Question

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.


StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction. StartFraction x over 4 EndFraction times 4 = StartFraction 36 over 16 EndFraction times 4. x = StartFraction 144 over 16 EndFraction. X = 9.

What property allowed her to go from StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction to StartFraction x over 4 EndFraction times 4 = StartFraction 36 over 16 EndFraction times 4 ?

Answer 1

Answer:

The property used here is: Multiplication property of Equality

Step-by-step explanation:

Claire solved the expression $\frac{x}{4}=\frac{36}{16}$ by two ways

Way 1: Solving using proportion:

$\frac{x}{4}=\frac{36}{16}$

By cross multiplying:

$16x=144$

Divide both sides by 16

$x=9$

Way 2:

She also solve the same expression $\frac{x}{4}=\frac{36}{16}$ by using following steps

Multiply both sides by 4

$4\times( \frac{x}{4})=4\times(\frac{36}{16})\\x=\frac{144}{16}\\x=9$

We need to tell the name of property that allowed her to go from $\frac{x}{4}=\frac{36}{16}$ to $4\times(\frac{x}{4})=4\times(\frac{36}{16})$

The property used here is: Multiplication property of Equality

The property states that if A , B and C are real numbers then

A = B and AC = BC are equivalent.

Answer 2

Answer:

C

Step-by-step explanation: