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How to add,subtract, and multiply distributive property

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2 Answers

The distributive property allows us to simplify equations. 

The following is a simple problem that shows how we can use the distributive property:

A florist is selling flower arrangements with 4 lilies and 3 roses. If John bought 5 arrangements, how many of each flower would he have?

5 x (4 + 3)

The distributive property says that we can distribute the 5 and simplify this to 5 x 4 + 5 x 3. By multiplying you would get 20 lilies and 15 roses or 35 flowers total.

If we do not distribute the 5, we would get 5 x 4 + 3. 20 lilies and 3 roses or 23 flowers total. 

The distributive property works the exact same way with subtraction, but remember, you only distribute to the numbers inside the parentheses. Variables can be distributed the same way.

Comments

with subtractions, one must take great care. For example 5-3*(6-2) = 5-3*6+3*2. Note that the rule that the product of two negatives is a positive was used. A common mistake is to say that the expression equals 5-3*6-3*2.

Comment

While the question is vague, this may help. 

The Order of Operations is the priority in which you perform operations in mathematics. The order of operation is: 

- Do operations within parentheses first,
- Exponents
- Multiplication and Division, Left to right, as you encounter them
- Addition and Subtraction, Left to right, as you encounter them

An example:

5(4+2)2(1+3) - 3(6-3)(7+1)2

Work the parentheses, and keep everything else unchanged: 5(4+2)2(1+3) - 3(6-3)(7+1)2 =5 (6)2(4) - 3(3)(8)2

Now your exponents: 5 (6)2(4) - 3(3)(8)2 = 5 (36)(4) - 3(3)(64)

Now Multiplication, Left to right: 5 (36)(4) - 3(3)(64) = 720 - 576

Now Addition and Subtraction, left to right: 720 - 576 = 144

Until you get used to it, feel free to do only one operation at a time, even if multiple instances appear in the same line, such as working with our parentheses in the example above:

5(4+2)2(1+3) - 3(6-3)(7+1)2 = 5(6)2(1+3) - 3(6-3)(7+1)2 =5(6)2(4) - 3(6-3)(7+1)2  and so on. 

Think of it like climbing a steep hill: if you take small steps, you are likely to make more progress (and not slip backwards) than if you try to run up the hill (and increase likelyhood of falling)