What is a ratio?
A ratio compares two amounts. “For every 2 wings there was 1 beak” is the ratio 2 : 1. You can say it as “2 to 1” or write it with a colon, as 2 : 1.
Source Common Core State Standards · Grade 6, understand the concept of a ratio (6.RP.A.1) ↗
How to calculate a ratio
Here it is with your numbers:
- Find the biggest number that goes into 12 and 8: 4.
- Divide each number by 4: 12 : 8 becomes 3 : 2.
It means for every 3 of the first, there are 2 of the second. The first makes up 60% of the whole and the second 40%.
Two ratios are equivalent when every number in one is multiplied by the same amount to get the other. That is why simplifying works, and why a missing number can be found by multiplying across and dividing.
Source Illustrative Mathematics · Grade 6, Unit 2, Lesson 5: Defining equivalent ratios ↗
Ratios equivalent to 3 : 2
| Multiply by | Equivalent ratio |
|---|---|
| × 1 | 3 : 2 |
| × 2 | 6 : 4 |
| × 3 | 9 : 6 |
| × 4You | 12 : 8 |
| × 5 | 15 : 10 |
| × 6 | 18 : 12 |
| × 7 | 21 : 14 |
| × 8 | 24 : 16 |
Ratio examples
| Example | Answer |
|---|---|
| 3 cups of flour to 4 cups of sugar. How much flour per cup of sugar? | 3/4 cup |
| $75 for 15 hamburgers. What does each cost? | 5 : 1, so $5 |
Source Common Core State Standards · Grade 6, unit rates (6.RP.A.2) ↗
| Example | Answer |
|---|---|
| It took 7 hours to mow 4 lawns. How many lawns in 35 hours at that rate? | 20 lawns |
Source Common Core State Standards · Grade 6, rate problems (6.RP.A.3.b) ↗
FAQs
How do you calculate a ratio?
Write the two amounts as A : B, then divide both numbers by the biggest number that goes into them. For example, 12 : 8 divides by 4 and becomes 3 : 2. To find a missing number, multiply across and divide.
Source Illustrative Mathematics · Grade 6, Unit 2, Lesson 5: Defining equivalent ratios ↗
How do you calculate a ratio between two numbers?
Put them side by side with a colon, like 3 : 4. To see how much of the first there is for every 1 of the second, divide the first by the second. 3 cups of flour to 4 cups of sugar is 0.75 cup of flour for each cup of sugar.
Source Common Core State Standards · Grade 6, unit rates (6.RP.A.2) ↗
How do you simplify a ratio?
Find the biggest number that divides both numbers exactly and divide each by it. 75 : 15 divides by 15 and becomes 5 : 1. Ratios stay equivalent when you multiply or divide every number by the same amount.
Source Illustrative Mathematics · Grade 6, Unit 2, Lesson 5: Defining equivalent ratios ↗
Sources
- Common Core State Standards: Grade 6, understand the concept of a ratio (6.RP.A.1)
- Common Core State Standards: Grade 6, unit rates (6.RP.A.2)
- Common Core State Standards: Grade 6, rate problems (6.RP.A.3.b)
- Illustrative Mathematics: Grade 6, Unit 2, Lesson 5: Defining equivalent ratios