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

C

Explanation:

Answer 2

The property used here is: Multiplication property of Equality

Explanation:

Claire solved the expression
`(x)/(4)=(36)/(16)` by two ways

Way 1: Solving using proportion:

`(x)/(4)=(36)/(16)`

By cross multiplying:

`16x=144`

Divide both sides by 16

`x=9`

Way 2:

She also solve the same expression
`(x)/(4)=(36)/(16)` by using following steps

Multiply both sides by 4

`4*( (x)/(4))=4*((36)/(16))\\x=(144)/(16)\\x=9`

We need to tell the name of property that allowed her to go from
`(x)/(4)=(36)/(16)` to
`4*((x)/(4))=4*((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.