November 2026 - Multiplying & Dividing Fractions Study Guide for nursing students in
Multiply straight across, numerator by numerator and denominator by denominator. To divide, invert the second fraction and multiply — keep, change, flip. No common denominator is needed for either, which is what makes these the easiest fraction operations to get right under time.
Try 4 short questions throughout this guide. Check each answer to learn from the explanation.
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Multiplying
Three steps, and the middle one is optional but saves work.
Convert any mixed numbers
Cancel common factors
Multiply across
Simplify
Cancelling before you multiply is worth the habit. For 4/9 × 3/8, cancel the 4 with the 8 (leaving 1 and 2) and the 3 with the 9 (leaving 1 and 3), which reduces the whole problem to 1/3 × 1/2 = 1/6. Multiplying first gives 12/72, the same answer after a harder simplification.
One more thing worth knowing: multiplying by a fraction smaller than 1 makes a number smaller. If a question asks for a fraction *of* something, the answer must come out below the original, which is a useful sanity check on the answer choices.
Dividing: keep, change, flip
Division by a fraction is multiplication by its reciprocal. The rule is mechanical and it always works.
Keep the first fraction exactly as it is.
Change the division sign to multiplication.
Flip the second fraction — swap its numerator and denominator.
Then multiply as usual, cancelling first if you can.
Question 1 of 4
What is 2/5 × 3/4?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: B. 3/10
Multiplying across gives 6/20, which simplifies to 3/10. 6/20 is offered as the unsimplified trap, 5/9 comes from adding numerators and denominators, and 8/15 is the result of cross-multiplying as if solving a proportion.
A division that looks harder than it is
Worked example
A container holds 3/4 of a litre of solution. Each dose is 1/8 of a litre. How many doses does the container hold?
The question is "how many 1/8s fit into 3/4", which is 3/4 ÷ 1/8.
Keep 3/4, change to multiplication, flip 1/8 to 8/1.
3/4 × 8/1 — cancel the 4 into the 8, leaving 3/1 × 2/1.
Multiply: 6/1 = 6.
6 doses. Note that dividing by a fraction below 1 made the answer larger than 3/4 — which is the check that you flipped the right fraction.
Flip the second fraction, never the first. Flipping the wrong one produces an answer that is often among the choices, because it is the most common error on this operation.
Question 2 of 4
What is 5/6 ÷ 2/3?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: C. 1 1/4
Keep, change, flip gives 5/6 × 3/2 = 15/12 = 1 1/4. 5/9 is what you get by flipping the first fraction instead of the second, 10/18 comes from multiplying straight across without flipping at all, and the last choice mis-converts 5/4, which is 1.25 rather than 1.20.
What each operation does to size
A quick plausibility check before you commit to an answer.
Operation
Second number
Result
Multiply
Less than 1
Smaller than the first number
Multiply
Greater than 1
Larger
Divide
Less than 1
Larger than the first number
Divide
Greater than 1
Smaller
Terms to know
Reciprocal
A fraction turned upside down. The reciprocal of 2/5 is 5/2.
Cancelling
Dividing a numerator and a denominator by a common factor before multiplying.
Improper fraction
A fraction larger than 1, such as 9/4. Convert mixed numbers to this form before multiplying.
Of
In a word problem, "of" nearly always means multiply.
Per
In a word problem, "per" or "how many fit into" usually means divide.
What the TEAS asks most
The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.
Keep, change, flip — flipping the second fraction only — then multiply.
How many doses of this size are in this quantity?
A division, and one where the answer should come out larger than the starting quantity.
What is two thirds of this amount?
"Of" means multiply. The answer must be smaller than the amount you started with.
Question 3 of 4
A bottle contains 2 1/4 litres. Each dose is 3/8 of a litre. How many full doses can be drawn from the bottle?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: B. 6
2 1/4 is 9/4, and 9/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6. Choice A comes from dividing by 1/2 rather than 3/8, 8 from multiplying instead of dividing somewhere in the working, and 9 from using the numerator 9 without dividing at all.
Key points
Multiply straight across; no common denominator is needed.
Divide by flipping the second fraction and multiplying.
Cancel before multiplying — it is faster and avoids simplifying a large fraction later.
Convert mixed numbers to improper fractions first.
Multiplying by less than 1 shrinks a number; dividing by less than 1 grows it.
Question 4 of 4
A recipe uses 3/4 cup of oats per serving. How much is needed for 2/3 of a serving?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: A. 1/2 cup
"Of" signals multiplication: 3/4 × 2/3 = 6/12 = 1/2. Since you want less than a full serving the answer has to be under 3/4, which rules out every other choice — 1 1/8 and 9/8 are the same number reached by dividing rather than multiplying, and 1 5/12 comes from adding the two fractions.
TEAS · Multiply and divide fractions
Knowledge Check Results
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