Grade 6 Math · Topic 02
You can write the same ratio three ways, and choosing the right form makes problems easier. The word form (3 to 5) reads naturally. The colon form (3:5) is compact and great for comparisons. The fraction form (3/5) is perfect when you want to scale up, simplify, or do math with the ratio.
Lesson alignment: 6.RP.A.2 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Keep the same ordered comparison while switching between word, colon, and fraction forms.
Think first: How can you write the same ordered comparison with words, a colon, and a fraction?
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
The three forms are 9 to 12, 9:12, and 9/12. To simplify, divide both by the GCF of 9 and 12, which is 3: 9 ÷ 3 = 3 and 12 ÷ 3 = 4. The simplified ratio is 3 to 4, 3:4, or 3/4.
Answer: 3 to 4, 3:4, 3/4
Worked example 2
Write the fraction 20/35. The GCF of 20 and 35 is 5. Divide both: 20 ÷ 5 = 4 and 35 ÷ 5 = 7. The simplified fraction is 4/7.
Answer: 4/7
Work these on paper first. Open “Check” when you are ready to compare your answer.
2/5
1/3
2/5
3/4
3/4
5/8
3/5
3/4
The school basketball team scored 24 baskets in a game. Of those, 9 were three-pointers and the rest were two-pointers. Write the ratio of three-pointers to two-pointers in simplest form, in all three forms.
Answer: 3 to 5, 3:5, 3/5.
Three-pointers =9, two-pointers =24-9=15. The ratio is 9:15. The GCF of 9 and 15 is 3, so 9 ÷ 3 = 3 and 15 ÷ 3 = 5, giving 3:5.
In a parking lot, 14 cars are red and 35 are not red. Aiden writes the ratio of red cars to non-red cars as 2/5. Is he correct?
Answer: Yes, 14/35 simplifies to 2/5.
Find the GCF of 14 and 35, which is 7. Now divide: 14 ÷ 7 = 2 and 35 ÷ 7 = 5, so 14/35 = 2/5.
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