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Concept 8 of 9

The Bridge Builder: Multiplying by Whole Numbers

1

Today's big idea

Write the whole number over 1, then multiply tops across and bottoms across.

4 x 2/3 becomes 4/1 x 2/3, which gives 8 over 3.

2

How it works

👀 What's going on?

How do you work out 4 x 2/3? One number is whole and the other is a fraction, so they do not look like they belong in the same sum at all.

💡 Here's the trick

4 × 2/34whole41×234 × 2 = 81 × 3 = 3/1 addedANSWER8/3

Look at the bridge above. The 4 gets a 1 written underneath it, turning it into 4/1, because anything divided by 1 is itself. Now both sides are fractions. Multiply the tops, 4 x 2 = 8, then the bottoms, 1 x 3 = 3, which gives 8/3.

🪄 How to do it

  1. 1.Write the whole number over 1, the way 4 becomes 4/1 in the picture above.
  2. 2.Multiply the two top numbers together.
  3. 3.Multiply the two bottom numbers and write the new fraction.

✍️ Try it

Work out 3 x 2/5, then work out 2 x 3/4. Is either answer bigger than one whole?

3 x 2/5 becomes 3/1 x 2/5 = 6/5, which is just past one whole. 2 x 3/4 becomes 2/1 x 3/4 = 6/4, which is one and a half. Multiplying by a whole number above 1 always makes a fraction grow.

⚠️ Watch out

You might be thinking the bottom gets multiplied by the whole number too, so 3 x 2/5 becomes 6/15. That is smaller than 2/5, and multiplying by 3 cannot shrink an amount. The 1 underneath is what keeps the bottom safe.

🌟 Why this matters

Tripling a recipe that needs 2/3 of a cup runs on this move. So does working out how far you walk when each lap is 3/4 of a kilometre.
Exam tip: An answer smaller than the fraction you started with means the bottom got multiplied by mistake.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“4 × 2/5 — multiply a whole by a fraction.”

  1. 1

    Turn 4 into a fraction

    Put a 1 under it → 4 becomes 4/1.

  2. 2

    Multiply tops across

    4 × 2 = 8.

  3. 3

    Multiply bottoms across

    1 × 5 = 5.

  4. 4

    Stack the new fraction ✓

    4 × 2/5 = 8/5

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

To multiply a whole by a fraction: put the whole over 1, then multiply straight across.

Problem 1 of 3

PROBLEM

4 × 2/3

5

Quick check

✅ VERIFICATION

Work out 5 x 3/4.

⚡ Finish the activity above first to answer.

Keep going!

Up next: The Grid Translator

75/100 → 0.75. The two outfits revealed.

Concept 9 of 9 →