Answer:
In this equation: 14/15x - 1/2 = 1/2
To clear the fraction 14/15x, we need to multiply by the reciprocal of its denominator, which is 15/14. Multiplying both sides of the equation by 15/14 gives us:
(15/14) * (14/15x) - (15/14) * (1/2) = (15/14) * (1/2)
Simplifying:
(15/14) * (14/15x) = (15/28)
On the left side of the equation, the 14 in the numerator and the 14 in the denominator cancel out, leaving:
(15/15x) = (15/28)
To clear the fraction on the right side, we need to multiply both sides by the reciprocal of its denominator, which is 28/15:
(28/15) * (15/15x) = (28/15) * (15/28)
Simplifying:
(28/15) * (15/15x) = 1
On the left side of the equation, the 15 in the numerator and the 15 in the denominator cancel out, leaving:
(28/15x) = 1
Now, we can solve for x by multiplying both sides of the equation by the reciprocal of (28/15), which is (15/28):
(15/28) * (28/15x) = (15/28) * 1
Simplifying:
(15/15x) = 15/28
The 15 in the numerator and the 15 in the denominator cancel out, leaving:
1/x = 15/28
To solve for x, we can take the reciprocal of both sides of the equation:
1/(1/x) = 1/(15/28)
Simplifying:
x = 28/15
Therefore, the smallest number that both sides of the equation can be multiplied by to clear it of fractions is 28/15.
Explanation: