Question

17/27 show work

Answer 1

divide 17/27

Answer 2

To simplify the fraction \( \frac{17}{27} \), we need to find the greatest common divisor (GCD) of the numerator (17) and the denominator (27).

1. Check if the numbers share any common factors:
- **17** is a prime number, which means its only divisors are 1 and 17.
- **27** factors into \( 3^3 \) (or \( 3 \times 3 \times 3 \)), which means its divisors are 1, 3, 9, and 27.

2. The only common factor between 17 and 27 is 1.

3. Since their GCD is 1, the fraction \( \frac{17}{27} \) is already in its simplest form.

Thus, the fraction \( \frac{17}{27} \) cannot be simplified any further. The final answer is:

\[
\frac{17}{27}
\]

Answer 3

To divide \( 17 \) by \( 27 \), you can express it as follows:

\[
\frac{17}{27}
\]

If you want to calculate this as a decimal, you can divide \( 17 \) by \( 27 \):

1. Perform the division:
- \( 17 \div 27 \) results in something less than 1, since \( 27 \) is greater than \( 17 \).

2. You can set up the division as:
- \( 17.000... \div 27 \)

3. Doing the division:
- \( 27 \) goes into \( 170 \) (the first three digits of 1700) **6 times** (because \( 27 \times 6 = 162 \)).
- Subtract \( 162 \) from \( 170 \) to get \( 8 \).
- Bring down the next \( 0 \) (making it \( 80 \)).
- \( 27 \) goes into \( 80 \) **2 times** (because \( 27 \times 2 = 54 \)).
- Subtract \( 54 \) from \( 80 \) to get \( 26 \).
- Bring down the next \( 0 \) (making it \( 260 \)).
- \( 27 \) goes into \( 260 \) **9 times** (because \( 27 \times 9 = 243 \)).
- Subtract \( 243 \) from \( 260 \) to get \( 17 \).
- You can continue this process, and you'll note that the remainder becomes \( 17 \), which would lead to repeating decimals.

After these steps, we find:

\[
17 \div 27 \approx 0.629629 \ldots
\]

So, the decimal representation of \( \frac{17}{27} \) is approximately \( 0.6296 \) (with the \( 629 \) repeating).

In summary:

\[
\frac{17}{27} \approx 0.6296 \text{ (with 629 repeating)}
\]