Simplifying ratios
A ratio compares two or more quantities. To simplify a ratio, divide every part by the same greatest common factor so the relationship stays the same but the numbers become smaller.
Method
- Write the ratio clearly.
If the ratio is given with a colon, keep the order the same: for example,
a:b.
- Find a common factor.
Look for the largest number that divides each part exactly.
- Divide every term by that factor.
Do this for all parts of the ratio.
- Write the simplified ratio.
Keep the same form as the original unless the question asks for another format.
Example idea
If both terms can be divided by 2, then dividing both by 2 gives an equivalent, simpler ratio.
Check your answer
- Each part should have no common factor greater than 1.
- The simplified ratio should represent the same relationship as the original.
- If you multiply the simplified ratio back by the factor you used, you should recover the original ratio.
Be careful not to divide only one part. Every term in the ratio must be reduced by the same amount.