Name the whole before using a ratio or percentage
A ratio compares quantities in a stated order. A part-to-part ratio and a part-to-whole fraction are different descriptions. In a new workshop example, red and clear materials have an additive-volume ratio 2:7. A 900 mL batch contains nine equal parts, so each part is 100 mL; red accounts for 200 mL and clear for 700 mL. Red:clear is 2:7, but red:total is 2:9. Multiplying the total by 2/7 would silently change the meaning of the comparison. The ratio calculation assumes the exercise’s stated additive volumes. It is not a general claim that mixing real substances never changes volume. Keep assumptions attached to the example. Write units at each step:900 mL divided by 9 parts gives 100 mL per part. Multiplying by 2 parts returns 200 mL. If a question asks litres instead, convert the final unit deliberately; do not report the same numerical value with a different label. A percent is a ratio expressed per hundred. In an original attendance record, 120 people registered, 90 attended and 36 of the attendees completed a questionnaire. Questionnaire completion among attendees is 36/90=40%. Completion among all registrants is 36/120=30%. Both calculations are valid answers to different questions. The phrase after “of” often identifies the base, but the full wording decides which group is requested. Before calculating, write a sentence identifying the requested numerator and denominator. Afterward, check whether the result describes the same population and quantity. A numerator of attendees cannot answer a question about questionnaire completion merely because it produces a convenient percentage. These academic calculations use fictional data, not drug dosing, treatment or personal financial recommendations. ATI’s mathematical scope includes ratios, rates, percentages, measurement and data; this unit covers selected examples within that larger range.
An art demonstration requires 640 mL of a fictional pigment mixture. Blue and white volumes must be in a 5:3 ratio, with volumes assumed additive for this exercise. What volume of white pigment is required?
- There are 5+3=8 total parts. Each part is 640/8=80 mL, so white uses 3×80=240 mL. The ratio is blue:white, not white:total. This is original arithmetic under the explicitly additive-volume assumption.
Compare the other answer choices
Using 5−3=2 of the 8 total parts gives the difference between the colour amounts, not the three-part white share.
3/5 compares white with blue, not white with the combined mixture.
400 mL is the blue share; the question requests white.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
OpenStax Prealgebra 2 e §5.6 Ratios and RateATI TEAS Version 7 Content OutlineOpenStax Prealgebra 2 e §6.1 Understand Percent