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Westkost [7]
3 years ago
13

How can knowing how to represent proportional relationships in different ways be useful to solving problems

Mathematics
1 answer:
Anna35 [415]3 years ago
8 0

Answer:

  appropriately writing the proportion can reduce or eliminate steps required to solve it

Step-by-step explanation:

The proportion ...

  \dfrac{A}{B}=\dfrac{C}{D}

is equivalent to the equation obtained by "cross-multiplying:"

  AD = BC

This equation can be written as proportions in 3 other ways:

  \dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}

  Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.

I find this most useful to ...

  a) put the unknown quantity in the numerator

  b) give that unknown quantity a denominator of 1, if possible.

__

The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.

<u>Example</u>:

  x/4 = 3/2

Usual method:

  2x = 4·3

  x = 12/2 = 6

Multiplying by the denominator:

  x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step

__

<u>Example 2</u>:

  x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...

  x/1 = 4/2 . . . . . . written with 1 in the denominator

  x = 2 . . . . simplify

Of course, this is the same answer you would get by multiplying by the denominator, 4.

The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.

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Answer:

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Step-by-step explanation:

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3 years ago
Hose is 32 feet long 32 feet long it needs to be cut into pieces equaling 5’3” How many whole pieces can be cut into how many wh
luda_lava [24]

Answer:

6

Step-by-step explanation:

Question tests the ability to get quotient

Here, 32 ft is divided by 5’3”

Normally, ft is denoted by ' while inches is denoted by ". So we divide 32 ft by 5ft and 3 inches

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The total is now 5.25'

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Answer:

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