5 2/3 divided by 4 in fraction

5 2/3 divided by 4 in fraction

The Correct Answer and Explanation is:

To solve the problem ( 5 \frac{2}{3} \div 4 ), we need to follow a few steps involving fraction operations. Let’s break down the solution:

Step 1: Convert the mixed number to an improper fraction

A mixed number, like ( 5 \frac{2}{3} ), consists of a whole number part and a fractional part. To convert it to an improper fraction, we multiply the whole number by the denominator of the fractional part, and then add the numerator of the fraction. Here’s how we do it:

[
5 \frac{2}{3} = \frac{(5 \times 3) + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}
]

So, ( 5 \frac{2}{3} ) becomes ( \frac{17}{3} ).

Step 2: Divide the improper fraction by 4

Now, we need to divide ( \frac{17}{3} ) by 4. To divide by a whole number, we multiply by the reciprocal of the whole number. The reciprocal of 4 is ( \frac{1}{4} ), so we rewrite the division as multiplication:

[
\frac{17}{3} \div 4 = \frac{17}{3} \times \frac{1}{4}
]

Step 3: Multiply the fractions

To multiply fractions, we multiply the numerators and the denominators:

[
\frac{17}{3} \times \frac{1}{4} = \frac{17 \times 1}{3 \times 4} = \frac{17}{12}
]

Step 4: Simplify the result (if necessary)

The fraction ( \frac{17}{12} ) is already in its simplest form, as 17 is a prime number and does not share any factors with 12.

Final Answer:

The result of ( 5 \frac{2}{3} \div 4 ) is ( \frac{17}{12} ).

Explanation:

When dividing fractions or mixed numbers, it’s essential to first convert mixed numbers to improper fractions. Then, dividing by a whole number can be done by multiplying by the reciprocal of that number. Finally, we perform the multiplication step and simplify the result if needed. The answer, ( \frac{17}{12} ), is an improper fraction that shows the division result in a precise fractional form. This method ensures that we apply correct fraction operations to handle the division of a mixed number by a whole number.