SAT Math: Find part-to-whole and part-to-part ratios
32+ practice questions in Praczo
The concept, explained
- 1
A part-to-part ratio compares two parts of the same group (boys to girls). A part-to-whole ratio compares one part to the total (boys to all students).
- 2
If the ratio of boys to girls is 3:5, the total parts = 3 + 5 = 8. Then boys-to-total = 3:8 and girls-to-total = 5:8.
- 3
To get counts: multiply the ratio by the actual total. Boys = (3/8) · total, girls = (5/8) · total.
- 4
Always check whether the problem gives you a part-to-part or part-to-whole ratio before computing — they're easy to confuse.
- ✗ Treating a part-to-part ratio of 3:5 as if the first part is 3/5 of the whole. It's actually 3/8.
- ✗ Forgetting to add the parts together to find the total before computing fractions.
SAT-style practice
A bag contains red and blue marbles in the ratio 2:7. If there are 45 marbles total, how many are red?
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