To solve the fraction [tex]\(\frac{23}{6}\)[/tex] and provide a detailed step-by-step solution, let's go through the essential steps:
1. Simplifying the Fraction:
The fraction [tex]\(\frac{23}{6}\)[/tex] is already in its simplest form because 23 is a prime number and does not have any common factors with 6 other than 1.
2. Finding the Decimal Value:
To convert the fraction into a decimal, we divide the numerator by the denominator:
[tex]\[
\frac{23}{6} \approx 3.8333333333333335
\][/tex]
This results in approximately 3.8333333333333335.
3. Finding the Quotient and Remainder:
When dividing two integers, we can also express the division in terms of a quotient and a remainder.
- The quotient is the integer part of the division: [tex]\(\left\lfloor \frac{23}{6} \right\rfloor\)[/tex]
[tex]\[
23 \div 6 = 3 \text{ (quotient)}
\][/tex]
- The remainder is what is left after subtracting the product of the quotient and the divisor from the original numerator:
[tex]\[
23 - (6 \times 3) = 23 - 18 = 5
\][/tex]
So, the remainder is 5.
4. Summary of Results:
- The decimal value of the fraction [tex]\(\frac{23}{6}\)[/tex] is approximately 3.8333333333333335.
- The quotient from the division is 3.
- The remainder from the division is 5.
So, in conclusion:
- Decimal form: 3.8333333333333335
- Quotient: 3
- Remainder: 5
