Questions: Evaluate the following expression. -11/20 + 4/25 ÷ 1/5 -11/20 + 4/25 ÷ 1/5 = (Type an integer or a simplified fraction.)

Solution Steps

To evaluate the expression \(-\frac{11}{20}+\frac{4}{25} \div \frac{1}{5}\), follow these steps:

1. First, handle the division of fractions: \(\frac{4}{25} \div \frac{1}{5}\) is equivalent to multiplying \(\frac{4}{25}\) by the reciprocal of \(\frac{1}{5}\), which is \(5\).
2. Simplify the result of the multiplication.
3. Add the result to \(-\frac{11}{20}\).
4. Simplify the final expression to its simplest form.

To simplify \(\frac{4}{25} \div \frac{1}{5}\), multiply \(\frac{4}{25}\) by the reciprocal of \(\frac{1}{5}\), which is \(5\). This gives: \[ \frac{4}{25} \times 5 = \frac{4 \times 5}{25} = \frac{20}{25} = \frac{4}{5} \]

Now, add the result from Step 1 to \(-\frac{11}{20}\): \[ -\frac{11}{20} + \frac{4}{5} \] Convert \(\frac{4}{5}\) to a fraction with a denominator of 20: \[ \frac{4}{5} = \frac{16}{20} \] Now, perform the addition: \[ -\frac{11}{20} + \frac{16}{20} = \frac{-11 + 16}{20} = \frac{5}{20} = \frac{1}{4} \]

Final Answer