Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Multiplication

Multiply by two-digit numbers - 2-digit x 2-digit

Q: Can you estimate to check the answer?

Yes. Round each number and multiply mentally. 47 times 23 is about 50 times 20=1000, close to 1081.

Q: Does the order of the numbers matter?

No. 47 times 23 and 23 times 47 give the same product, though one may be quicker to set out.

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Theory

To multiply by a two-digit number, find two partial products: one for the ones digit and one for the tens digit (with a zero placeholder). Add them for the answer.

A two-digit multiplier is split into its ones and tens. The number is multiplied by each part.

Each result is a partial product. The tens row is really tens, so it gets a zero placeholder in the ones place.

Adding the two partial products gives the final answer.

$47 \times 23 = 1081$. Partial products $47\times3=141$ and $47\times20=940$; their sum is $1081$.

Two rows of multiplying, then one addition.

Step	Multiply	Partial product
Ones	$47\times3$	$141$
Tens	$47\times20$	$940$
Add	$141+940$	$1081$

The tens row needs a zero. \(47\times20\) ends in \(0\), which keeps the digits in their correct places before adding.

How to multiply by a two-digit number

Multiply the top number by the ones digit for the first partial product.
Write a zero in the ones place, then multiply by the tens digit.
Line up both partial products by place value.
Add them to get the final answer.

Example 1 — Small numbers

Calculate $24 \times 12$.

Solution

$24\times2=48$, $24\times10=240$.

$24 \times 12$

$=$

$288$

Example 2 — Both partials

Calculate $47 \times 23$.

Solution

$141$ then $940$.

$47 \times 23$

$=$

$1081$

Example 3 — Larger digits

Calculate $58 \times 34$.

Solution

$232$ then $1740$.

$58 \times 34$

$=$

$1972$

Example 4 — Class costs

32 students each pay $21 for a trip. What is the total?

Solution

$32 \times 21$

$=$

$672$

The total is $672.

Common pitfalls

Missing the tens zero. The second partial product is tens, so it needs a $0$ in the ones place.

Multiplying only one digit. Both digits of the top number are multiplied in each row.

Misaligned adding. Line the partial products up by place value before adding them.

Frequently asked questions

How do you multiply two two-digit numbers?

Multiply the top number by the ones digit, then by the tens digit with a zero placeholder, and add the two partial products. $47\times23=141+940=1081$.

What is a partial product?

It is the result of multiplying by just one digit of the multiplier. Two-digit multiplication has two partial products that are added together.

Why write a zero in the second row?

The second digit is tens, so multiplying by it gives a number of tens. The zero in the ones place keeps every digit in its correct column.

Can you estimate to check the answer?

Yes. Round each number and multiply mentally. $47\times23$ is about $50\times20=1000$, close to $1081$.

Does the order of the numbers matter?

No. $47\times23$ and $23\times47$ give the same product, though one may be quicker to set out.

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Multiply by two-digit numbers - 3-digit x 2-digit

Step	Multiply	Partial product
Ones	\(47\times3\)	\(141\)
Tens	\(47\times20\)	\(940\)
Add	\(141+940\)	\(1081\)

Multiply by two-digit numbers - 2-digit x 2-digit

📖 Theory

How to multiply by a two-digit number

Common pitfalls

Frequently asked questions

Theory