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How to Combine Ratios

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

How to Combine Ratios - introduction visual

Video Lesson

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Flashcards

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Ratio combination showing a to b = 2 to 5 and b to c = 5 to 3, with final combined ratio a to b to c = 2 to 5 to 3.How to combine ratios when the middle term is different, a : b = 3 : 5 and b : c = 2 : 7, with final combined ratio a : b : c = 6 : 10 : 35Combined ratios calculation of water to cement (4:3) and cement to sand (2:5) to get final ratio 8:6:15.Example of combined ratios to find sand needed when water to cement is 4:3 and cement to sand is 2:5, with 24 buckets of water.

🛎️ Same Middle Number

  • If the middle number is already the same, combine the ratios directly.
  • Example: if a:b=2:5a:b = 2:5 and b:c=5:3b:c = 5:3, then a:b:c=2:5:3a:b:c = 2:5:3.

🛎️ Different Middle Numbers

  • If the middle numbers are different, make them the same first using the LCM.
  • Example: a:b=3:5a:b = 3:5 and b:c=2:7b:c = 2:7 → make both have b=10b = 10.

🛎️ Writing the Combined Ratio

  • Once the middle numbers match, write all three parts together as one ratio.
  • Example: 8:68:6 and 6:156:15 combine to give 8:6:158:6:15.

🛎️ What the Combined Ratio Means

  • A combined ratio shows how three quantities compare at the same time.
  • Example: 24:18:4524:18:45 means for every 24 of the first amount, there are 18 of the second and 45 of the third.

Practice Questions

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Interactive Activity

Combine two ratios into one using LCM

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