Multiply by two-digit numbers - 2-digit x 2-digit
Theory
To multiply two two-digit numbers, split the second number into tens and ones and find two partial products, then add them. The written method (long multiplication) sets these out in columns, with a zero placeholder in the tens row. This Year 5 maths page shows the area model and the written method, how to estimate first, and the common mistakes.
\(46 \times 27\) means \(46 \times 7\) plus \(46 \times 20\). These two answers are the partial products.
In the written method the first row is \(46 \times 7 = 322\). The second row is \(46 \times 20 = 920\): write a zero in the ones first, because you are multiplying by tens, then multiply by \(2\).
The area model splits both numbers: \(23 \times 14\) gives four parts, \(20 \times 10\), \(20 \times 4\), \(3 \times 10\) and \(3 \times 4\).
Long multiplication is two short multiplications added together:
Long multiplication
- Estimate by rounding both numbers to the nearest ten.
- Row 1: multiply the top number by the ones digit.
- Row 2: write a \(0\) in the ones, then multiply the top number by the tens digit.
- Add the two rows and compare with the estimate.
| \(34 \times 1\) | \(=\) | \(34\) |
| \(34 \times 20\) | \(=\) | \(680\) |
| \(34 + 680\) | \(=\) | \(714\) |
The answer is \(714\).
| \(46 \times 7\) | \(=\) | \(322\) |
| \(46 \times 20\) | \(=\) | \(920\) |
| \(322 + 920\) | \(=\) | \(1242\) |
The answer is \(1242\).
| \(50 \times 40\) | \(=\) | \(2000\) |
| \(52 \times 8\) | \(=\) | \(416\) |
| \(52 \times 30\) | \(=\) | \(1560\) |
| \(416 + 1560\) | \(=\) | \(1976\) |
The estimate is \(2000\); the exact answer is \(1976\).
| \(200 + 80\) | \(=\) | \(280\) |
| \(30 + 12\) | \(=\) | \(42\) |
| \(280 + 42\) | \(=\) | \(322\) |
\(23 \times 14 = 322\).
| \(75 \times 4\) | \(=\) | \(300\) |
| \(75 \times 20\) | \(=\) | \(1500\) |
| \(300 + 1500\) | \(=\) | \(1800\) |
The answer is \(1800\).
| \(36 \times 9\) | \(=\) | \(324\) |
| \(36 \times 20\) | \(=\) | \(720\) |
| \(324 + 720\) | \(=\) | \(1044\) |
There are \(1044\) seats.
| \(64 \times 3\) | \(=\) | \(192\) |
| \(64 \times 10\) | \(=\) | \(640\) |
| \(192 + 640\) | \(=\) | \(832\) |
The \(1\) in \(13\) is \(1\) ten, so the second row is \(64 \times 10 = 640\). The answer is \(832\).
Common pitfalls
Frequently asked questions
How do you multiply two two-digit numbers?
Multiply the top number by the ones digit, then by the tens (as tens), and add. \(46 \times 27 = 322 + 920 = 1242\).
Why do you put a zero in the second row?
Because you are multiplying by tens. The \(2\) in \(27\) means \(20\), so \(46 \times 20 = 920\).
What is a partial product?
One of the rows you add in long multiplication, such as \(46 \times 7\) and \(46 \times 20\).
How do you estimate a two-digit multiplication?
Round both numbers to the nearest ten and multiply: \(52 \times 38 \approx 50 \times 40 = 2000\).
Can I use an area model instead?
Yes. Split both numbers into tens and ones, find the four areas and add them. \(23 \times 14 = 200 + 80 + 30 + 12 = 322\).