What is the answer in fraction form for 5/8÷5?
The Correct Answer and Explanation is:
To solve the division problem ( \frac{5}{8} \div 5 ), we will first convert the whole number into a fraction. The number 5 can be expressed as ( \frac{5}{1} ). Therefore, the expression becomes:
[
\frac{5}{8} \div \frac{5}{1}
]
When dividing by a fraction, it is equivalent to multiplying by its reciprocal. The reciprocal of ( \frac{5}{1} ) is ( \frac{1}{5} ). Thus, we can rewrite the expression as:
[
\frac{5}{8} \times \frac{1}{5}
]
Next, we multiply the numerators and the denominators together:
[
\frac{5 \times 1}{8 \times 5} = \frac{5}{40}
]
Now, we simplify the fraction ( \frac{5}{40} ). To simplify, we need to find the greatest common divisor (GCD) of 5 and 40. The GCD of 5 and 40 is 5. We divide both the numerator and the denominator by their GCD:
[
\frac{5 \div 5}{40 \div 5} = \frac{1}{8}
]
Thus, the final answer to ( \frac{5}{8} \div 5 ) is:
[
\frac{1}{8}
]
In summary, the operation ( \frac{5}{8} \div 5 ) involves converting the whole number into a fraction and then applying the rule of multiplying by the reciprocal. This process leads us to multiply the fractions directly, and then simplify the result. In mathematical operations, it’s important to keep track of the conversions between whole numbers and fractions, especially in division scenarios. By understanding these steps, we can accurately perform operations involving fractions and ensure our results are in their simplest form. The answer, ( \frac{1}{8} ), reflects the correct division of the fraction ( \frac{5}{8} ) by the integer 5.