Is 3 : 4 the same strength as 5 : 7? The numbers are all different, so looking is not enough.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Make one quantity match
Scale both ratios until their first numbers agree, then compare what is left.
With those two
3 : 4 scaled by 5 is 15 : 20. 5 : 7 scaled by 3 is 15 : 21. Different, so not equivalent.
Which is stronger
At the same 15 of the first, one has 20 of the second and one has 21. Less of the second means a stronger mix.
Make one part match, then compare
Which is stronger, 3 : 2 or 4 : 3? Scale both so the second part matches: 9 : 6 and 8 : 6. With the same amount of the second thing, 9 beats 8, so 3 : 2 is stronger. This is finding a common denominator, applied to ratios.
Or reduce both to a unit
3 : 2 is 1.5 : 1 and 4 : 3 is about 1.33 : 1. Now they are directly comparable and 3 : 2 is clearly stronger. Reducing to "per one" is the most general method and it is what unit rates in the next chapter formalise.
Ratios as fractions
Writing 3 : 2 as 3/2 and 4 : 3 as 4/3 turns the comparison into an ordinary fraction comparison. Since 9/6 beats 8/6, the answer is the same. The three methods are the same idea in three costumes.
Check it makes sense
Before calculating, guess: 3 : 2 is one and a half parts of the first per part of the second, while 4 : 3 is only one and a third. So 3 : 2 should be stronger. When the calculation agrees with the estimate, you can trust it.
Step 2: Try It Yourself
Tap and try it out.
| Syrup | Water |
|---|---|
| 3 | 4 |
| 6 | 8 |
| 9 | 12 |
| 12 | 16 |
Every row is the same ratio. 3 to 4 is the same comparison as 15 to 20.
Step 3: Watch an Example
One step at a time.
Watch Leo Compare Two Jugs
Jug A is 2 : 3 syrup to water. Jug B is 3 : 5.
- Step 1
He scales A by 3 to reach 6 syrup: 6 : 9.
Step 4: Your Turn
Practice makes it stick.
Two Recipes
Problem 1 of 2
Scale 2 : 3 so the first number is 6. What is the second number?
The Comparison
Problem 2 of 2
Is 4 : 6 equivalent to 6 : 9?
Same or Not
1 of 4
Scale 3 : 5 so the first number is 12. What is the second?
2 of 4
Scale 5 : 2 so the first number is 20. What is the second?
3 of 4
Is 6 : 8 equivalent to 9 : 12?
4 of 4
Is 2 : 5 equivalent to 3 : 7?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Scale 4 : 7 so the first number is 12. What is the second?
What You Learned
- Two ratios are equivalent when one scales to the other.
- To compare, scale until one quantity matches in both.
- Then whichever has less of the other quantity is the stronger mix.