Question
21. \( -\frac{2}{5}-\left(-\frac{3}{4}\right) \)
Ask by Grant Sanders. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \( \frac{7}{20} \) or 0.35.
Solution
Calculate or simplify the expression \( -\frac{2}{5}-\left(-\frac{3}{4}\right) \).
Calculate the value by following steps:
- step0: Calculate:
\(-\frac{2}{5}-\left(-\frac{3}{4}\right)\)
- step1: Remove the parentheses:
\(-\frac{2}{5}+\frac{3}{4}\)
- step2: Reduce fractions to a common denominator:
\(-\frac{2\times 4}{5\times 4}+\frac{3\times 5}{4\times 5}\)
- step3: Multiply the numbers:
\(-\frac{2\times 4}{20}+\frac{3\times 5}{4\times 5}\)
- step4: Multiply the numbers:
\(-\frac{2\times 4}{20}+\frac{3\times 5}{20}\)
- step5: Transform the expression:
\(\frac{-2\times 4+3\times 5}{20}\)
- step6: Multiply the numbers:
\(\frac{-8+3\times 5}{20}\)
- step7: Multiply the numbers:
\(\frac{-8+15}{20}\)
- step8: Add the numbers:
\(\frac{7}{20}\)
The result of \( -\frac{2}{5}-\left(-\frac{3}{4}\right) \) is \( \frac{7}{20} \) or 0.35.
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Simplify this solution Beyond the Answer
Let’s break it down! First, we need to handle the double negative. Subtracting a negative is the same as adding, so your equation transforms into: \[ -\frac{2}{5} + \frac{3}{4} \] Next, to combine these fractions, we need a common denominator. The least common multiple of 5 and 4 is 20! Converting the fractions: \[ -\frac{2}{5} = -\frac{8}{20} \quad \text{and} \quad \frac{3}{4} = \frac{15}{20} \] Now, add these together: \[ -\frac{8}{20} + \frac{15}{20} = \frac{7}{20} \] So, the final result is: \[ -\frac{2}{5}-\left(-\frac{3}{4}\right) = \frac{7}{20} \]
