Question

Simplify. 1/4n - 1/2 / n/5 - 1/20n

Answer 1

To simplify the expression 1/4n - 1/2 / n/5 - 1/20n, invert the second fraction and multiply. Simplify each fraction individually and then substitute them back into the original expression. Combine like terms to get the final simplified expression: (6 - 4n)/(20n)

Step-by-step explanation:

To simplify the expression 1/4n - 1/2 / n/5 - 1/20n, we can use the concept of division of fractions. To divide one fraction by another, we first invert the second fraction and multiply the two fractions together. Simplifying each fraction individually, we have:

1. 1/4n = 1/(4n)
2. 1/2 = 2/(2*1) = 2/2 = 1
3. n/5 = n/(5*1) = n/5
4. 1/20n = 1/(20n)

Now, substituting these simplified fractions back into the original expression, we have:

1/(4n) - 1 / (n/5) - 1/(20n)

Since division is the same as multiplying by the reciprocal, we can rewrite the expression as follows:

1/(4n) - (1*5/n) - 1/(20n)

Simplifying further, we get:

1/(4n) - 5/n - 1/(20n) = (1*5 - 4n + 1)/(20n)

Combining like terms, the final simplified expression is:

(6 - 4n)/(20n)