How Do You Write a Mixed Fraction by Division?

To write a mixed fraction, you essentially perform division and express the result as a whole number and a proper fraction. The reference provided seems to discuss converting mixed numbers to improper fractions. However, let's discuss how division relates to mixed fractions.

Mixed fractions are composed of a whole number and a proper fraction (where the numerator is less than the denominator). Division is the underlying operation that allows us to express an improper fraction (where the numerator is greater than or equal to the denominator) or a division problem's result as a mixed fraction.

Here's a breakdown of how division turns into a mixed fraction:

Perform the Division: Divide the numerator (the number being divided) by the denominator (the number you're dividing by).
Identify the Whole Number: The quotient (the result of the division) becomes the whole number part of the mixed fraction.
Determine the Remainder: The remainder is the number left over after the division.
Form the Fraction: The remainder becomes the numerator of the fractional part, and the original denominator stays the same.

Let's illustrate with an example: Suppose you want to express 15/4 as a mixed number.

Divide 15 by 4. 4 goes into 15 three times (3 x 4 = 12).
The whole number is 3.
The remainder is 15 - 12 = 3.
The fractional part is 3/4.

Therefore, 15/4 as a mixed number is 3 3/4.

Converting Mixed Numbers to Improper Fractions (Related Concept)

Although the original question asked about writing a mixed fraction by division, the reference focuses on changing a mixed number back into an improper fraction. It's helpful to understand this related process. The video suggests:

Multiply the whole number by the denominator.
Add the numerator to the result from step 1. This sum becomes the new numerator.
Keep the same denominator.

For example, to convert the mixed number 3 3/4 to an improper fraction:

Multiply 3 (whole number) by 4 (denominator): 3 x 4 = 12
Add 3 (numerator): 12 + 3 = 15
Keep the denominator: 4

So, 3 3/4 = 15/4