Math Core

A theater has 23 rows with 14 seats in each row. How many seats is that? To find out, you need to multiply two two-digit numbers. The trick is the same one you used for one-digit numbers: break the numbers into tens and ones.

Multiplying tens by tens

First, practice multiplying two multiples of ten. Use a basic fact, then think about place value.

$20 \times 30$ : $2 \times 3 = 6$ , and tens times tens makes hundreds. So $20 \times 30 = 600$ .
$40 \times 50$ : $4 \times 5 = 20$ , so $40 \times 50 = 2{,}000$ .

Count the zeros at the end of the two factors, and put that many zeros after the basic fact. In $40 \times 50$ , the basic fact 20 already ends in a zero, so the answer has three zeros in all.

The area model

Split both numbers into tens and ones. Now the rectangle splits into four parts instead of two.

Worked example: Four partial products

Find $23 \times 14$ .

Write $23 = 20 + 3$ and $14 = 10 + 4$ .

A 23 by 14 rectangle. The width is split into 20 and 3. The height is split into 10 (bottom) and 4 (top), making four parts.

Find the area of each part:

	20	3
10	$10 \times 20 = 200$	$10 \times 3 = 30$
4	$4 \times 20 = 80$	$4 \times 3 = 12$

Add all four parts: $200 + 30 + 80 + 12 = 322$ . The theater has 322 seats.

Multiplying two two-digit numbers

Break each number into tens and ones. Multiply every part of one number by every part of the other. That makes four partial products. Add them all.

The standard algorithm

The standard algorithm groups the partial products into two rows. The first row multiplies by the ones digit. The second row multiplies by the tens digit.

Worked example: Two rows

Find $34 \times 27$ .

\begin{array}{r} 34 \\ \times\,27 \\ \hline 238 \\ +\,680 \\ \hline 918 \end{array}

Row 1: $34 \times 7 = 238$ . ( $7 \times 4 = 28$ : write 8, carry 2. $7 \times 3 = 21$ , plus 2 is 23.)
Row 2: $34 \times 20 = 680$ . Because the 2 is really 20, write a 0 in the ones place first. Then $2 \times 34 = 68$ goes in front of it.
Add the rows: $238 + 680 = 918$ .

So $34 \times 27 = 918$ .

Common mistake

Don't forget the zero in the second row! The 2 in 27 stands for 20, so the second row is $34 \times 20 = 680$ , not $34 \times 2 = 68$ . If you write 68, your answer will be much too small.

Worked example: A word problem

A school has 45 classrooms. Each classroom has 38 books on its shelf. How many books is that in all?

Find $45 \times 38$ . Multiply 38 by each part of 45:

$38 \times 5 = 190$
$38 \times 40 = 1{,}520$

Add: $190 + 1{,}520 = 1{,}710$ . There are 1,710 books.

Tip

You can multiply in either order. $45 \times 38$ and $38 \times 45$ give the same answer. Doing it both ways is a good way to check your work.

Practice

Practice 1

Find $30 \times 40$ .

Type a number.

Practice 2

Find $12 \times 13$ .

Type a number.

Practice 3

Find $21 \times 34$ .

Type a number.

Practice 4

Find $46 \times 15$ .

Type a number.

Practice 5

A farm packs 24 boxes of apples. Each box holds 36 apples. How many apples does the farm pack?

Type a number.

Practice 6

Find $58 \times 32$ .

Type a number.

Practice 7

Jin found $43 \times 25$ like this. First he found $43 \times 5 = 215$ . Then he wrote 86 for the second row and added to get 301. What is the correct product?

Type a number.

Practice 8

Find $67 \times 89$ .

Type a number.