Dividing fractions · Kode bersama Martin

Dividing by a fraction = multiplying by the reciprocal. One flip and division becomes the multiplication you already know.

Flip the second fraction and divide turns into times

Dividing fractions sounds scary. In fact it is multiplication in disguise. There is one rule: dividing by a fraction means multiplying by the reciprocal.

The reciprocal is made by swapping the numerator and the denominator. From 2/3 you get 3/2. From 5/1 (that is, from five) you get 1/5.

So 1/2 : 2/3 you rewrite as 1/2 × 3/2 and then you go as in the last lesson: top times top, bottom times bottom. You get 3/4.

Why does it work? The question “how many times does 1/4 fit into 2” is division: 2 : 1/4. Into one whole fit four quarters, into two wholes eight. Result 8. And that is exactly what the flip gives: 2 × 4/1 = 8. Dividing by a small piece gives a big number — that is why the denominator climbs to the top when you flip.

Sofie and Filip prepare decorations for the class dance. They have 3/4 of a metre of ribbon and each bow uses 1/8 of a metre. Filip guesses: “So two, three bows?” Sofie writes on the box: 3/4 : 1/8 = 3/4 × 8/1 = 24/4 = 6. “Six bows.” Filip does not believe it, so he folds and cuts the ribbon. Six pieces, exactly. “Dividing by an eighth made it bigger,” he wonders. Sofie nods: “Small divisor, lots of pieces. That is why the eighth flips up.”

💡

You always flip only the second fraction — the one you divide by, the divisor. Leave the first fraction alone.

How to divide fractions step by step

The method has three steps.

Step 1: copy the first fraction unchanged.

Step 2: rewrite the divide sign as times and flip the second fraction (swap numerator and denominator).

Step 3: multiply as in the last lesson — with cancelling crossways if you like — and simplify the result.

A full example: 3/5 : 9/10. I copy 3/5, flip: × 10/9. Cancel crossways: three against nine (left 1 and 3), ten against five (left 2 and 1). I count 1/1 × 2/3 = 2/3.

Dividing by a whole number: rewrite it as a fraction and flip. So 4/5 : 2 = 4/5 × 1/2 = 4/10 = 2/5. That makes sense — a half of 4/5.

A whole number divided by a fraction: 6 : 3/4 = 6 × 4/3 = 24/3 = 8.

A check in your head: when you divide by a fraction smaller than 1, the result must come out bigger than the original number. When the divisor is bigger than 1, the result is smaller. This quick test catches most typos.

Calculate 2/3 : 4/5

Step 1: I copy the first fraction: 2/3.

Step 2: I change divide to times, I flip the second fraction: 2/3 × 5/4.

Step 3: I cancel crossways — two on top against four on the bottom, common divisor 2. Left is 1/3 × 5/2.

Step 4: I multiply: 5/6.

Result: 2/3 : 4/5 = 5/6. Check: I divide by a number smaller than 1 (4/5), so the result should be bigger than 2/3. And 5/6 really is bigger than 2/3 (= 4/6). That checks out.

How many half-litre bottles can you fill with 5/2 litres of juice?

I ask: how many times does 1/2 fit into 5/2? That is division: 5/2 : 1/2.

Step 1: I copy 5/2.

Step 2: I flip the divisor: 5/2 × 2/1.

Step 3: I cancel — two against two. Left is 5/1 × 1/1 = 5.

Result: 5 bottles. Check by thinking: 5/2 litres is two and a half litres. Five half-litres fit into that. Maths and common sense say the same thing.

Calculate 7/8 : 7

I rewrite seven as a fraction: 7/1. I count 7/8 : 7/1.

Step 1: I copy 7/8. Step 2: I flip: × 1/7. Step 3: I cancel crossways — seven on top against seven on the bottom. Left is 1/8 × 1/1.

Result: 7/8 : 7 = 1/8. The thought: I share seven eighths of a cake among seven people, each gets one eighth. When you divide by a number bigger than 1, the result shrinks — that checks out.

⚠️

Do not flip the first fraction and do not flip both. Only the divisor flips — the fraction after the divide sign. If you flip both, you get the reciprocal of the right answer and the mistake is hard to see.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Mulai with ten. When it goes well, add more.

Divide fractions by flipping to multiplication. Write the answer as a fraction a/b.

Practise the questions

On paper: flip and multiply

Write each question in three steps: copy — flip — multiply. Shortcuts only when you are sure.

Calculate: 3/4 : 2/5 and 5/6 : 5/12. On the second one look for cancelling crossways.
Calculate: 9/10 : 3 and 4 : 2/3. First rewrite the whole number as a fraction with denominator 1.
You have 6/5 kg of dough, one pizza uses 2/5 kg. How many pizzas can you make? Write it as division and solve.
By each result write one check sentence: should it have come out bigger, or smaller than the first number? Why?

Now you 💪

I know the rule: dividing by a fraction = multiplying by the reciprocal.
I flip only the divisor, never the first fraction.
I can check the result by thinking: divisor smaller than 1 → result bigger.

✅

Done when: All the questions on paper have the three visible steps (copy — flip — multiply) and each has a sentence checking whether the result should have come out bigger or smaller.

What to take from this lesson

Divided by a fraction turns into times the reciprocal.
Reciprocal = swapped numerator and denominator.
Only the second fraction (the divisor) flips.
Rewrite a whole number as a fraction with denominator 1 before dividing.
Dividing by a number smaller than 1 makes the result bigger — use that as a check.