KA-0024Ratio as parts of a whole
4 points, difficulty 2 of 3Level 5–6about 75sRed and blue counters are in the ratio 3 to 5. There are 40 counters altogether. How many are red?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Add the parts of the ratio first.
2The strategy
A ratio of 3 to 5 splits the whole into 3 + 5 = 8 equal parts. Find what one part is worth, then take as many parts as the question asks for.
3The full solution
8 parts make 40, so one part is 5. Red is 3 parts, so 3 x 5 = 15.
Solution— no shortcut on this one
The ratio 3 to 5 means the counters split into 3 + 5 = 8 equal parts. Since 8 parts make 40 counters, one part is 40 divided by 8 = 5. Red takes 3 parts, so there are 3 x 5 = 15 red counters. Check: blue is 5 x 5 = 25, and 15 + 25 = 40. The transferable idea: add the parts before you divide anything.
Why this is on the test: Ratio questions are lost by dividing by one side of the ratio rather than by the total number of parts.