# Mental Multiplication: 2 Digit Numbers by 1 Digit Numbers

Mental multiplication is hard, but there are strategies and tricks that you can use to do this.  In a previous post, we have learned an alternative way on how to multiply 2-digit number by 2-digit number faster, and in this post, I am going to share another way, on how to do mental multiplication of of 2-digit numbers by 1-digit numbers. In this strategy, we will split the numbers into tens and ones, multiply separately, then add the products. Let’s have our first example.

The Math Trick

Example 1: 25 × 7

In this example, we split 25 into tens and ones 20 and 5. Then, we multiply both of them by 7.

Step 1: 20 × 7 = 140

Step 2: 5 × 7 = 35

Step 3: 140 + 35 = 175.

Notice that although there are three steps, two multiplications and 1 addition, these steps are a lot easier to do mentally because the product in Step 1 is always a multiple of 10 (that is, its ones digit is 0). This becomes easier to add to the product in Step 2.

Example 2: 47 × 3

Split 47 into 40 and 7, then multiply both by 3.

Step 1: 40 × 3 = 120

Step 2: 7 × 3 = 21

Step 3: 120  + 21 = 141

Of course, there are cases that it is difficult to do the mental calculation especially if the numbers are large such as the next example. But this will depend on the ability of the person who is doing mental calculation. Of course, this kind of mental calculation requires a lot of practice.

Example 3:　68 × 9

Step 1: 60 × 9 = 540

Step 2: 8 × 9 = 72

Step 3: 540 + 72 = 612

In this example, we need to perform carry over during division, so it is harder than the previous two examples.

The Idea Behind the Trick

We learn the idea behind this trick (or method) in school mathematics. It is called the distributive property of multiplication over addition.  The distributive property says that if you have three numbers a, b, and c, then

$a(b + c) = ab + ac$.

Looking at the first example, we can see that

$7(25) = 7(20) + 7(5)$

splitting 25 into 20 and 5.

Let’s Practice!

Using the strategy above, see if you can multiply the following mentally.

1.)  34 × 5

2.)  23 × 4

3.) 64  × 2

4.) 83  × 3

5.) 36  × 8