Multiplying and dividing big numbers

1Multiplying by 10, 100 and 1 000

When you multiply by 10, every digit moves one place to the left and a 0 fills the ones place: 345 × 10 = 3 450. Multiply by 100 and the digits move two places: 345 × 100 = 34 500.

2Multiplying by a one-digit number

Break the big number into its place values, multiply each part, then add the parts. These parts are called partial products.

2 347 × 6:

• 2 000 × 6 = 12 000
• 300 × 6 = 1 800
• 40 × 6 = 240
• 7 × 6 = 42

12 000 + 1 800 + 240 + 42 = 14 082. The column method does the same steps, starting with the ones and carrying.

3Multiplying by a two-digit number

Split the two-digit number into tens and ones. For the moto rides, 1 200 × 23:

• 1 200 × 20 = 24 000
• 1 200 × 3 = 3 600

24 000 + 3 600 = 27 600 Frw. That is what Mugisha's brother spent.

4Dividing by breaking the number into parts

Four friends share 8 436 Frw equally. Work out 8 436 ÷ 4 by splitting 8 436 into parts that are easy to share:

• 8 000 ÷ 4 = 2 000
• 400 ÷ 4 = 100
• 36 ÷ 4 = 9

2 000 + 100 + 9 = 2 109 Frw each. These parts are called partial quotients.

5Long division and remainders

Work out 9 275 ÷ 6. Divide from the left, one place at a time:

• 9 thousands ÷ 6 = 1, remainder 3. Bring the 3 down to the hundreds: 32.
• 32 ÷ 6 = 5, remainder 2. Bring down: 27.
• 27 ÷ 6 = 4, remainder 3. Bring down: 35.
• 35 ÷ 6 = 5, remainder 5.

So 9 275 ÷ 6 = 1 545 remainder 5. Check: 1 545 × 6 = 9 270, and 9 270 + 5 = 9 275.

6What does the remainder mean?

250 pupils visit Lake Kivu, and each boat carries 6 pupils. 250 ÷ 6 = 41 remainder 4. Forty-one boats are full, but 4 pupils are still on the shore! They need one more boat, so the school needs 42 boats. Always ask what the remainder means in the story.

Practise: open the Arithmetic simulation and play the Multiply and Divide games to make your times tables quick. Quick tables make big sums easy.

Try it yourself

Work each one in your exercise book first. Then tap Show answer to check.