Grade 6 Math · Topic 01
A ratio compares two amounts of the same kind. If a fruit bowl has 4 apples and 6 oranges, the ratio of apples to oranges is 4 to 6. Ratios can be written three ways: with the word “to” (4 to 6), with a colon (4:6), or as a fraction (4/6). Order matters —“apples to oranges” is not the same as “oranges to apples.”
Lesson alignment: 6.RP.A.1 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Change the two amounts, then compare apples with oranges or compare one part with the whole group.
Think first: If you reverse the order, what changes in the comparison? What changes when a part is compared with the whole?
Swipe horizontally to see the full diagram.
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Read each step, then cover the explanation and see if you can explain why it works.
Worked example 1
Write the comparison in the order asked —boys to girls, so boys come first: 12 to 15, 12:15, or 12/15. To simplify, find the GCF of 12 and 15, which is 3. Divide both parts: 12 ÷ 3 = 4 and 15 ÷ 3 = 5. The simplified ratio is 4:5.
Answer: 12:15 = 4:5
Worked example 2
This is a part-to-whole ratio, so first find the whole. Total cups = 3 + 2 = 5. Sugar (the part we want) is 2 cups. So the ratio of sugar to the whole mixture is 2:5. It is already simplified because 2 and 5 share no factor besides 1.
Answer: 2:5
Work these on paper first. Open “Check” when you are ready to compare your answer.
2:3
2:3
2:5
2:3
3:4
4:7
1:3
2:3
In Ms. Garcia's class there are 10 students who walk to school and 15 who take the bus. Write the ratio of walkers to bus riders in simplest form, and the ratio of walkers to the total number of students.
Answer: Walkers : bus riders = 2:3; walkers : total = 2:5.
Walkers : bus riders is 10:15. Divide both by 5 to get 2:3. The total is 10 + 15 = 25 students, so walkers : total is 10:25 = 2:5.
A pet store has 24 goldfish and 32 guppies. Marcus says the ratio of goldfish to guppies is 3:4. Is he right? Explain.
Answer: Yes. 24:32 simplifies to 3:4.
Find the GCF of 24 and 32, which is 8. Divide both: 24 ÷ 8 = 3 and 32 ÷ 8 = 4, giving 3:4. Marcus is correct.
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