Which of the following is equivalent to the rational number [3x / 4x]?

a) 6x / 8x
b) 12x / 24x
c) 48x / 56x
d) 3x / 5x

a

Correct

thanks jen and anonymous

You're welcome

To determine which of the given options is equivalent to the rational number [3x / 4x], we need to simplify the expression and compare it with each choice.

The expression [3x / 4x] is a fraction with the numerator 3x and the denominator 4x. To simplify, we can cancel out any common factors between the numerator and denominator. In this case, both 3x and 4x have a common factor of x.

Canceling out this common factor, we get:

[3x / 4x] = (3x / x) / (4x / x) = 3/4

Now, let's compare this simplified fraction, 3/4, with each of the given options to determine which is equivalent:

a) 6x / 8x = (6x / x) / (8x / x) = 6/8 = 3/4
b) 12x / 24x = (12x / x) / (24x / x) = 12/24 = 1/2
c) 48x / 56x = (48x / x) / (56x / x) = 48/56 = 6/7
d) 3x / 5x = (3x / x) / (5x / x) = 3/5

From the above comparisons, we can see that option a), 6x / 8x, is equivalent to the rational number [3x / 4x].