Multiplication is a shortcut for repeated addition.
When we multiply...
5 × 4
...we add 5 to itself, 4 times:
5 × 4 = 5 + 5 + 5 + 5 = 20
...or add 4 to itself, 5 times:
5 × 4 = 4 + 4 + 4 + 4 + 4 = 20
In the last lesson, you learned how to multiply numbers by 0, 1, 2, 3, 4 and 5.
Now, let's learn how to multiply numbers by 6, 7, 8 and 9.
6 × 4 = ?
To multiply by 6, you can either skip count by 6, or use this trick:
If you know 5 times a number, just add one more of that number to figure out 6 times that number.
So to figure out 6 × 3, you just figure out 5 × 3 and add 3 more.
6 × 3 = 5 × 3 + 3 = 15 + 3 = 18
Why does that work? Take a look:
6 = 5 + 1
We can break multiplying by 6 down into two easier multiplication problems:
Multiplying by 6 = Multiplying by 5 + Multiplying by 1
Can you multiply these numbers?
6 × 2 = ?
Let's try multiplying by 5 times 2 first, and adding one more 2.
6 × 2 = 12
Great work.
7 × 3 = ?
You can either skip count by 7 three times, or you can use a trick.
We know that:
7 = 5 + 2
So:
Multiplying by 7 = Multiplying by 5 + Multiplying by 2
Tip: It's like you can multiply by 5 and skip count up two more times.
Let's see if it works.
7 × 3 =
5 × 3 + 2 × 3 =
15 + 2 × 3 =
15 + 6 =
21
It works.
Let's try one more.
7 × 5 = ?
Can you do it in your head?
7 × 5 = 35
Awesome.
9 × 6 = ?
You can skip count by 9, but that can be a little hard.
Luckily, there's a trick.
We know that:
9 = 10 - 1
So we can break it down into two steps:
Multiplying by 9 = Multiplying by 10 - Multiplying by 1
Let's try this trick to solve our example.
9 × 6 = 60 - 6 = 54
Nice work! 👍
Can you now solve this using the trick?
9 × 4 = ?
9 × 4 = 40 - 4 = 36
Very good. 👏
8 × 4 = ?
You can either skip count by 8 four times,
Or you can use a trick. 😃
We know that:
8 = 10 - 2
So,
Multiplying by 8 = Multiplying by 10 - Multiplying by 2
Let's try the trick.
8 × 4 = 40 - 8 = 32
Great job! 👏
Can you solve this on your own?
8 × 7 = ?
You can split it down into two easier multiplication problems and a subtraction, like this:
8 × 7 =
(10 × 7) - (2 × 7) =
70 - 14 =
56
Way to go.
You just learned a bunch of tricks, but your goal is actually to know all of these by heart, because you'll use them your whole life!
Now, let's practice to help you build this skill.