Multiplying big numbers

A dairy fills 235 milk cans every day. How many cans in 30 days? In a year (365 days)? To answer, we multiply.

What is this?

Long multiplication breaks the bigger number into easy pieces. To multiply 235 × 30:

• 235 × 3 = 705.
• Add a zero because we multiplied by 30, not 3: 7,050.

For 235 × 365, we split 365 into 300 + 60 + 5:

• 235 × 5 = 1,175.
• 235 × 60 = 14,100.
• 235 × 300 = 70,500.
• Add: 1,175 + 14,100 + 70,500 = 85,775.

We write this in a stacked column form:

       2 3 5
    ×  3 6 5
    --------
     1 1 7 5    (235 × 5)
    1 4 1 0 0   (235 × 60, shift left by 1)
   7 0 5 0 0    (235 × 300, shift left by 2)
   ---------
   8 5 7 7 5

A neat shortcut for multiplying by 10, 100, 1,000: just add zeros to the right.

• 47 × 10 = 470.
• 47 × 100 = 4,700.
• 47 × 1,000 = 47,000.

This trick saves a lot of time when one of the numbers is a round number.

To check a multiplication, divide the answer by one of the factors. If you get the other factor back, you did it right.

Worked examples

Example 1. 458 × 6.

• 6 × 8 = 48 → 8, carry 4.
• 6 × 5 = 30 + 4 = 34 → 4, carry 3.
• 6 × 4 = 24 + 3 = 27.
• Answer: 2,748.

Example 2. A dairy makes 285 litres of milk daily. How much in 30 days?

• 285 × 30 = (285 × 3) × 10 = 855 × 10 = 8,550 litres.

Example 3. A truck carries 125 cans, each holding 40 litres. Total litres?

• 125 × 40 = 125 × 4 × 10 = 500 × 10 = 5,000 litres.

Try it

1. 348 × 7.
2. 256 × 25.
3. 145 × 132.
4. A factory makes 1,250 packets a day. How many in 31 days?
5. 64 boxes, each with 125 mangoes. Total mangoes?

Hands-on

Daily-to-yearly. Pick something that happens once a day at home , for example, "we drink 3 litres of milk a day". Multiply by 365 to find the yearly total.

Pack and stack. Count the items in one small box (say, biscuits in a small pack). Multiply by the number of boxes in a carton. Predict the total. Then check.