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Written Multiplication: 2-Digit × 1-Digit

Maths · Stage 2 Extension
Year 4
★ Extension · Stage 3 (Years 5–6)
Lesson Guide
Explanation
You know your tables up to 10 times 10, but what about 23 times 4? There is no 23 times table and you are never going to learn one. Instead you break 23 into pieces you already know: 20 and 3. Multiply each piece by 4, then add the two answers together. Every written multiplication method is really just this idea, dressed up.
Your Turn
Break these into tens and ones: 34, 51, 68. Check: 30 and 4; 50 and 1; 60 and 8.
Watch Out
Splitting 23 into 2 and 3 instead of 20 and 3 is the mistake to avoid. The 2 is worth twenty.
Explanation
Draw a rectangle 23 across and 4 down, then cut it where the 20 ends. The left part is 20 by 4, which is 80. The right part is 3 by 4, which is 12. Put the two pieces back together and you get 92. That is 23 times 4. The picture is doing exactly what you did in your head a moment ago, and it is worth drawing a few times, because the written method you are about to meet is this picture with the rectangle rubbed out.
Your Turn
Draw the rectangle for 32 times 3 and split it. Check: 30 by 3 is 90, 2 by 3 is 6, so 96.
Watch Out
The two pieces get ADDED at the end, not multiplied. You are putting a rectangle back together.
Explanation
Now the short way. Write 23 with the 4 underneath, lined up on the right. Start at the ones: 3 times 4 is 12. Twelve is too big for one column, so you write the 2 and carry the 1 — and that carried 1 is really one whole ten. Then the tens: 2 times 4 is 8, plus the carried 1 makes 9. Answer: 92. Same answer as the rectangle, because it is the same sum.
Your Turn
Set out 26 times 3 the short way. Check: 6 times 3 is 18, write 8 carry 1; 2 times 3 is 6 plus 1 is 7. Answer 78.
Watch Out
The little carried digit is a TEN, not a one. Write it above the tens column, not squashed anywhere.
Explanation
Bigger numbers make bigger carries. For 47 times 6: seven sixes are 42, so you write the 2 and carry 4 — four whole tens. Then four sixes are 24 tens, plus the carried 4 makes 28 tens, which is 280. Write both digits and you get 282. Always sanity-check at the end: 47 is nearly 50, and 50 times 6 is 300, so an answer near 300 is believable. If you had got 92 or 2820 you would know something had gone wrong.
Your Turn
Work out 38 times 7, then check it against 40 times 7. Check: 266, and 40 times 7 is 280 — close, so it is believable.
Watch Out
Forgetting to ADD the carry after multiplying the tens is the single most common error here. Multiply, then add the carry.
Explanation
You now have three methods and they all give 170 for 34 times 5. Splitting in your head is fastest when the numbers are friendly. The area model is worth drawing when you want to see what is happening, or when you are stuck. The written method is the one to reach for when the carries get messy or the numbers get big. Good mathematicians are not the ones who always use the fanciest method — they are the ones who pick the right method for the numbers in front of them.
Your Turn
For each of these, decide in your head which method you would use and then do it: 20 times 7, 49 times 8, 15 times 6. Check: 140, 392, 90.
Watch Out
Reaching for the written method every single time is slow. If the number is round, just split it and go.
📌 Key Points — this lesson in a nutshell
  • Split the 2-digit number into tens and ones, multiply each, then add.
  • The area model and the written method are the same sum — one drawn, one written.
  • A carried digit is a ten, and it can be bigger than 1.
  • Multiply the tens then add the carry — not the other way round.
  • Check against a round number: 47 × 6 should land near 50 × 6 = 300.
Step 1: Introduction
Step 1 of 5
23 × 4 is not in any times table You know 2 × 4 and 3 × 4. Nobody learns a 23 times table — and nobody needs to. Break the big number into pieces you already know: 20 + 3 23 is just 20 and 3. Multiply each piece, then add.
23 × 4 drawn as a rectangle 20 3 4 80 12 20 × 4 = 80   and   3 × 4 = 12 80 + 12 = 92 The whole rectangle is 23 wide and 4 tall. Its area is the answer.
The same sum, written down 23 ×  4 92 ones: 3 × 4 = 12 tens: 2 × 4 = 8, plus the 1 1 ← the carried ten Start at the ones, on the right. 3 × 4 = 12. Twelve will not fit in one column, so write the 2 and carry the 1 ten above the tens column. Then 2 × 4 = 8 tens, plus the carried 1 makes 9 tens.
47 × 6 — carrying 4 47 ×  6 282 4 7 × 6 = 42 → write 2, carry 4 4 × 6 = 24, plus 4 = 28 A carry can be any digit, not just 1. And the tens answer can spill into hundreds: 28 tens is 280, so the 2 lands in the hundreds column. Check it: 47 is nearly 50, and 50 × 6 = 300. 282 is close. Good.
Three ways, same answer In your head 30 × 5 = 150 4 × 5 = 20 170 Area model 150 20 170 Written method 34 × 5 170 All three are correct. Pick the fastest one you trust. Round numbers? Do it in your head. Messy carries? Write it out. Speed comes from choosing well.
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