Are these fraction equivalent? ?

NO! NO! NO!

The two fractions are not equal for every value of x:

When x = 0, 9x/16x is undefined.

If x is any value other than 0, then the x's cancel out and the fractions are equivalent.

As you study more algebra and calculus, you're going to get a lot more of these sorts of trick questions. So when checking for equality, it's good to make sure to check for all values of x (or whatever your variables are).

Yes. 36/64 simplifies to 9/16.

9x/16x simplifies to 9/16 because the x's cancel out.

They're not equivelant, 6/8=.75 5/7=.71

yes it is because if you canceled x out you had

9 36
- * 4 then it = -
16 64

9x/16x = 9/16
36/64 [ 36 and 64 divide by 4 ] = 9/16

Therefore, these fractions are equivalent

36/64 = 9x/16x
9/16 = 9x/16x
9 = 16(9x)/16x
9 = 9x/x
9 = 9
(36/64 ≡ 9x/16x) (<== identity)

Yes, these are equal.
Divide both of them by 4, u will get 9/16.
On the other hand, 9x/16x. So x will be removed.
So the trend of increasing is same so equivilant fractions.

36/64 = 18/32 = 9/16

9x/16x = 9/16

YES , are equivalent.

Yes, they are equivalent.
There are two ways to know for sure.
1. Simplify each fraction to see if the numerator and denominator in each are equivalent.
36/64 = 9/16
9x/16x = 9/16
2. If two fractions are equal, they form a proportion. And the cross products of a proportion are always equal. Write the fractions as a proportion and then cross multiply.
36/64 = 9x/16x
36(16x) = 64(9x)
576x = 576x
Yep, they are equal.

True, x can be any number. But, it has to be the same number each time it is used in a single expression. So, these fractions are equal.

Yes, the x cancels out.