7 × 8 is hard to remember. But it can be built from facts you already know.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Cut the array
Cut 7 × 8 into 5 × 8 and 2 × 8. Both of those you know.
Then add the two parts
40 and 16 makes 56. So 7 × 8 = 56.
This has a name.
Distributive property lets you split one factor into two parts and multiply each separately.
A hard fact split into easy ones
7 × 8 feels hard. Draw the array and cut it into a 5 × 8 part and a 2 × 8 part. That is 40 + 16 = 56. You have replaced one fact you did not know with two you did. The cut can go anywhere as long as you count both pieces.
This has a name: the distributive property
Splitting 7 × 8 into (5 × 8) + (2 × 8) is the distributive property. It is one of the most useful rules in all of maths, and you will still be using it in algebra years from now. Meeting it here as a picture rather than a formula is the best possible start.
Choosing where to cut
Cut so that both pieces use facts you know well. Splitting 7 into 5 and 2 works because the 5s are easy. Splitting into 3 and 4 also works. Splitting into 6 and 1 is fine too, and gives 48 + 8 = 56. Every valid cut gives the same total.
Step 2: Try It Yourself
Move the cut and watch the two products change.
7 × 8 = 56
7 × 8 = (7 × 5) + (7 × 3) = 35 + 21 = 56
The array is cut into 7 × 5 and 7 × 3. Two easier facts that add to the same total.
Step 3: Watch an Example
One step at a time.
Watch Ana Split a Hard Fact
Ana is asked for 7 × 8 and cannot recall it.
- Step 1
She pictures the array: 7 rows of 8.
Step 4: Your Turn
Practice makes it stick.
Splitting a Six
Problem 1 of 2
6 × 7 split as (5 × 7) + (1 × 7). What is 35 + 7?
Splitting an Eight
Problem 2 of 2
8 × 6 split as (4 × 6) + (4 × 6). What is 24 + 24?
Build the Hard Ones
Split each one into two facts you already know.
1 of 3
7 × 6 = ? Try (5 × 6) + (2 × 6).
2 of 3
9 × 4 = ? Try (5 × 4) + (4 × 4).
3 of 3
8 × 7 = ? Try (5 × 7) + (3 × 7).
Step 5: Quick Check
Show what you know.
Question 1 of 2
7 × 8 = ?
Question 2 of 2
Why cut an array in two?
What You Learned
- A hard fact can be cut into two easy ones.
- 7 × 8 is (5 × 8) + (2 × 8).
- Add the two products to get the answer.