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How to add,subtract, and multiply distributive property
I am working on adding, subtracing, and multiplying distributive property. I am confused because i do not know what steps to take in order to do each problem
10/22/2012 | Lando from Chicago, IL | 2 Answers | 0 Votes
Distributive Property
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2 ANSWERS
David H.
Colorado Springs, CO
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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.
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.
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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.
Part (a)
<h3>Answer:
2(2.4+w) = 14.2</h3>
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Explanation:
L = 2.4 = length
W = unknown width
The perimeter of any rectangle is P = 2(L+W)
We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2
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Part (b)
<h3>Answer:
w = 4.7</h3>
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Explanation:
We'll solve the equation we set up in part (a)
2(2.4+w) = 14.2
2(2.4)+2(w) = 14.2
4.8+2w = 14.2
2w = 14.2-4.8
2w = 9.4
w = 9.4/2
w = 4.7
The width must be 4.7 cm.
