Math Core

The 7s, 8s and 9s have the biggest answers, so they look scary. But you already know most of them! Thanks to the commutative property, $7 \times 4$ is the same as $4 \times 7$ , a 4s fact. Only a few facts are truly new, and each one has a strategy.

Multiplying by 9: ten groups, take one away

9 groups is 1 group less than 10 groups. So find the 10s fact, then subtract one group.

What is $9 \times 6$ ?

$10 \times 6 = 60$ .
Take away one group of 6: $60 - 6 = 54$ .

$9 \times 6 = 54$ .

The 9s also have a cool pattern. Look at the table:

$n$	1	2	3	4	5	6	7	8	9	10
$9 \times n$	9	18	27	36	45	54	63	72	81	90

For $9 \times 1$ through $9 \times 9$ :

The tens digit is one less than the number you multiply by. For $9 \times 7$ , the tens digit is 6.
The two digits add up to 9. Since $6 + 3 = 9$ , the ones digit is 3. So $9 \times 7 = 63$ .

Multiplying by 8: double the 4s

8 is double 4. So find the 4s fact, then double it.

What is $8 \times 7$ ?

$4 \times 7 = 28$ .
Double 28: 56.

$8 \times 7 = 56$ .

Multiplying by 7: fives and twos

7 is $5 + 2$ . So 7 groups is 5 groups plus 2 groups.

What is $7 \times 7$ ?

$5 \times 7 = 35$ .
$2 \times 7 = 14$ .
$35 + 14 = 49$ .

$7 \times 7 = 49$ .

Strategies for 7, 8 and 9

× 9: find × 10, then subtract one group.
× 8: find × 4, then double.
× 7: find × 5 and × 2, then add.
Flip it: if one factor is small, like $8 \times 3$ , use the fact you know: $3 \times 8 = 24$ .

$n$	1	2	3	4	5	6	7	8	9	10
$7 \times n$	7	14	21	28	35	42	49	56	63	70
$8 \times n$	8	16	24	32	40	48	56	64	72	80

Worked example: A 9s fact

What is $9 \times 8$ ?

$10 \times 8 = 80$ . Take away one 8: $80 - 8 = 72$ .

Check with the pattern: the tens digit is $8 - 1 = 7$ , and $7 + 2 = 9$ . So $9 \times 8 = 72$ .

Worked example: The trickiest fact

What is $8 \times 8$ ?

$4 \times 8 = 32$ . Double 32: 64.

$8 \times 8 = 64$ .

Worked example: Divide by 7

What is $56 \div 7$ ?

Think: $7 \times ? = 56$ . You found above that $8 \times 7 = 56$ .

$56 \div 7 = 8$ .

Common mistake

With the 9s strategy, subtract a whole group, not 1. For $9 \times 6$ , it is $60 - 6 = 54$ , not $60 - 1 = 59$ .

Tip

A handy memory trick: 5, 6, 7, 8. That is, $56 = 7 \times 8$ .

Practice

Practice 1

What is $9 \times 7$ ?

Type a number.

Practice 2

What is $8 \times 6$ ?

Type a number.

Practice 3

What is $7 \times 6$ ?

Type a number.

Practice 4

Which is equal to $9 \times 4$ ?

Practice 5

What is $81 \div 9$ ?

Type a number.

Practice 6

What is $64 \div 8$ ?

Type a number.

Practice 7

A spider has 8 legs. How many legs do 7 spiders have?

Type a number.