Equivalent ratios describe the same comparison with different numbers, like 2:3 and 8:12. You build one by multiplying or dividing both parts by the same number, never by adding. If both parts get the same treatment, the comparison stays fair, and that fair scaling is the whole skill.
I once watched a girl scale a juice recipe by doubling only the orange juice and leaving the water alone. Her drink tasted twice as strong, and she could not see why, because she had changed one part and not the other. Once both parts doubled together, the taste stayed right at every size.
What Is an Equivalent Ratio?
An equivalent ratio names the same comparison as another ratio, using bigger or smaller numbers. The ratios 2:3 and 8:12 are equivalent, because 8:12 divides by 4 to give 2:3, and both describe 2 parts of one thing for every 3 parts of another.
Think of a recipe as a promise about taste. The promise in 2:3 is two parts of one ingredient for every three parts of another, and any scaled copy keeps that promise. The numbers change, but the relationship between them never does.
A ratio in its simplest form is the smallest whole-number version of that promise. The ratio 12:18 simplifies to 2:3 when both parts divide by 6, and 2:3 is the version children should reach before they compare anything.
How Do You Find an Equivalent Ratio?
Find an equivalent ratio by multiplying or dividing both parts by the same nonzero number, and check the result by simplifying back. For 3:4, multiplying both parts by 5 gives 15:20, and dividing 15:20 by 5 returns 3:4, so the two ratios match exactly.
I teach one question for every step: what did the known part get multiplied or divided by? In a recipe with 3 cups of flour to 2 cups of sugar, 9 cups of flour means the flour part tripled, so the sugar part triples too, from 2 to 6 cups. The new ratio, 9:6, keeps the recipe honest.
Scaling down works the same way. For 18:24, both parts divide by 6 to give 3:4, and both parts divide by 3 to give 6:8. Every scaled copy is a true copy, as long as both parts share the same multiplier.
How Do You Check If Two Ratios Are Equivalent?
Check two ratios by simplifying each one to its simplest form, or by cross-multiplying and comparing the products. The ratios 8:12 and 6:9 both simplify to 2:3, and 8 × 9 equals 72 while 12 × 6 also equals 72, so they are equivalent.
Cross-multiplication is the quick check I give children for tests. Write the two ratios as fractions, multiply across the equals sign, and compare: if both products match, the ratios are equivalent, and if they differ, they are not. For 8:12 and 6:9, both products are 72, so the check passes.
Simplifying first is often faster with small numbers. Divide each ratio by the greatest common factor of its two parts, and compare the simplest forms. Children who simplify first rarely get fooled by big numbers that hide a simple comparison.
What Is a Ratio Table?
A ratio table lines up equivalent ratios in columns so the pattern stays visible and missing values are easy to find. For paint mixed as 2 cups of blue to 5 cups of white, the table runs 2:5, 4:10, 6:15 and 8:20, with each step multiplying both parts by the same number.
Ratio tables turn guessing into reading. To find a missing value, ask what the known part was multiplied by, then do the same to the other part: in 3:4 = 12:?, the first part went from 3 to 12, a times-4 step, so the second part is 4 × 4, or 16. Standard 6.RP.A.3 asks children to reason with tables of equivalent ratios, and the table is the tool that makes that reasoning visible.
Tables also settle comparisons. Two paint mixes, 2:5 and 3:7, look close until their tables meet at a shared value, and then the fairer comparison shows itself. I tell children to trust the table over the eye, because eyes guess and tables prove.
Common Mistakes I See With Equivalent Ratios
The first mistake is adding the same number to both parts. Adding 2 to both parts of 1:3 gives 3:5, but 3:5 is not equivalent to 1:3, because scaling needs multiplication, not addition. I ask one question every time: did both parts get multiplied, or merely topped up?
The second mistake is changing only one part. Doubling the flour and leaving the sugar alone changes the recipe, and doubling only the first part of any ratio breaks the comparison. Both parts must travel together, or the ratio tells a different story.
The third mistake is stopping before the simplest form. A child who compares 12:18 with 8:12 without simplifying sees two different pairs, while simplifying both to 2:3 shows they match. When the second part of a ratio becomes 1, the result is a unit rate, and the unit rates guide shows how that single-number form helps with prices and speeds.
Practise With the Free Worksheet
The practical ratio worksheet gives your child six pages of ratio practice, from simplifying ratios to sharing amounts and solving real-life problems. It uses the same fair-scaling habit on every page, so children build equivalent ratios, check them, and use them, one step at a time.
Try These Three Yourself
- Write two equivalent ratios for 4:5. (Answer: 8:10 and 12:15, because multiplying both parts by 2 gives 8:10 and by 3 gives 12:15.)
- Are 6:8 and 9:12 equivalent? (Answer: Yes. Both simplify to 3:4, because 6:8 divides by 2 and 9:12 divides by 3.)
- Find the missing value: 5:7 = 20:? (Answer: 28, because 5 went to 20 by multiplying by 4, so 7 × 4 is 28.)
FAQ
What does equivalent mean in a ratio?
It means the two ratios describe the same comparison. The ratios 2:3 and 8:12 are equivalent, because both say 2 parts of one thing for every 3 parts of another.
Can you multiply both parts by any number?
Yes, by any nonzero number. Multiplying both parts by 2, 3 or 10 keeps the comparison fair, but multiplying by zero would wipe both parts out, so zero never counts.
How is an equivalent ratio different from a unit rate?
An equivalent ratio keeps the same comparison at any size, while a unit rate is the version where the second part is 1. The ratio 2:3 scaled to 1 is a unit rate of 2/3 per 1.
Why can’t you add the same number to both parts?
Adding changes the relationship instead of scaling it. Adding 2 to both parts of 1:3 gives 3:5, which is a stronger mix, not the same comparison.
When do children learn equivalent ratios?
In Grade 6, as part of ratio and rate reasoning. It is the skill behind recipe scaling, map scales, and every proportion problem that follows.
Scale one ratio tonight. Multiply both parts by the same number, check it by simplifying back, and let fair scaling do the work. Find more Grade 6 guides on the Grade 6 hub.