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.
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.
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!
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.