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Arithmetic (Beginner) · Quick Reference
Ratios Cheat Sheet
In one line: a ratio compares two or more quantities, showing how much of one thing there is compared to another.
Key Ideas
1Writing a Ratio. Ratios can be written as a:b, a to b, or a/b.
2Simplifying Ratios. Divide all terms by their greatest common factor, just like simplifying a fraction.
3Equivalent Ratios. Ratios that represent the same relationship, made by multiplying or dividing all terms by the same number.
4Part-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).
5Dividing 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.
Worked Examples
Simplify the ratio 12:18.
2:3
A class has 15 boys and 20 girls. Write the ratio of boys to total students.
3:7
Divide $60 in the ratio 2:3.
$24 and $36
Practice Yourself
Simplify 10:15.
2:3
Simplify 8:20.
2:5
Are 3:4 and 9:12 equivalent?
Yes
Divide 50 in the ratio 2:3.
20 and 30