Multiplication

Now that we've went over Addition and Subtraction, let's talk about Multiplication!

Multiplication: Repeated Addition

Multiplication of Whole Numbers
-For any whole numbers r and s, the product of r and s is the sum with s occuring r times.
   
            r x s = s + s + s . . . + s
                        r times


One way of representing multiplication is with a rectangular array. Base 5, 10, and 100 pieces are commonly used to make rectangular arrays. Singular pieces called units are also used. The pieces can be set up according to the numbers in the problem.

©LEARNING THINGS

I remember using base pieces throughout Elementary School, except ours were green. This method really helped me learn, because it was hands on. We could actually see what we were adding, subtracting, multiplying and dividing.



Number Properties
Closure Property for Multiplication: states that the product of any two whole numbers is a whole number.
-For any whole numbers a and b,
  a x b is a unique whole number

Identity Property for Multiplication: the number 1
-For any whole number b
  1 x b = b x 1 = b

- When multiplied by another number, it leaves the identity for the number unchanged.
For example,
1 x 4 = 4      1 x 50 = 50     1 x 0 = 0

Commutative Property for Multiplication: states that in any product of two numbers, the numbers may be interchanged (commuted) without affecting the product.
-For any whole numbers a and b,
  a x b = b x a

For example,
342 x 26 = 26 x 342

Associative Property of Multiplication: states that in any product of three numbers, the middle number may be associated with and multiplied by either of the two end numbers.
- For any whole numbers a,b, and c,
   a x (b x c) = (a x b) x c

Distributive Property of Multiplication: when multiplying a sume of two numbers by a third number, we can add the two numbers and then multiply the third number, or we can multiply each number of the sum by the third number and then add the two products.
- For any whole numbers a,b, and c
   a x (b + c) = a x b + a x c

-For example, to compute 35 x (10 + 2), we can compute 35 x 12, or we can add 35 x 10 to 35 x 2. This property is called the distributive property for multiplication over addition.
   35 x 12 = 35 x (10 + 2) = (35 x 10) + (35 x 2)



A times table is a very helpful tool when kids are learning multiplication facts. Teachers often use activities such as timed worksheets. Students may be given one minute to do as many multiplication problems as they can. Here the perfect squares are highlighted. Once kids become more familiar with these multiples and factors, they will  be able to do more challenging problems much more efficiently.

Table from :Vaughn Aubuchon

In Elementary School we were required to memorize our perfect squares, factors, and multiples. Although this seemed difficult at the time, it was well worth it in the future. Today I know my multiplication facts, because of this table. 

Video by: King Yakko