Question

Why can you use cross products to solve the proportion StartFraction 18 over 5 EndFraction = StartFraction x over 100 EndFraction for x?

Answer 1

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Answer:

  it is application of the multiplication property of equality

Step-by-step explanation:

You can use "cross products" to solve any proportion. What looks like a "cross product" is just application of the multiplication property of equality. That property says the variable value is unchanged if both sides of the equation are multiplied by the same value.

For your fraction, the "cross product" is what you get when you multiply both sides of the equation by 500.

  $\dfrac{18}{5}=\dfrac{x}{100}\qquad\text{given}\\\\\dfrac{18\cdot5\cdot100}{5}=\dfrac{x\cdot5\cdot100}{100}\qquad\text{multiply by 5\cdot100 }\\\\18\cdot100=5\cdot x\qquad\text{cancel common factors; looks like cross product}$

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Note that the next step here is to divide by the x-coefficient, the 5 that was in the left-side denominator.

  $\dfrac{18\cdot100}{5}=x\qquad\text{divide by 5}$

Please also note that this is exactly the same result you would get by multiplying the original equation by the original denominator of x.