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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(1)/(4)-(-(9)/(40)) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{1}{4}-\left(-\frac{9}{40}\right)$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

\newline

-\frac{1}{4}-\left(-\frac{9}{40}\right)

\newline

Answer:

Understand and Identify Operations: Understand the expression and identify the operations to be performed. $\newline$ We need to subtract the second fraction from the first one, and since the second fraction is negative, subtracting it will actually mean adding its absolute value to the first fraction.
Convert Subtraction to Addition: Convert the subtraction of a negative number to addition. $\newline$ $-\frac{1}{4} - (-\frac{9}{40})$ is equivalent to $-\frac{1}{4} + \frac{9}{40}$ .
Find Common Denominator: Find a common denominator for the fractions to combine them. $\newline$ The common denominator for $4$ and $40$ is $40$ .
Convert to Common Denominator: Convert the first fraction to have the common denominator. $\newline$ $-\frac{1}{4}$ is equivalent to $-\frac{10}{40}$ because $1 \times 10 = 10$ and $4 \times 10 = 40$ .
Combine Fractions: Combine the fractions. $\newline$ Now we have $-\frac{10}{40} + \frac{9}{40}$ , which can be combined by adding the numerators and keeping the common denominator.
Perform Addition: Perform the addition. $\newline$ $-\frac{10}{40} + \frac{9}{40} = \frac{-10 + 9}{40} = -\frac{1}{40}$ .
Simplify Fraction: Simplify the fraction, if possible. $\newline$ The fraction $-\frac{1}{40}$ is already in its simplest form because $1$ and $40$ have no common factors other than $1$ .

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