## Distributive Property of Multiplication over Addition and Subtraction | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Distributive property
Try it with numbers Visual Representation Visual Representation 2 Guided practice 1 Worksheet 1 Geometric Representation Why do we need to know? Distributing variables Guided practice 2 Worksheet 2 Factoring Guided practice 3 Worksheet 3 |
## What is the Distributive Property?The distributive property of multiplication over addition and subtraction is stated mathematically as
a·(b+c) = a·b+a·c. Here is a diagram that shows what we mean by
distribute.
The distributive property also works with subtraction. a·(b-c) = a·b-a·c
## Try it with NumbersLet's check out the distributive property. We will use real numbers. Let a=2, b=3, and c=5. The equation can then be written 2·(3+5) = 2·3+2·5. We will take the left side of the equation first and simplify it.
We just showed that the left half of the equation equals 16. Now we need to show that the right half of the equation is also 16.
So you can see that the distributive property of multiplication works.
## Visual Representation of the Distributive propertyRemember back to when you were learning how to multiply. Your teacher may have put a diagram like the following to represent 2·3:
With 2 rows and 3 columns to represent 2·3, we can easily count the dots to conclude that 2·3 = 6.
## Visual Representation of the Distributive propertyNow let's use this representation of numbers with the distributive property. First we will represent 2·3+2·5, which is the right hand side of the equation.
Note that at the start, there are 2 rows of 3 dots (2·3) and 2 rows of 5 dots (2·5). You can see there are 16 dots. We mathemagically transform the dots to 2·(3+5) dots, which shows that 2(3 + 5) = 2·3 + 2·5 = 16.
## Guided Practice 1Write down each problem on a piece of paper. Simplify the expression using the distributive property. SHOW ALL OF YOUR WORK! DO NOT SIMPLIFY INSIDE THE PARENTHESIS FIRST! When you have an answer, click on the equation to see each step. Did you get each step right? If you got it right, move on to the next one. If you got it wrong, click on it to try it again. ## Rulea(b + c) = ab + ac ## Process
## Example## You try it← Click on the expression to see the next step
## Worksheet 1Click the "Make Worksheet" button to build a worksheet in a new window. Print the worksheet, do the problems on the worksheet, then check the answers at the bottom of the worksheet.
## Geometric Representation of the Distributive property
## Why do we need to know the distributive property?The distributive property of multiplication is very important in solving algebraic equations. Look at the example of solving equations below. Notice that this example uses the distributive property. Don't worry if you don't yet understand how to solve these equations yet.
It is also important in factoring. When we have an expression that equals 0, we can factor
to find the solutions. In these cases, we use the distributive property the
## Distributing Variables
Since variables represent numbers, we can put a variable any place we find a number. Here are some examples:
x·(3+2) = x·3+x·2 4·(a+2) = 4a+4·2 2·(3+t) = 2·3+2t x·(y+z) = xy+xz
## Guided Practice 2Write down each problem on a piece of paper. Simplify the expression using the distributive property. SHOW ALL OF YOUR WORK! DO NOT SIMPLIFY INSIDE THE PARENTHESIS FIRST! When you have an answer, click on the equation to see each step. Did you get each step right? If you got it right, move on to the next one. If you got it wrong, click on it to try it again. ## Rulea(b + c) = ab + ac ## Process
## Example## You try it← Click on the expression to see the next step
## Worksheet 2Click the "Make Worksheet" button to build a worksheet in a new window. Print the worksheet, do the problems on the worksheet, then check the answers at the bottom of the worksheet.
## Factoring Using the Distributive PropertyNOT IMPLEMENTED YET
## Guided Practice 4NOT IMPLEMENTED YET
## Worksheet 4Click the "Make Worksheet" button to build a worksheet in a new window. Print the worksheet, do the problems on the worksheet, then check the answers at the bottom of the worksheet.
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