01 Key Concepts
Writing a Ratio
Ratios can be written as a:b, a to b, or a/b.
Simplifying Ratios
Divide all terms by their greatest common factor, just like simplifying a fraction.
Equivalent Ratios
Ratios that represent the same relationship, made by multiplying or dividing all terms by the same number.
Part-to-Part vs. Part-to-Whole
A part-to-part ratio compares two parts (boys:girls). A part-to-whole ratio compares a part to the total (boys:total students).
Dividing a Quantity in a Given Ratio
Add the ratio parts to find the total number of shares, then divide the quantity by that total to find the value of one share.
02 Solved Examples
Example 1 Simplify the ratio 12:18.
- Find the GCF of 12 and 18, which is 6.
- Divide both terms by 6: 12÷6=2, 18÷6=3.
Answer: 2:3
Example 2 A class has 15 boys and 20 girls. Write the ratio of boys to total students.
- Total students = 15 + 20 = 35.
- Ratio of boys to total = 15:35.
- Simplify by dividing by 5: 3:7.
Answer: 3:7
Example 3 Divide $60 in the ratio 2:3.
- Total shares = 2 + 3 = 5.
- Value of 1 share = 60 ÷ 5 = 12.
- First part = 2 x 12 = 24. Second part = 3 x 12 = 36.
Answer: $24 and $36
03 Practice Questions
1Simplify 10:15.
2:3
2Simplify 8:20.
2:5
3Are 3:4 and 9:12 equivalent?
Yes
4Divide 50 in the ratio 2:3.
20 and 30
5A recipe uses 2 cups flour to 1 cup sugar. Write this ratio.
2:1
📄 Ratios — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.