A recipe with 3 cups of flour for every 2 cups of milk has a ratio of 3 to 2.
Ratio compares two amounts, saying how much of one goes with the other.
Step 1: Picture It
Start with something you already know.
A bead bracelet
- A bracelet repeats one pattern: 3 red beads, then 1 white bead.
- A short bracelet might have 6 red beads and 2 white.
- A long one might have 30 red beads and 10 white.
- Every bracelet still has 3 red for every 1 white.
A ratio is the pattern, not the count: 3 red for every 1 white.
Order matters too: red to white is 3 : 1, but white to red is 1 : 3.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Priya makes juice. One batch uses 2 cups of mango and 3 cups of apple. She makes 4 batches. How many cups of juice does she have in all?
cups
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Three ways to write it
The same ratio is written 3 to 2, or 3 : 2, or 3/2. All three are read "three to two".
Order matters
3 : 2 flour to milk is not the same recipe as 2 : 3. Say which quantity comes first.
Part to part, part to whole
With 3 cups of flour and 2 of milk there are 5 cups in all, so flour to total is 3 : 5.
Step 3: Try It Yourself
The table, the line, and the counters all say the same thing.
| Flour | Milk |
|---|---|
| 3 | 2 |
| 6 | 4 |
Every row is the same ratio. 3 to 2 is the same comparison as 6 to 4.
Step 4: In Real Life
Mixing paint
A painter mixes 2 parts blue to 1 part white for sky blue. 2 to 1. The ratio names the mix, and any bucket size follows it.
Step 5: Watch an Example
One step at a time.
Watch Ana Read a Ratio
A box holds 8 red pens and 12 blue pens.
- Step 1
Ana is asked for red to blue. Red is named first, so the red count goes first: 8 to 12.
Watch Leo Read a Ratio
A parking lot holds 9 cars and 6 vans. Leo writes the first line, and you write the rest.
- Step 1
The lot holds 9 cars and 6 vans, and Leo is asked for vans to cars, and then vans to total.
Step 6: Your Turn
Practice makes it stick.
Market Money
Problem 1 of 17
Maya saved some of her market money and spent the rest. Write the ratio of the money saved to the money earned in all. What is the second number, in dollars?
dollars
The Ribbon
Problem 2 of 17
One ribbon is cut into a blue piece and a green piece. Ribbon costs $2 a foot. Write the ratio of the blue piece's cost to the green piece's cost. What is the second number, in dollars?
dollars
Read the Comparison
Write the two counts in the order the question names them. Check whether the second number is a part or the whole.
Problem 3 of 17
4 cats and 6 dogs. Cats to total: what is the second number?
Problem 4 of 17
9 boys and 11 girls. Girls to boys: what is the first number?
Problem 5 of 17
3 red counters and 9 blue counters. Red to total: what is the second number?
Problem 6 of 17
7 forks and 5 spoons. Spoons to forks: what is the second number?
Problem 7 of 17
5 apples and 4 pears. Apples to total: what is the first number?
Whose Step?
One line in each page is a slip. Find it, then fix it.
Problem 8 of 17
Dev was asked for red to total, for a box of 5 red pens and 7 blue pens. One line is a slip. Which?
Dev's answer for: 5 red pens, 7 blue pens, red to total
- 15 red pens, 7 blue pens
- 25 + 7 = 12 pens in all
- Answerred to total = 5 : 7
Problem 9 of 17
What should Dev's line 3 read?
Problem 10 of 17
Noor was asked for cars to buses, in a yard with 3 buses and 8 cars. One line is a slip. Which?
Noor's answer for: 3 buses, 8 cars, cars to buses
- 13 buses, 8 cars
- 2cars are named first
- Answercars to buses = 3 : 8
Problem 11 of 17
What should Noor's line 3 read?
Problem 12 of 17
Sam was told a club has girls to boys in the ratio 3 : 2, and asked how many girls it has. One line is a slip. Which?
Sam's answer for: girls to boys is 3 : 2. How many girls?
- 1girls to boys = 3 : 2
- 23 + 2 = 5 parts
- Answerso the club has 3 girls
Problem 13 of 17
What should Sam's line 3 read?
Pick the Move
Decide the first move before you make it. The question names what goes where.
Problem 14 of 17
A bowl holds 4 plums and 6 pears. You need the plums to total ratio. What is the first move?
Problem 15 of 17
A bag holds 12 marbles. 5 of them are red and the rest are blue. You need the red to blue ratio. What is the first move?
Same Comparison?
Decide what is true of the situation without changing any numbers.
Problem 16 of 17
A mix uses 4 cups of oats for every 3 cups of raisins. Select every statement that is true of this mix.
Problem 17 of 17
A box holds 6 red pens and 4 blue pens. Select every ratio that is written correctly for this box.
Step 7: Quick Check
Show what you know.
Question 1 of 2
6 pens and 9 pencils. Pens to total: what is the second number?
Question 2 of 2
What does a ratio do?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
A bag holds red and blue counters. For every 2 red there are 3 blue. The bag holds 15 counters in all. How many are red?
red counters
Stretch 2 of 2
A bowl holds only apples and pears. Apples to total is 3 : 7. What is the first number in the pears to total ratio?
What You Learned
- A ratio compares two amounts.
- It can be written 3 to 2, 3 : 2, or 3/2.
- The order matters, and part-to-whole is a different comparison from part-to-part.
For the grown-up
The misconception this lesson targets is that a ratio counts. A child who reads 3 : 2 as "there are three and there are two" is right by accident when the amounts happen to be 3 and 2, and wrong every other time: 30 and 20 have the same ratio. Two smaller slips ride alongside it. The first is order: 3 : 2 and 2 : 3 describe different mixes, so the labels matter as much as the numbers. The second is part-to-part against part-to-whole, where 3 girls and 2 boys give 3 : 2 one way and 3 : 5 the other, and only the wording says which is wanted. Asking "three of what, compared with what?" out loud catches all three.
A ratio compares, it does not count — A ratio of 3 : 2 says that for every 3 of the first thing there are 2 of the second. It does not say there are exactly 3 and 2 — there might be 30 and 20, or 300 and 200. What a ratio fixes is the relationship, not the amounts.
Order matters — A paint mix of 3 : 2 red to blue is not the same as 2 : 3 red to blue. The first is redder. Always write down which quantity each number refers to, because a ratio with its labels lost is worse than useless — it is confidently wrong half the time.
Part to part, and part to whole — If a class has 3 girls to 2 boys, the part-to-part ratio is 3 : 2 and the class has 5 parts altogether. So girls are 3 out of 5 of the class, which is 3/5. Ratios and fractions are related but ask different questions, and confusing them is a real source of error.
Where ratios show up — Recipes, map scales, paint mixing, gear ratios, exchange rates, screen aspect ratios and concrete mixes are all ratios. In every case what matters is the relationship holding as the quantities scale. That is why ratios earn a whole chapter.
What the two numbers stand for — 3 cups of flour to 2 cups of water: a ratio of 3 : 2. It does not say there are 3 cups. It says for every 3, there are 2. Double the recipe: 6 : 4. Same taste. A ratio fixes the relationship, not the amount.