What number must replace x
and y
for the three fractions to become equivalent? 1/=x/7=24/7
To find the number that must replace x, we can set up the equation:
1/x = 24/7
To solve for x, we can cross multiply:
7 = 24 * x
To isolate x, we divide both sides of the equation by 24:
x = 7 / 24
Therefore, x must be replaced by 7/24.
To find the number that must replace y, we can set up the equation:
x/7 = 24/y
To solve for y, we can cross multiply:
x * y = 24 * 7
To isolate y, we divide both sides of the equation by x:
y = (24 * 7) / x
Since we already found that x = 7/24, we can substitute this value into the equation:
y = (24 * 7) / (7/24)
To divide by a fraction, we can multiply by its reciprocal:
y = (24 * 7) * (24/7)
Canceling out the common factors:
y = 24 * 24
Simplifying:
y = 576
Therefore, y must be replaced by 576.
To find the values of x and y that make the three fractions equivalent, you need to solve for x and y separately.
First, let's start by setting up the equation for the first fraction: 1/x = 7/24.
To solve for x, you can cross multiply:
1 * 24 = x * 7
This simplifies to:
24 = 7x
Next, divide both sides of the equation by 7 to isolate x:
24/7 = x
Therefore, x is equal to 24/7.
Now, let's move on to the equation for the second fraction: x/7 = 24/7.
Since we already found the value of x in the previous step, we can simply substitute it into the equation:
(24/7)/7 = y
To simplify this, divide 24/7 by 7:
24/49 = y
Therefore, y is equal to 24/49.
So, the number that replaces x to make the three fractions equivalent is 24/7, and the number that replaces y is 24/49.
To find the values of x and y in the equation 1/x / 7 = 24/7, we will solve it step by step.
Step 1: Simplify the equation
To simplify the equation, we can cross-multiply. This means multiplying the numerator of one fraction by the denominator of the other fraction.
(1/x) * 7 = 24
7/x = 24
Step 2: Isolate the variable
To isolate the variable x, we can multiply both sides of the equation by x.
(7/x) * x = 24 * x
7 = 24x
Step 3: Solve for x
To solve for x, divide both sides of the equation by 24.
7/24 = (24x)/24
7/24 = x
Therefore, x = 7/24.
So, the value of x that will make the equation 1/x / 7 = 24/7 equivalent is x = 7/24.
There is no need to solve for y in this case, as y is not present in the equation.