How do you change a mixed number into an improper fraction?

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electreto05's profile pic

electreto05 | College Teacher | (Level 1) Assistant Educator

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A mixed number consists of an integer part and a fraction. In fact the mixed number can be seen as the sum of the integer part plus the fractional part.

For example, the mixed number 3 (1/5), can be expressed as:

3 (1/5) = 3 + (1/5)

If we solve the operation as a sum of fractions, we have:

3 + (1/5) = (3/1) + (1/5) = (15 + 1)/5 = 16/5

So that:

3 (1/5) = 16/5

A faster way is to multiply the denominator of the fraction by the integer and then add the numerator; the result is the new numerator and denominator is retained; The procedure is as follows:

3 (1/5) = [(5*3) + 1]/5 = 16/5

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kalau | (Level 2) Adjunct Educator

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How u change a mixed number into a improper fraction? 

A mixed number has three components:  A coefficient, a numerator, and denominator.

Let's say we have two and one fourth.` `

2 1/4

2 is the coefficient, 1 is the numerator, and 4 is the denominator.

The denominator remains the same for an improper fraction.   

To get the numerator, we will multiply the denominator with the coefficient, and then add the denominator.

4*2 + 1 = 8+1 = 9

Therefore, 2 1/4 is the same as 9/4 as an improper fraction.

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srost | eNotes Newbie

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To reverse a mixed number into an improper fraction, we look at the denominator of the fraction to let us know how many parts of a whole we have. 

Let's take the mixed number 6 (2/3). Here we are dealing with thirds (1/3).

We then need to ask: How many thirds are in a whole? 3! 

So, in our mixed number we have 6 wholes which  can multiply by 3 to determine how many thirds all together. 6 x 3= 18

We are not done yet! Although we know we have 18/3 in 6 wholes, we can't forget to add the 2/3 from our mixed number.

So now we have this equation: 18/3 + 2/3= 20/3.

20/3 = 6 (2/3)

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mck3mama | eNotes Newbie

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Multiply the denominator and the whole number.  Then add the numerator.  For example, 5 2/3 as an improper fraction would be 17/3.  (3x5)+2.