Which number would replace X to make these fractions equivalent? 6/X = 9/12
To make the fractions equivalent, we need to find the value of X that will make both fractions equal.
We can start by cross-multiplying:
6 * 12 = X * 9
Simplifying, we get:
72 = 9X
To isolate X, we can divide both sides of the equation by 9:
X = 72/9
Simplifying the division, we find:
X = 8
Therefore, the number that would replace X to make the fractions equivalent is 8.
To find the value of X that would make the fractions 6/X and 9/12 equivalent, we can set up a proportion:
6/X = 9/12
To solve this proportion, we can cross multiply:
6 * 12 = X * 9
72 = 9X
Now, we can solve for X by dividing both sides of the equation by 9:
72/9 = X
X = 8
Therefore, the number 8 would replace X to make the fractions 6/8 and 9/12 equivalent.
To determine the value of X that would make the fractions 6/X and 9/12 equivalent, you need to find a common denominator.
Step 1: Find the common denominator
Since the denominator of the first fraction is X and the denominator of the second fraction is 12, the common denominator is 12X.
Step 2: Rewrite the fractions with the common denominator
To convert the first fraction to have a denominator of 12X, you need to multiply the numerator and denominator by (12/X):
(6/X) * (12/X) = 72/(X^2)
To convert the second fraction to have a denominator of 12X, you need to multiply the numerator and denominator by (X/12):
(9/12) * (X/12) = 9X/144 = (X/16)
Step 3: Set up the equation
Now that both fractions have the same denominator, you can set them equal to each other:
72/(X^2) = X/16
Step 4: Solve for X
To solve this equation, you can cross multiply:
72 * 16 = X^2 * X
1152 = X^3
Now, take the cube root of both sides to solve for X:
X = ∛1152
Calculating the cube root of 1152 using a calculator or manually, you find:
X ≈ 10.08
Therefore, the number 10.08 (approximately) would replace X to make the fractions 6/X and 9/12 equivalent.