Doubling a recipe of 3 flour to 2 milk gives 6 flour to 4 milk. It tastes the same.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why the taste does not change
Both amounts grew by the same factor, so the comparison between them is untouched.
A ratio table
Writing the pairs in a table shows the pattern: 3:2, 6:4, 9:6, 12:8.
Both, or neither
Multiplying only one quantity changes the recipe. Both must be multiplied by the same number.
Scaling both parts keeps the ratio
3 : 2 is equivalent to 6 : 4, 9 : 6 and 30 : 20. Multiply both numbers by the same amount and the comparison is unchanged, exactly as multiplying the top and bottom of a fraction leaves its value alone.
A ratio table organises the scaling
Write the two quantities in two columns and generate rows: 3 and 2, 6 and 4, 9 and 6. Each row is an equivalent ratio. Tables make it easy to jump to the row you actually need, and they make the multiplicative pattern visible.
Simplest form
30 : 20 reduces to 3 : 2 by dividing both by 10. The simplest form uses the smallest whole numbers and is easiest to compare with other ratios. Finding it means dividing by the greatest common factor — the factor work from Grade 4, still earning its keep.
Testing whether two ratios are equivalent
Are 12 : 8 and 15 : 10 equivalent? Reduce both: 3 : 2 and 3 : 2. Yes. Reducing both to simplest form is the most reliable test, and it works no matter how large or awkward the original numbers are.
Step 2: Try It Yourself
Tap and try it out.
| Flour | Milk |
|---|---|
| 3 | 2 |
| 6 | 4 |
| 9 | 6 |
Every row is the same ratio. 3 to 2 is the same comparison as 9 to 6.
Step 3: Watch an Example
One step at a time.
Watch Leo Scale a Recipe
Leo has a 4 : 5 recipe and wants 20 of the first ingredient.
- Step 1
He works out what 4 was multiplied by: 20 ÷ 4 = 5.
Step 4: Your Turn
Practice makes it stick.
The Paint
Problem 1 of 2
2 : 3 blue to yellow. With 8 blue, how much yellow?
yellow
The Class
Problem 2 of 2
3 : 4 teachers to helpers. With 12 teachers, how many helpers?
helpers
Scale It
1 of 4
5 : 2 scaled by 3. What is the second number?
2 of 4
3 : 7. With 9 of the first, how many of the second?
3 of 4
6 : 8. Scaled down, what is the simplest first number?
4 of 4
Is 4 : 6 the same comparison as 6 : 9?
Step 5: Quick Check
Show what you know.
Question 1 of 2
4 : 5. With 16 of the first, how many of the second?
Question 2 of 2
To keep a ratio the same, what must you do?
What You Learned
- Equivalent ratios are the same comparison written with different numbers.
- Multiply both quantities by the same number.
- A ratio table lays the pattern out in rows.