Word Problems with Division of Fractions: Step-by-Step Guide + Free Worksheet

Here is a word problem that trips up thousands of students every year: “A baker has 3/4 of a cup of flour. Each muffin needs 1/8 of a cup. How many muffins can the baker make?” If you have ever stared at a question like that and felt unsure whether to multiply or divide — this guide is exactly what you need.

To solve word problems with division of fractions, you identify the total amount and the size of each group, write a division sentence, and then apply the keep-change-flip rule to convert division into multiplication. The method works for every real-world scenario: cutting ribbon, portioning food, measuring distances, and more.

• Understand what division of fractions actually means in a real-world context.
• Use a reliable 6-step method to set up and solve any fraction division word problem.
• Avoid the three most common errors that cost students marks.
• Practice with 10 graded problems and check your answers instantly.

Start Here: A Fully Solved Example

Before I explain any rules, I want you to see the method in action. Work through this example with me — the concept will click faster from a real problem than from a definition.

Notice what happened: dividing by a small fraction (1/8) gave an answer larger than the original number (3/4). That is not a mistake — it is exactly what should happen. Six eighth-sized scoops fit inside three-quarters of a cup.

  VISUALISING 3/4 ÷ 1/8
  ┌─────────────────────────────────────┐
  │  One whole cup                      │
  │  [  1/8 ][  1/8 ][  1/8 ][  1/8 ]  │
  │  [  1/8 ][  1/8 ][  1/8 ][  1/8 ]  │
  └─────────────────────────────────────┘

  3/4 of the cup is shaded:
  [  1/8 ][  1/8 ][  1/8 ][  1/8 ]
  [  1/8 ][  1/8 ]  ← 6 eighth-sized pieces

  3/4 ÷ 1/8 = 6  ✓
  

What Is Division of Fractions?

Division of fractions answers one specific question: how many times does one fraction fit inside another? It is the same idea as whole-number division, just applied to parts of a whole.

The formal definition: dividing a/b by c/d means finding how many groups of size c/d are contained in a/b. Mathematically, a/b ÷ c/d = a/b × d/c, because dividing by a number is identical to multiplying by its reciprocal.

The reciprocal of a fraction is simply that fraction flipped upside down. The reciprocal of 1/8 is 8/1 (= 8). The reciprocal of 3/5 is 5/3.

How to Solve Word Problems with Division of Fractions: The 6-Step Method

Every fraction division word problem — no matter how it is worded — can be solved with these six steps. I use this exact sequence with my students, and it eliminates almost all setup errors.

1. Read the problem twice. Underline the numbers and the question being asked.
2. Identify the dividend. This is the total amount you are starting with.
3. Identify the divisor. This is the size of each group or piece.
4. Write the division sentence: dividend ÷ divisor.
5. Apply keep-change-flip: keep the dividend fraction, change ÷ to ×, flip the divisor fraction.
6. Multiply and simplify. Multiply numerators, multiply denominators, then reduce. Check your answer in context.

The step most students skip is Step 4 — writing the division sentence before calculating. That one habit prevents the most common error: setting up the problem backwards.

Three More Worked Examples (Easy to Hard)

Common Mistakes: Wrong vs. Right

These three errors account for the vast majority of wrong answers on fraction division word problems. Recognising them is half the battle.

Practice Worksheet: 10 Word Problems (Easy to Hard)

These 10 problems follow the same method as the worked examples above. Try each one on paper using the 6-step method. When you are done, reveal the answer key below — or download the full PDF to print and use offline.

How to use this worksheet: Print the PDF (or copy the problems into your notebook), solve each one showing all working, then self-check with the answer key. If you get a problem wrong, go back to the 6-step method and identify which step went wrong.

1. A piece of rope is 3/4 of a metre long. You cut it into pieces that are each 1/4 of a metre. How many pieces do you get?
2. A baker has 2/3 of a cup of sugar. Each batch of cookies needs 1/6 of a cup. How many batches can the baker make?
3. A road is 5/6 of a kilometre long. Workers pave 1/3 of a kilometre per day. How many days will it take to pave the whole road?
4. A jug holds 7/8 of a litre of juice. Each glass holds 1/4 of a litre. How many glasses can be filled?
5. A spool has 4/5 of a metre of ribbon. Each bow needs 2/5 of a metre. How many bows can be made?
6. A recipe calls for 3/8 of a cup of butter. If you want to make 1/2 of the recipe, how much butter do you need?
7. A tank is 5/6 full of water. If each bucket holds 1/9 of the full tank, how many buckets of water are in the tank?
8. A plank of wood is 7/10 of a metre long. Each shelf needs 7/20 of a metre. How many shelves can be cut?
9. A cyclist rode 9/10 of a kilometre. If each lap of a track is 3/10 of a kilometre, how many laps did the cyclist complete?
10. A container holds 11/12 of a litre of paint. Each small tin holds 1/6 of a litre. How many small tins can be filled?

Worked Practice: Check Your Method

Stuck on a problem? Expand each one below to see the full working.