Claire correctly solved the proportion StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction for x by using cross products to get the equation 16 x = 144 and then dividing both sides by 16 to get x = 9. She showed that she can use cross products to solve the proportion because she gets the same answer if the solves it as shown.

What the hell is this?

Claire correctly solved the proportion using cross products. Let me explain how she did it.

To solve this proportion:

StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction

Claire used the cross products property, which states that if two ratios are equal, then the products of the means (the middle terms) and the extremes (the outer terms) are also equal.

So, when Claire multiplied the numerator of the first fraction (x) by the denominator of the second fraction (16), and multiplied the denominator of the first fraction (4) by the numerator of the second fraction (36), she obtained:

x * 16 = 4 * 36

This simplifies to:

16x = 144

Next, Claire divided both sides of the equation by 16 to isolate x:

(16x) / 16 = 144 / 16

This simplifies to:

x = 9

Therefore, Claire found that x equals 9.

Claire showed that she can use cross products to solve the proportion because when she multiplied the means and the extremes, she obtained the same equation (16x = 144) and the same solution (x = 9) as solving it step by step. This demonstrates the validity of using the cross products property to solve proportions.

crap. Use real math, ok?

x/4 = 36/16

no idea what "as shown" is

and you didn't even ask a question.