Converting improper fractions to mixed numbers

In this lesson, we are going to convert improper fractions to mixed numbers. It’s a piece of cake, we have prepared some examples.

Content:

• Steps for converting an improper fraction to a mixed number
• Example 1
• Example 2
• Example 3
• Videos
• References

Don’t forget that an improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Also, a mixed number is a number containing a whole number and a proper fraction.

Steps for writing an improper fraction as a mixed number

To write an improper fraction as a mixed number, follow these steps:

• Divide the numerator by the denominator.
• The quotient is the whole number part of the mixed number.
• The remainder over the original denominator is the fractional part of the mixed number.

Don’t worry, it is not as difficult as you may think, we will understand these steps with some examples. At this point, we should remember the parts of a division: dividend, divisor, quotient, and remainder:}.

1) Rewrite ⁷/₂ as a mixed number

To convert this improper fraction, first, we divide 7 by 2. Next, the quotient (3) of this division is the whole number part. Finally, we write the remainder (1) over the original denominator (2) to get the fractional part.

In that way, the improper fraction ⁷/₂ is equivalent to 3¹/₂.

2) Rewrite ⁵/₃ as a mixed number

To write ⁵/₃ as a mixed number, first, we divide the numerator (5) by the denominator (3). The quotient (1) is the whole number part of the mixed number. Next, the remainder (2) over the original denominator (3) is the fractional part of the mixed number.

We can also use a graphical method to do this conversion. First, we model the fraction ⁵/₃. In this diagram 1 circle represents 1 whole.

As you may have noticed, we have 1 whole circle and ²/₃ of a circle. Therefore, the improper fraction ⁵/₃ is equivalent to the mixed number 1²/₃.

3) Rewrite 19/5 as a mixed number

We start by dividing the numerator (19) by the denominator (5). Next, the whole number part is the quotient (3) of the division. Finally, we write the remainder (4) over the original denominator (5).

4) Rewrite ¹²/₂ as a mixed number or whole number

When the remainder is 0, the improper fraction is a whole number. In this case, when we divide 12 by 2, the remainder is 0. Therefore, the improper fraction ¹²/₂ is equivalent to 6 wholes.

Videos

In the next video, we will convert more improper fractions to mixed numbers.

And here you will find more examples.

In this video we will see more examples:

References

For this lesson, we have used these books:

• Martin-Gay, E. (2020). Basic college mathematics with early integers (4th ed.; pp. 245-246). Pearson.
• Tussy, K., Gustafson, D. y Koenig, D. (2013). Prealgebra (4th ed.; pp. 362-363). Cengage Learning.