Find the value of x that makes the fractions equivalent.
start fraction x over 8 end fraction equals start fraction 15 over 24 end fraction
(1 point)
Responses
3
3
4
4
5
5
6
6
First, let's set up the equation:
x/8 = 15/24
To make the fractions equivalent, we need to find a common denominator. In this case, the common denominator is 24.
Since the denominator of the first fraction is already 8, we don't need to make any changes to it. However, we need to multiply the numerator and denominator of the second fraction by 3 to get a denominator of 24.
x/8 = (15 * 3) / (24 * 3)
Simplifying further:
x/8 = 45/72
To get rid of the denominator 8, we can multiply both sides of the equation by 8:
8 * (x/8) = 8 * (45/72)
The 8s on the left side cancel out, and we are left with:
x = (45/72) * 8
Now, let's simplify:
x = 360/72
To further simplify, we can divide both the numerator and denominator by their greatest common divisor, which is 8:
x = (360/8) / (72/8)
x = 45/9
Finally, simplifying the fraction:
x = 5
So, the value of x that makes the fractions equivalent is 5.