Track which quantity a fraction acts on
A fraction of a quantity is a multiplication relationship. In a sequence, the quantity can change before the next fraction is applied. Label the base at every step: original inventory, quantity removed, remaining inventory, and the requested final quantity. A fraction is not a fixed number of objects until its base is known. Worked example: a studio starts with 60 blank cards, gives away one quarter, and decorates two fifths of those left. The first removal is 15, so 45 remain. The decorated portion is(2/5)×45=18, and the undecorated remainder is 45−18=27. Applying two fifths to the original 60 would answer a different question. Reporting 18 would confuse the decorated part with the remaining part. A compact check writes the retained fractions as a product: 60×(3/4)×(3/5)=27. This is a second route to the same answer, not a second counted diagnostic family. Keep whole-number units attached to the result and ask whether the answer is less than the quantity available at that step. The guide uses ordinary stock and artwork contexts; it provides no clinical dose or treatment calculation. Calculator availability for your actual exam remains a question for your institution and testing instructions.
A workshop has 72 unmounted prints. It sends one third of them to an exhibition. It then mounts three eighths of the prints that remain. How many prints are still unmounted at the workshop?
- One third of 72 is 24, leaving 48 at the workshop. Three eighths of 48 is 18 newly mounted. The unmounted remainder is 48−18=30 prints. The second fraction uses 48 as its base, not 72.
Compare the other answer choices
This is the number newly mounted, not the number still unmounted.
This subtracts three eighths of the original 72 from the remaining 48, even though the second fraction applies to the remainder.
This subtracts three eighths of 72 and ignores the prior exhibition allocation.
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.
NROC/LibreTexts—Multiplying Fractions and Mixed Numbers