Lesson 2 of 5 | Arithmetic Methods
Ratios, Proportions, and Unit Consistency
Arithmetic Methods
Core idea
A ratio compares like quantities after their units agree. Preserve the order: a:b is not interchangeable with b:a.
Method
Represent shares as ak and bk. If a total is known, solve (a+b)k = total. For a proportion a/b = c/d, cross-multiply only after checking that denominators are non-zero and the paired quantities describe the same relationship.
Worked example
Red and blue tokens are in the ratio 3:5 and total 64. Eight equal parts represent 64, so one part is 8. Counts are 24 and 40. Check: 24+40=64 and 24:40 reduces to 3:5.
Common traps
- Comparing metres with centimetres before conversion.
- Treating a ratio as a difference.
- Dividing the total by one ratio term rather than the sum of terms.