Multiplication

If someone dumped a jar of pennies in front of you and asked you to count all of them, how would you approach the task? Would you count each penny one by one? Probably not! You would most likely pile pennies into groups of two, three, or possibly five pennies, then add the groups. If you put the pennies into groups of 3 and formed 10 groups of pennies, it might not take too long to add 3 ten times for a total of 30 pennies. You might even skip-count by 3. But, if there were 300 pennies, skip-counting by 3, or adding 3 one hundred times would take quite a long time.

The easiest way to find the total number of items in equal groups is to use multiplication. Multiplication allows you to do repeated addition quickly and efficiently. You can write a multiplication sentence to show 100 groups of 3 pennies. The numbers you multiply are called factors. The answer is the product.

Multi-digit by one-digit:
Properties of Multiplication:

 100 x 3 = 300 productfactor factor 100 factor x 3 factor 300 product

Multiplying a 2- or 3-digit number by a 1-digit number requires an understanding of place value. To multiply 34 by 6, think of 34 as 3 tens and 4 ones.

Step 1: Multiply the ones.Step 2: Multiply the tens.
 tens ones 2 3 4     4 ones x 6 = 24 ones x 6 2 0 4     24 ones = 2 tens 4 ones
 tens ones 2 3 4     3 tens x 6 = 18 tens x 6 2 0 4     18 tens + 2 tens = 20 tens

The properties of multiplication help to make multiplication easy to understand. The Commutative Property shows that changing the order of the factors does not change the product.

 x  x x  x x  x x  x x  x

 5 groups of 2 5 x 2 = 10
 x  x  x  x  x x  x  x  x  x

 2 groups of 52 x 5 = 10

The Associative Property shows that changing the grouping of the factors does not change the product.

 (4 x 2) x 1 = 4 x (2 x 1) 8 x 1 = 4 x 2 8 = 8
The Identity Property shows that the product of one and any number is that number.
 7 x 1 = 7             1 x 32 = 32

The Property of Zero shows that the product of zero and any number is zero.
 0 x 9 = 0             766 x 0 = 0