# Mixed numbers and fractions: how to convert from one to the other

This is a fifth grade lesson about fractions and mixed numbers. First, this lesson has some review exercises about mixed numbers. Then, we learn how to change mixed numbers into fractions - both the concept and the shortcut. Lastly, we convert improper fractions into mixed numbers by thinking of them as DIVISIONS.

### Mixed numbers as pictures

1. Write the mixed numbers that these pictures illustrate.

 a. b. c. d.

2. Draw pictures of “pies” that illustrate these mixed numbers.

 a.  4 2 3
 b.  2 3 5
 c.  3 2 6
 d.  4 7 8
 e.  6 8 10

3. Write the mixed number that is illustrated by each number line.

 a.
 b.

4. Write the fractions and mixed numbers that the arrows indicate.

 a. b. c. d.

5. Mark the fractions on the number lines.

 a. 10 6 , 17 6 , 12 6 , 5 6 , 14 6

 b. 9 8 , 22 8 , 13 8 , 24 8 , 11 8

 6. a. Mark 1 3 5 on the number line.     b. Write the mixed number that is 4 5 to its right: _______

 c. Mark 2 1 5 on the number line.     d. Write the mixed number that is 3 5 to its left: _______

 Changing mixed numbers to fractions To write 3 3 4 as a fraction, count how many fourths there are:
 Each pie has four fourths, so the three complete pies have 3 × 4 = 12 fourths. Additionally, the incomplete pie has three fourths. The total is 15 fourths or 15/4.

Shortcut:

Numerator: 3 × 4 + 3 = 15

Denominator: 4

 = 15 4

 Multiply the whole number times the denominator, then add the numerator. The result gives you the number of fourths, or the numerator, for the fraction. The denominator will remain the same.

7. Write as mixed numbers and as fractions.

 a.   1 2 5 = 5

 b. =

 c. =

 d. =

 e. =

 f. =

 8. May changed 5 9 13 into a fraction, and explained how the shortcut works. Fill in.

There are ____ whole pies, and each pie has _____ slices. So ____ × ____

 tells us the number of slices in the whole pies. Then the fractional part 9/13 means that we add _____ slices to that. In total we get ____ slices, each one a 13th part. So the fraction is .

9. Write as fractions. Think of the shortcut.

 a.  7 1 2
 b.  6 2 3
 c.  8 3 9
 d.  6 6 10
 e.  2 5 11
 f.  8 1 12
 g.  2 5 16
 h.  4 7 8

### Changing fractions to mixed numbers

 To write a fraction, such as 58 7 , as a mixed number, you need to figure out:
• How many whole “pies” there are, and
• How many slices are left over.
 In the case of 58 7 , each whole “pie” will have 7 sevenths. (How do you know?) So we ask:
• How many 7s are there in 58?  (Those make the whole pies!)
• After the 7s are gone, how many are left over?

That is solved by the division 58 ÷ 7!  That division tells you how many 7s there are in 58.

Now, 58 ÷ 7 = 8 R2. So you get 8 whole pies, with 2 slices or 2 sevenths left over.

 To write that as a fraction, we get 58 7 = 8 2 7 .
 Example: 45 4 is the same as 45 ÷ 4, and 45 ÷ 4 = 11 R1. So, we get 11 whole pies and
 1 fourth-part or slice left over. Writing that as a mixed number, 45 4 = 11 1 4 .

The Shortcut: Think of the fraction bar as a division symbol, then DIVIDE. The quotient tells
you the whole number part, and the remainder tells you the numerator of the fractional part.

10. Rewrite the “division problems with remainders” as problems of “changing fractions to mixed
numbers.”

a.  47 ÷ 4 = 11 R3

 47 4 =  11 3 4

b.  35 ÷ 8 = 4 R3

 =

c.  19 ÷ 2 = ___ R ___

 =

d.  35 ÷ 6 = ___ R ___

 =

e.  72 ÷ 10 = ___ R ___

 =

f.  22 ÷ 7 = ___ R ___

 =

11. Write these fractions as mixed numbers (or as whole numbers, if you can).

 a. 62 8
 b. 16 3
 c. 27 5
 d. 32 9
 e. 7 2
 f. 25 4
 g. 50 6
 h. 32 5
 i. 24 11
 j. 39 3
 k. 57 8
 l. 87 9

This lesson is taken from Maria Miller's book Math Mammoth Fractions 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.