Есептеңіз: (1/15 + 1/15 + ... + 1/15 - 3/13 - 3/13) (45 рет) - (39 рет)
Understand the Problem
Сұрақ сыныптағы белгілі бір математикалық сандық өрнекті есептеуді талап етеді. Осы өрнектегі үлескерлерді (1/15, 3/13) қорытындылап, нәтижесін табу керек.
Answer
The result is $-6$.
Answer for screen readers
The final answer is $-6$.
Steps to Solve
- Sum of Fractions with Common Denominator
First, we need to find the sum of the fractions $\frac{1}{15}$ repeated 45 times. This can be calculated as:
$$ 45 \times \frac{1}{15} = \frac{45}{15} = 3 $$
- Sum of the Other Fractions
Next, we sum the fractions $\frac{3}{13}$ repeated 39 times: $$ 39 \times \frac{3}{13} = \frac{39 \times 3}{13} = \frac{117}{13} = 9 $$
- Combine the Results
Finally, we combine the results from the two sums: $$ 3 - 9 = -6 $$
The final answer is $-6$.
More Information
The problem involves calculating the sum of two sequences of fractions. The first sequence consists of a repeated fraction of $\frac{1}{15}$, while the second is a repeated fraction of $\frac{3}{13}$. Understanding how to sum fractions and then combine results is key.
Tips
- Confusing cumulative sums with individual sums; ensure to multiply the number of terms correctly.
- Not simplifying fractions correctly, leading to incorrect values. Always reduce fractions to their simplest form.
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