Calculating a Series of Fractions
In this article, we will explore how to calculate a series of fractions involving different numbers and operations.
The Given Expression
The given expression is:
10/56 + 10 phần 140 + 10 phần 260 + ... + 10 phần 1,400
Breaking Down the Expression
Let's break down the expression into smaller parts to make it easier to calculate.
1. 10/56
To evaluate this fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.
10 ÷ 2 = 5 56 ÷ 2 = 28
So, the simplified fraction is:
5/28
2. 10 phần 140
This part of the expression means 10 divided by 140. We can simplify this fraction as well.
10 ÷ 10 = 1 140 ÷ 10 = 14
So, the simplified fraction is:
1/14
3. 10 phần 260
This part of the expression means 10 divided by 260. Again, we can simplify this fraction.
10 ÷ 10 = 1 260 ÷ 10 = 26
So, the simplified fraction is:
1/26
4. ... (and so on)
The expression continues with more fractions of the same pattern. We can simplify each fraction in the same way.
5. 10 phần 1,400
This part of the expression means 10 divided by 1,400. We can simplify this fraction as well.
10 ÷ 10 = 1 1,400 ÷ 10 = 140
So, the simplified fraction is:
1/140
Adding Up the Fractions
Now that we have simplified each fraction, we can add them up.
5/28 + 1/14 + 1/26 + ... + 1/140
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 28, 14, 26, and 140. The LCM is 2,520.
So, we can convert each fraction to have a denominator of 2,520.
- 5/28 = 450/2,520
- 1/14 = 180/2,520
- 1/26 = 90/2,520
- ... (and so on)
- 1/140 = 18/2,520
Now, we can add up the fractions:
450/2,520 + 180/2,520 + 90/2,520 + ... + 18/2,520
The result is a large fraction, but we can simplify it by dividing both the numerator and the denominator by their GCD.
Conclusion
In this article, we have shown how to calculate a series of fractions involving different numbers and operations. By breaking down the expression into smaller parts, simplifying each fraction, and adding them up, we can evaluate the entire expression.
