Question
Find \( -\frac{1}{4}\left(-\frac{4}{5}\right) \). Write your answer as a fraction in simplest form.
Ask by Ross Marsh. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answer is \( \frac{1}{5} \).
Solution
To solve the expression −(1/4) × (−4/5), follow these steps:
Step 1: Multiply the two fractions.
Remember that multiplying two fractions means multiplying the numerators together and the denominators together:
(−1/4) × (−4/5) = (−1 × −4) / (4 × 5)
Step 2: Multiply the numerators and the denominators.
(−1 × −4) = 4 and (4 × 5) = 20
So, the expression becomes 4/20.
Step 3: Simplify the fraction.
Both the numerator and the denominator are divisible by 4:
4 ÷ 4 = 1, 20 ÷ 4 = 5
Thus, the simplified fraction is 1/5.
Final Answer: 1/5
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Simplify this solution The Deep Dive
To find \( -\frac{1}{4}\left(-\frac{4}{5}\right) \), we begin by multiplying the two fractions. First, we multiply the numerators and the denominators: \[ -\frac{1}{4} \times -\frac{4}{5} = \frac{1 \times 4}{4 \times 5} = \frac{4}{20} \] Next, we simplify the fraction \( \frac{4}{20} \). Both the numerator and the denominator can be divided by 4: \[ \frac{4 \div 4}{20 \div 4} = \frac{1}{5} \] Thus, \( -\frac{1}{4}\left(-\frac{4}{5}\right) = \frac{1}{5} \). The final answer is \( \frac{1}{5} \).
