratio.
- Example: and combine to give .
🛎️ What the Combined Ratio Means
- A combined ratio shows how three quantities compare at the same time.
- Example: means for every 24 of the first amount, there are 18 of the second and 45 of the third.
Practice Questions
Test your understanding
If and , what is ?
Correct! 🎉 +10 pointsNot quite right
is 3 in both ratios, so you can directly combine to get .
If and , what is ?
Correct! 🎉 +10 pointsNot quite right
Since is 7 in both ratios, you can directly combine them to get .
If and , what is ?
Correct! 🎉 +20 pointsNot quite right
To combine the ratios, first make the values equal by finding the LCM of 5 and 2, which is 10. Then scale each ratio: becomes , and becomes . So the combined ratio is .
In a bag, the ratio of blue balls to green balls is . The ratio of red balls to green balls is . What is the combined ratio of red:green:blue?
Correct! 🎉 +20 pointsNot quite right
Since green appears in both ratios, match that value first. The LCM of 4 and 2 is 4. Scale red:green to , and blue:green stays the same. Be careful with the order: red:green:blue = .
If and , what is ?
Correct! 🎉 +20 pointsNot quite right
To combine the ratios, match the value of since it appears in both ratios. The LCM of 6 and 4 is 12. Scale to and to . So the combined ratio is .
In a fruit blend, the ratio of apples to bananas is . The ratio of bananas to grapes is . If you used 25 apples, how many grapes are in the mix?
Correct! 🎉 +30 pointsNot quite right
Bananas appear in both ratios, so link them to make one full ratio: apples:bananas:grapes = . Since 25 apples represent the 5 parts for apples, divide 25 by 5 to find that one part equals 5. Grapes are 2 parts, so grapes.
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Interactive Activity
Combine two ratios into one using LCM
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