How to Multiply Two-Digit Numbers by Two-Digit Numbers

In the last lesson, you learned how to multiply 1-digit numbers by 4-digit numbers.

Now, let's learn how to multiply 2-digit numbers by 2-digit numbers.

Understanding 2-Digit by 2-Digit Multiplication

42 × 23 = ?

Looks tough. 🙀 But no worries.

We can break it down into simple steps.

The trick is to split the '23' into '20' + '3'.

Pause and look through those steps to see if you get it. 👆

We split the problem into two easier multiplication problems:

42 × 23 =
42 × (20 + 3) =
(42 × 20) + (42 × 3) =

Tip: ( and ) are called parenthesis. They show which operations, like multiplication or addition, you do first.

Tip: You actually just used something called the distributive property of multiplication. You'll learn more about it in a later lesson. 

So, let's try to find the product of each simpler part. This will make sense in a moment.

First, let's find 42 × 3.

42 × 3 = 126

Now, let's find 42 × 20.

Because 20 is a multiple of 10, we can solve 42 × 20 by finding 42 × 2 and adding a '0' at the end of the product.

Very good. 👍

42 × 20 = 840

Now, let's add the two products.

So,

42 × 23 = 966

Great work! 👏 

That's basically how you can think about multiplying two 2-digit numbers. You break it down into two simpler multiplications, that you add together at the end.

Now, let's learn a trick to do this even more quickly.

Multiplication Using the Column Method

Let's solve the same example together, now in a better way.

42 × 23 = ?

First, write the numbers in column form, starting with the bigger number.

Next, start by multiplying 42 by 3, just the way we did before.

First, multiply 2 by 3.

Then, multiply 4 by 3.

Well done! 👏

Now, let's multiply 42 by 20. ✅

To do this, put a '0' at the end of our product, and just find 42 × 2.

First, multiply 2 by 2.

Next, multiply 4 by 2.

Nice job.

Can you guess the last step?

Finally, add the two products. ✅

So,

42 × 23 = 966

We got the same answer as before, this time using just the column method. ✅ 

Let's try one last example, because this is a really important skill. 

35 × 79 = ?

First, write the numbers in column form, starting with the bigger number.

We start by multiplying 79 × 5.

Very good! 👏

Now, let's put a zero at the Ones place of the next product. We always do this.

Also, let's clear-out any carries from the first multiplication (to avoid any confusion).

Great. 👏

Now, let's multiply 79 × 3.

Finally, let's add the two products to get the answer. 

So,

35 × 79 = 2,765 ✅

Awesome!

2-Digit by 2-Digit Multiplication Review

STEP 1: Write the numbers in column form, one below the other, starting with the bigger number.

STEP 2: Multiply the top factor by the Ones place digit of the bottom factor and write the product.

STEP 3: Put a '0' at the Ones place of the next product. Clear-out any carry from the first multiplication (to avoid confusion).

STEP 4: Multiply the top factor by the Tens place digit of the bottom factor and write the product.

STEP 5: Add the two products together to get the answer.

Congratulations! 🎉 

Now, you know how to multiply two-digit by two-digit numbers. 

Start the practice below to help you master the skill.