Multiplication facts and multi-digit multiplication | Math basics

The multiplication facts

The multiplication facts are the products of the numbers $$1$$ through $$10$$ . Find $a \times b$ where row $$a$$ meets column $$b$$ :

$\times$	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$7$$	$$8$$	$$9$$	$$10$$
$$1$$	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$7$$	$$8$$	$$9$$	$$10$$
$$2$$	$$2$$	$$4$$	$$6$$	$$8$$	$$10$$	$$12$$	$$14$$	$$16$$	$$18$$	$$20$$
$$3$$	$$3$$	$$6$$	$$9$$	$$12$$	$$15$$	$$18$$	$$21$$	$$24$$	$$27$$	$$30$$
$$4$$	$$4$$	$$8$$	$$12$$	$$16$$	$$20$$	$$24$$	$$28$$	$$32$$	$$36$$	$$40$$
$$5$$	$$5$$	$$10$$	$$15$$	$$20$$	$$25$$	$$30$$	$$35$$	$$40$$	$$45$$	$$50$$
$$6$$	$$6$$	$$12$$	$$18$$	$$24$$	$$30$$	$$36$$	$$42$$	$$48$$	$$54$$	$$60$$
$$7$$	$$7$$	$$14$$	$$21$$	$$28$$	$$35$$	$$42$$	$$49$$	$$56$$	$$63$$	$$70$$
$$8$$	$$8$$	$$16$$	$$24$$	$$32$$	$$40$$	$$48$$	$$56$$	$$64$$	$$72$$	$$80$$
$$9$$	$$9$$	$$18$$	$$27$$	$$36$$	$$45$$	$$54$$	$$63$$	$$72$$	$$81$$	$$90$$
$$10$$	$$10$$	$$20$$	$$30$$	$$40$$	$$50$$	$$60$$	$$70$$	$$80$$	$$90$$	$$100$$

Order doesn't matter: $3 \times 8 = 8 \times 3$ . That halves the number of facts to learn.
Fives: half of times ten. $5 \times 6 = 60 \div 2 = 30$ .
Nines: times ten, minus one group. $9 \times 8 = 80 - 8 = 72$ . The digits of a nines fact always add to $$9$$ .
Fours: double, then double again. $4 \times 6 = 12 \cdot 2 = 24$ .
Break apart: $7 \times 8 = 7 \times 5 + 7 \times 3 = 35 + 21 = 56$ .

The trickiest facts are usually $6 \times 7 = 42$ , $6 \times 8 = 48$ and $7 \times 8 = 56$ . Practice them until they're automatic.

Estimate to catch mistakes: $46 \times 23$ is about $50 \times 20 = 1{,}000$ , so $$1{,}058$$ is reasonable.

Multiply as if there were no decimal points. Then count the total number of decimal places in the factors and put that many in the product.

Quick check

What is $6 \times 8$ ?

Quick check

What is $9 \times 7$ ?

$\times$	$\(1\)$	$\(2\)$	$\(3\)$	$\(4\)$	$\(5\)$	$\(6\)$	$\(7\)$	$\(8\)$	$\(9\)$	$\(10\)$
$\(1\)$	$\(1\)$	$\(2\)$	$\(3\)$	$\(4\)$	$\(5\)$	$\(6\)$	$\(7\)$	$\(8\)$	$\(9\)$	$\(10\)$
$\(2\)$	$\(2\)$	$\(4\)$	$\(6\)$	$\(8\)$	$\(10\)$	$\(12\)$	$\(14\)$	$\(16\)$	$\(18\)$	$\(20\)$
$\(3\)$	$\(3\)$	$\(6\)$	$\(9\)$	$\(12\)$	$\(15\)$	$\(18\)$	$\(21\)$	$\(24\)$	$\(27\)$	$\(30\)$
$\(4\)$	$\(4\)$	$\(8\)$	$\(12\)$	$\(16\)$	$\(20\)$	$\(24\)$	$\(28\)$	$\(32\)$	$\(36\)$	$\(40\)$
$\(5\)$	$\(5\)$	$\(10\)$	$\(15\)$	$\(20\)$	$\(25\)$	$\(30\)$	$\(35\)$	$\(40\)$	$\(45\)$	$\(50\)$
$\(6\)$	$\(6\)$	$\(12\)$	$\(18\)$	$\(24\)$	$\(30\)$	$\(36\)$	$\(42\)$	$\(48\)$	$\(54\)$	$\(60\)$
$\(7\)$	$\(7\)$	$\(14\)$	$\(21\)$	$\(28\)$	$\(35\)$	$\(42\)$	$\(49\)$	$\(56\)$	$\(63\)$	$\(70\)$
$\(8\)$	$\(8\)$	$\(16\)$	$\(24\)$	$\(32\)$	$\(40\)$	$\(48\)$	$\(56\)$	$\(64\)$	$\(72\)$	$\(80\)$
$\(9\)$	$\(9\)$	$\(18\)$	$\(27\)$	$\(36\)$	$\(45\)$	$\(54\)$	$\(63\)$	$\(72\)$	$\(81\)$	$\(90\)$
$\(10\)$	$\(10\)$	$\(20\)$	$\(30\)$	$\(40\)$	$\(50\)$	$\(60\)$	$\(70\)$	$\(80\)$	$\(90\)$	$\(100\)$