HSPT: Ratios: split a total into parts
Learn to share a total by a ratio using equal parts, and to answer for the group the question asks about.
How do you use a ratio to find how many items are in one group?
Short answer
Add the ratio numbers to get the total parts. Divide the total by that number to find one part, then multiply by the group's share of parts.
Know first: Ratios as part to part, Division facts
Step 1 of 5
A ratio splits a total into equal parts
A ratio like 3:7 doesn't tell you how many things there are. It tells you how a total is shared: for every 3 of one kind, there are 7 of the other. Think of the total as 3 + 7 = 10 equal parts.
Once you know the total, divide it by the number of parts to get the size of one part. Then multiply by how many parts each group gets.
Step 2 of 5
Split the total by the ratio
Worked example: Cats and dogs at a shelter
The ratio of cats to dogs at a shelter is 3:7. There are 90 cats and dogs in all. How many are cats?
- A27
- B63
- C36
- D87
- 1
Count the parts
3 + 7 = 10 parts.
- 2
Find one part
90 ÷ 10 = 9 animals per part.
- 3
Find the cats
Cats get 3 parts: 3 × 9 = 27.
- 4
Check
Dogs: 7 × 9 = 63. And 27 + 63 = 90.
- 5
See why the other choices are there
63 is the number of dogs. 36 is how many more dogs there are than cats. 87 subtracts 3 from 90, using the ratio number as a count.
Answer
27 cats
| Group | Parts | Count |
|---|---|---|
| Cats | 3 | 27 |
| Dogs | 7 | 63 |
| Total | 10 | 90 |
Each part is 9 animals, so every count is 9 times its number of parts.
Wrong: Cats are 3/7 of the animals.
Right: Cats are 3/10 of the animals.
3:7 compares cats with dogs. The whole is 3 + 7 = 10 parts, so cats are 3 parts out of 10.
Step 3 of 5
Find one part first
Check yourself · Question 1
The ratio of boys to girls in a class is 4:3. There are 35 students. How many are girls?
Answer: B
There are 4 + 3 = 7 parts, so one part is 35 ÷ 7 = 5 students. Girls have 3 parts: 3 × 5 = 15. Check: boys are 4 × 5 = 20, and 20 + 15 = 35.
Trap answer: 20
Wrong group
- Why it looks right
- 20 comes from the correct method, and it is the first group named in the ratio.
- Why it's wrong
- The question asks for girls, the second number in 4:3. Girls get 3 parts, not 4.
- The right answer
- 15, because 3 × 5 = 15.
Check yourself · Question 2
A jar holds red and green marbles in the ratio 7:4. There are 15 more red marbles than green ones. How many marbles are in the jar?
Answer: C
The difference is 7 − 4 = 3 parts, and those 3 parts are 15 marbles, so one part is 5. The jar holds 7 + 4 = 11 parts: 11 × 5 = 55. Check: 35 red and 20 green differ by 15.
Common mistake
"In a 4:3 ratio, the girls are 3/4 of the class."
- Why it's tempting
- The two ratio numbers look like a fraction ready to use.
- Do this instead
- A ratio compares part to part. Add the ratio numbers to get the whole, then use parts out of that total.
Step 4 of 5
What to remember
Remember
- Add the ratio numbers to get the total number of parts.
- Divide the total by the parts to find one part, then multiply by each group's share.
- Check that the groups add back to the total, and answer for the group asked.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
How big was one part in the practice question, and which wrong choice is the other group?