Basic Math & Pre-Algebra For Dummies
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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.

    image0.jpg

    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:

    image4.jpg

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

    image5.jpg

    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:

  1. image10.jpg
  2. image11.jpg
  3. image12.jpg
  4. image13.jpg

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

    image14.jpg

    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

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