Long multiplication, step by step
Multiply big numbers by a 2- or 3-digit number, one digit at a time. Read one step, play with it, then tap “I understand this”.
Why it works: break the number up
47 × 36 looks hard. But 36 is just 30 + 6. So we work out 47 × 6 and 47 × 30, then add the two answers.
That is exactly what long multiplication does. The first row is 47 × 6. The second row is 47 × 30, and the 0 at the end is there because we are multiplying by tens.
The multiplication rectangle
Change the numbers. The rectangle splits into tens and ones, and the two colours are the two rows of the long sum.
The steps
- Write the numbers under each other, ones under ones and tens under tens. Put the bigger number on top.
- Multiply by the ones digit of the bottom number. Start at the right, one digit of the top number at a time.
- Carry: if you get 10 or more, write the ones digit down and carry the tens small on top of the next digit. Add it after the next multiplication.
- Write a 0 in the ones column of the next row, then multiply by the tens digit. Cross out the old carries first.
- Add the rows to get the answer.
Multiply first, then add the carried number. 6 × 4 + 4 means 24 + 4 = 28, not 6 × 8.
Estimate first. 47 × 36 is close to 50 × 40 = 2 000. If your answer is 300 or 20 000, something went wrong.
7 × 6 = 42 is 4 tens and 2 ones. The 2 ones belong in the ones column. The 4 tens belong with the tens, but there is no tens answer yet. We park them above the tens column to add on in a moment.
Watch a sum being worked out
Show me how
Pick a sum and tap “Next step”. Watch the carries go on top and the zero go in.
Your turn
The board asks one step at a time. Type with the number buttons. When you must carry, tap the spot on top where the little number goes.
Long multiplication practice
Choose a level. You get a new sum every time.
Sums finished: 0
Three traps to watch for
In the second row you multiply by tens. Without the 0, 47 × 30 becomes 141 instead of 1 410, and the answer is far too small.
The small number on top must be added after the next multiplication. Cross it out once you have used it, so you do not add it twice.
When you start the second row, cross out the carries from the first row. They belong to the first row only.
Check with an estimate: round both numbers to the nearest 10 and multiply. Your answer should be close to that.
Multiplying by a 3-digit number
When you multiply by a 3-digit number you get three rows. The second row gets one placeholder 0 (tens), and the third row gets two placeholder zeros (hundreds).
1 206 × 245 = 1 206 × 5 + 1 206 × 40 + 1 206 × 200
Choose “1 206 × 245” in “Show me how” to see all three rows.
Check yourself
- 47 × 36 = 47 × 6 + 47 × 30: each row is one part.
- Multiply first, then add the carry.
- Second row: write a 0 first, because you multiply by tens.
- Estimate first: round both numbers and multiply.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 3 A4 pagesPractice sheet
- Numbers9 pages · PDFPaperMemo
Ready for more? The Grade 7 multiplication quiz gives you new sums every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Let your child estimate first (round to the nearest 10). It catches most mistakes before they happen.
- Times tables are the foundation. If 7 × 8 is a struggle, practise times tables first and then come back.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.