Choose a method
Write conversion factors so the unwanted units cancel. For a part-to-part ratio, first add the parts when the question supplies the overall total.
Avoid this trap
A rate in units per minute is not a total. Area conversions square the length factor; mixed units cannot be combined until they are aligned.
Check and transfer
Use a small proportional table to show how both quantities change together. A direct proportional rule has a zero starting value.
Worked example with a numerical check
A mural uses blue and white paint in a 2:3 volume ratio. If the total is 20 liters, how many liters are blue? The total consists of five ratio parts. Blue accounts for two of those five parts. The requested value is 8.
Contrast and diagnose
A conveyor moves at 4 meters per minute. How many centimeters does it move in 2 minutes? Multiply speed by two minutes to get meters. Use one hundred centimeters per meter. The requested value is 800. An incorrect approach: Convert units but omit the second minute.
Transfer practice
4 identical packets contain 24 seeds altogether. How many seeds are in 6 such packets? Try first. Check: 36. Divide to obtain the seed count per packet. Multiply that unit rate by the requested number of packets.
A mural uses blue and white paint in a 2:3 volume ratio. If the total is 20 liters, how many liters are blue?
- The total consists of five ratio parts.
- Blue accounts for two of those five parts.
- The requested value is 8.
Compare the other answer choices
Report one ratio part rather than two.
Report total paint.
Treat part-to-part 2:3 as a part-to-total fraction.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Math specifications