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zepelin [54]
2 years ago
11

How does the distributive property work

Mathematics
1 answer:
jonny [76]2 years ago
7 0

Explanation:

The distributive property tells you that multiplication distributes over addition. In equation form, it looks like ...

  a(b +c) = ab +ac

__

<h3>Groups and Multiples of Groups</h3>

The parentheses are a grouping symbol. In the above equation, they indicate that the sum (b+c) is to be treated as a group. When it is multiplied by 'a', everything in the group is multiplied by 'a'.

In the real world, there are many ways things are grouped. Baseball cards are packaged together with bubble gum; Cracker Jacks® are packaged together with a prize; left gloves are packaged together with right gloves; a bicycle is a package that has a frame, 2 wheels, a seat, handlebars. If you purchase a number of any of these packages, each of the items in the package is part of your purchase that number of times.

For example, 3 bicycles will have 3 frames, 3×2 = 6 wheels, 3 seats, 3 sets of handlebars. In algebraic form, this might look like ...

  3(f +2w + s + h) = 3f +6w +3s +3h

__

<h3>Eliminating Parentheses</h3>

Using the distributive property to eliminate parentheses is like regrouping the contents of the packages so like items are grouped together. In our above example, the 3 frames were grouped together when we considered that part of the group of 3 bicycles. <em>The multiplier multiplies every member of the group</em>.

__

<h3>Adding Parentheses</h3>

The reverse of the distributive property tells us we can regroup items into sets. It tells us we can take 3 frames, 6 wheels, 3 seats, and 3 handlebars and group them together in a way that makes 3 bicycles, each having a frame, 2 wheels, a seat, and handlebars.

  3f +6w +3s +3h = 3(f +2w + s + h)

Often, we're asked to choose the multiplier to be the <em>greatest common factor (GCF) </em>of the numbers of things in the group. That makes each group as small as possible. The multiplier only needs to be <em>a</em> common factor, not necessarily <em>the greatest</em> common factor.

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Answer:

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3 years ago
A farmer wants to fence in a rectangular field that encloses 3600 square feet. One side of the field is along a river and does n
andriy [413]

Answer:

C(x) = \$3.50(\frac{x^2+7200}{x})

Step-by-step explanation:

Data provided in the question:

Area of the field = 3600 square feet

Fencing charges = $3.50 per foot

Let the side along the river be 'x' feet and the other side of the 'B'

now,

Area of rectangle = Bx = 3600 square feet

or

B = \frac{3600}{x} feet

and total length to be fenced = x + 2B

therefore,

Total cost of fencing = Fencing charges × total length to be fenced

or

Total cost of fencing = $3.50 × ( x + 2B )

substituting the value of B from (1)

Total cost of fencing, C(x) = \$3.50(x+2\times\frac{3600}{x})

or

C(x) = \$3.50(\frac{x^2+7200}{x})

4 0
3 years ago
Original: $458<br> Discount:<br> New: $137.40
Vanyuwa [196]

Answer:

Your answer would be 30% discount

Step-by-step explanation:

137.40 / 458 = .3

8 0
3 years ago
A Man is redecorating his bedroom .he can choose from 5 paint colors 6 beds and 5 dressers how many ways can he choose to design
Ipatiy [6.2K]
5_{(paint\ colors)}\ \cdot\ 6_{(beds)} \ \cdot\ 5_{(dressers)}=150_{(chooses)} \\\\Ans.\ 150\ chooses.
8 0
3 years ago
Read 2 more answers
How many ways can you make 65 cents using nickels dimes and quarters
Neporo4naja [7]

Answer:

14 ways in all.

Step-by-step explanation:

A. If you use 2 quarters, you have to make the remaining 15� with either no

dimes or 1 dime and the rest in nickels.

That's 2 ways.

B. If you use 1 quarter, you have to make the remaining 40� with either no

dimes, 1 dime, 2 dimes, 3 dimes or 4 dimes and the rest, if any, in nickels.

That's 5 more ways.  

C. If you don't use any quarters, you have to make the entire 65� with either

0, 1, 2, 3, 4, 5 or 6 dimes and the rest in nickels.

That's 7 more ways.  2+5+7 = 14 ways in all.

4 0
3 years ago
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