Math Core

You know your times tables up to $10 \times 10$ . But what about $6 \times 243$ ? You can't memorize every fact like that. Instead, you break the big number into place-value parts, multiply each part, and add.

Multiplying tens, hundreds and thousands

Start with a basic fact and think about place value:

$4 \times 3 = 12$ (4 groups of 3 ones is 12 ones)
$4 \times 30 = 120$ (4 groups of 3 tens is 12 tens)
$4 \times 300 = 1{,}200$ (4 groups of 3 hundreds is 12 hundreds)
$4 \times 3{,}000 = 12{,}000$ (4 groups of 3 thousands is 12 thousands)

Use the basic fact, then write the same number of zeros as the tens, hundreds or thousands number has.

Partial products

To multiply a bigger number, write it in expanded form. Multiply each part by the one-digit number. Each answer is called a partial product. Add the partial products to get the final product.

Worked example: Using an area model

Find $4 \times 36$ .

Break 36 into $30 + 6$ . Draw a rectangle 4 tall and 36 wide, split into a 30 part and a 6 part.

A 4 by 36 rectangle split into a 4 by 30 part (left) and a 4 by 6 part (right).

Left part: $4 \times 30 = 120$
Right part: $4 \times 6 = 24$

Add the parts: $120 + 24 = 144$ . So $4 \times 36 = 144$ .

Multiplying by a one-digit number

Break the big number into thousands, hundreds, tens and ones. Multiply each part by the one-digit number. Then add the partial products.

6 \times 243 = 6 \times 200 + 6 \times 40 + 6 \times 3

The standard algorithm

The standard algorithm is a short way to write the same steps. You multiply from right to left, one place at a time, and carry (regroup) when a place gets 10 or more.

Worked example: Three digits, two ways

Find $6 \times 243$ .

Partial products: $6 \times 200 = 1{,}200$ , $6 \times 40 = 240$ and $6 \times 3 = 18$ . Then $1{,}200 + 240 + 18 = 1{,}458$ .

Standard algorithm:

\begin{array}{r} \scriptstyle 2\,1\phantom{0} \\ 243 \\ \times\,6 \\ \hline 1458 \end{array}

Ones: $6 \times 3 = 18$ . Write 8 and carry 1 ten.
Tens: $6 \times 4 = 24$ , plus the carried 1 is 25. Write 5 and carry 2 hundreds.
Hundreds: $6 \times 2 = 12$ , plus the carried 2 is 14. Write 14.

Both ways give 1,458.

Common mistake

Multiply first, then add the carried number. In the tens place above, it is $6 \times 4 + 1 = 25$ . A common mistake is to add first, $6 \times (4 + 1) = 30$ , which gives the wrong answer.

Worked example: A four-digit number with a zero

Find $7 \times 3{,}062$ .

\begin{array}{r} 3062 \\ \times\,7 \\ \hline 21434 \end{array}

Ones: $7 \times 2 = 14$ . Write 4, carry 1.
Tens: $7 \times 6 = 42$ , plus 1 is 43. Write 3, carry 4.
Hundreds: $7 \times 0 = 0$ , plus 4 is 4. Write 4, carry nothing.
Thousands: $7 \times 3 = 21$ . Write 21.

So $7 \times 3{,}062 = 21{,}434$ . Check with partial products: $21{,}000 + 0 + 420 + 14 = 21{,}434$ .

Tip

A zero digit still needs a spot in the answer. Even when $7 \times 0 = 0$ , you must still add any carried number and write a digit in that place.

Practice

Practice 1

Find $5 \times 700$ .

Type a number.

Practice 2

Find $3 \times 42$ .

Type a number.

Practice 3

Find $8 \times 57$ .

Type a number.

Practice 4

Which shows the partial products for $5 \times 263$ ?

Practice 5

Find $4 \times 316$ .

Type a number.

Practice 6

Find $9 \times 208$ .

Type a number.

Practice 7

A school buys 7 boxes of pencils. Each box holds 144 pencils. How many pencils does the school buy?

Type a number.

Practice 8

Find $6 \times 2{,}475$ .

Type a number.