Question

15/ 9,976

Answer 1

whats the answer

Answer 2

To simplify the fraction \( \frac{15}{9,976} \), we can first check if both the numerator and the denominator have any common factors.

1. The prime factorization of the numerator \( 15 \) is \( 3 \times 5 \).
2. For the denominator \( 9,976 \), let's factor it:
- \( 9,976 \) is an even number, so it is divisible by \( 2 \):
\[
9,976 \div 2 = 4,988
\]
\[
4,988 \div 2 = 2,494
\]
\[
2,494 \div 2 = 1,247
\]
- Now, \( 1,247 \) needs to be factored further. It is not even, so check for divisibility by \( 3 \):
\[
1 + 2 + 4 + 7 = 14 \quad \text{(not divisible by 3)}
\]
- Check divisibility by \( 5 \) (not applicable as it does not end in \( 0 \) or \( 5 \)).
- Check divisibility by \( 7 \):
\[
1,247 \div 7 = 178.142857... \quad \text{(not divisible)}
\]
- Check divisibility by \( 11 \):
\[
1,247 \div 11 = 113.363636... \quad \text{(not divisible)}
\]
- Check divisibility by \( 13 \):
\[
1,247 \div 13 = 96.6923077... \quad \text{(not divisible)}
\]
- Check divisibility by \( 17 \):
\[
1,247 \div 17 = 73.3529411... \quad \text{(not divisible)}
\]
- Finally, check divisibility by \( 19 \):
\[
1,247 \div 19 = 65.1052631... \quad \text{(not divisible)}
\]
- We find that \( 1,247 = 19 \times 67 \) after testing.

So the full factorization of \( 9,976 \) is:
\[
9,976 = 2^3 \times 19 \times 67
\]

Since \( 15 \) does not share any common factors with \( 9,976 \), the greatest common divisor (gcd) of \( 15 \) and \( 9,976 \) is \( 1 \).

Thus, the fraction \( \frac{15}{9,976} \) is already in its simplest form.

Final answer:
\[
\frac{15}{9,976}
\]

Answer 3

To calculate the value of the fraction \( \frac{15}{9,976} \):

\[
\frac{15}{9,976} \approx 0.0015
\]

Therefore, the approximate decimal value of \( \frac{15}{9,976} \) is \( 0.0015 \).