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Three Kinds of Fractions Study Guide (page 3)

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Updated on Oct 5, 2011

Changing Mixed Numbers Into Improper Fractions

Fractions are easier to multiply and divide as improper fractions rather than as mixed numbers. To change a mixed number into an improper fraction:

  1. Multiply the whole number by the bottom number.
  2. Add the top number to the product from step 1.
  3. Write the total as the top number of a fraction over the original bottom number.

 

Example: Changeinto an improper fraction.

1. Multiply the whole number (2) by the bottom number (4): 2 × 4 = 8
2. Add the result (8) to the top number (3): 8 + 3 = 11
3. Put the total (11) over the bottom number (4):
4. Check: Reverse the process by changing the improper fraction into a mixed number. Since you get back , your answer is right.

 

Example: Change into an improper fraction.

1. Multiply the whole number (3) by the bottom number (8): 3 × 8 = 24
2. Add the result (24) to the top number (5): 24 + 5 = 29
3. Put the total (29) over the bottom number (8):
4. Check: Change the improper fraction into a mixed number. Since you get back , your answer is right.

Tip

Reach into your pocket or coin purse and pull out all your change. You need more than a dollar's worth of change for this exercise, so if you don't have enough, borrow some loose change and add that to the mix. Add up the change you collected and write the total amount as an improper fraction. Then convert it to a mixed number.

Three Kinds of Fractions Sample Questions

  1. Change into a mixed number.
  2. Change into an improper fraction.

Solutions

Question 1

1.

Divide the bottom number (3) into the top number (14) to get the whole number portion (4) of the mixed number:

2.

Write the remainder of the division (2) over the original bottom number (3):

3.

Write the two numbers together:

4.

Check: Change the mixed number back into an improper fraction to make sure you get the original

Question 2

1.

Multiply the whole number (3) by the bottom number (5):

3 × 5 =15

2.

Add the result (15) to the top number (2):

15 + 2 = 17

3.

Put the total (17) over the bottom number (5):

4.

Check: Change the improper fraction back to a mixed number.

 

Dividing 17 by 5 gives an answer of 3 with a remainder of 2:

 

Put the remainder (2) over the original bottom number (5):

 

Write the two numbers together to get back the original mixed number:

Find practice problems and solutions for these concepts at Three Kinds of Fractions Practice Questions.

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