How to Convert between Mixed Numbers and Improper Fractions

By Mark Zegarelli

When the numerator (top number) is greater than the denominator (bottom number), that fraction is an improper fraction. An alternative form for an improper fraction is as a mixed number, which is made up of a whole number and a fraction.

For example, you can represent the improper fraction 3/2 as the equivalent mixed number 1-1/2. The mixed number 1-1/2 means 1 + 1/2. To see why 3/2 = 1-1/2, realize that three halves of a cake is the same as one whole cake plus another half. Every improper fraction has an equivalent mixed number, and vice versa.

Sometimes at the beginning of a fraction problem, converting a mixed number to an improper fraction makes the problem easier to solve. Here’s how to make the switch from mixed number to improper fraction:

  1. Multiply the whole number by the fraction’s denominator (bottom number).

  2. Add the numerator (top number) to the product from Step 1.

  3. Place the sum from Step 2 over the original denominator.

Similarly, at the end of some problems, you may need to convert an improper fraction to a mixed number. To do so, simply divide the numerator by the denominator. Then build a mixed number:

  • The quotient is the whole number.

  • The remainder is the numerator of the fraction.

  • The denominator of the fraction stays the same.

Think of the fraction bar as a division sign.

Sample questions

  1. Convert the mixed number 2-3/4 to an improper fraction.

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    Multiply the whole number (2) by the denominator (4), and then add the numerator (3):

    2 x 4 + 3 = 11

    Use this number as the numerator of your answer, keeping the same denominator:

    image1.jpg

  2. Convert the mixed number 3-5/7 to an improper fraction:

    image2.jpg

    Multiply the whole number (3) by the denominator (7), and then add the numerator (5). This time, do the whole process in one step:

    image3.jpg

  3. Convert the improper fraction 11/2 to a mixed number:

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    Divide the numerator (11) by the denominator (2):

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    Now build a mixed number using the quotient (5) as the whole number and the remainder (1) as the numerator, keeping the same denominator (2):

    image6.jpg

  4. Convert the improper fraction 39/5 to a mixed number:

    image7.jpg

    Divide the numerator (39) by the denominator (5):

    image8.jpg

    Build your answer using the quotient (7) as the whole number and the remainder (4) as the numerator, keeping the same denominator (5):

    image9.jpg

Practice questions

  1. Convert the mixed number 5-1/4 to an improper fraction.

  2. Change 7-2/9 to an improper fraction.

  3. Express the mixed number 10-5/12 as an improper fraction.

  4. Convert the improper fraction 13/4 to a mixed number.

  5. Express the improper fraction 29/10 as a mixed number.

  6. Change 100/7 to a mixed number.

Following are the answers to the practice questions:

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  2. image11.jpg

  3. image12.jpg

  4. image13.jpg

    Divide the numerator (13) by the denominator (4):

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    Build your answer using the quotient (3) as the whole number and the remainder (1) as the numerator, keeping the same denominator (4):

    image15.jpg

  5. image16.jpg

    Divide the numerator (29) by the denominator (10):

    image17.jpg

    Build your answer using the quotient (2) as the whole number and the remainder (9) as the numerator, keeping the same denominator (10):

    image18.jpg

  6. image19.jpg

    Divide the numerator (100) by the denominator (7):

    image20.jpg

    Build your answer using the quotient (14) as the whole number and the remainder (2) as the numerator, keeping the same denominator (7):

    image21.jpg