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May 2012

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 Adding mixed numbers
a free lesson with a video

In my video below (also available at my Youtube channel) we study adding mixed numbers when their fractional parts are like fractions. This is not a difficult concept - all you have to remember is that if the sum of the fractional parts is more than 1, you need to convert that to "whole pies" and whatever is left over.

The lesson below also explains the same ideas. It is taken from Math Mammoth Fractions 1 book.

1. Can you figure out these addition problems without reading the instruction in the blue box below? Write an addition sentence for each problem. Read the instructions below afterwards.

+ a.

+ b.

Adding mixed numbers You can simply add the whole numbers and fractional parts separately: 1 1 7   +   5 3 7   =   6 4 7           or in columns →     1 1 7 +  5 3 7 6 4 7

However, many times the sum of the fractional parts goes over one whole pie. + = 1 3 6 + 1 4 6 = 2 7 6   →    3 1 6 Even so, you can first simply add the fractional parts as usual. Then, change the fraction that is more than one pie into whole pie(s) and a fractional part that is less than one pie.

2. These mixed numbers have a fractional part that is more than "one pie". Change them so that the fractional part is less than one. The first one is done for you.

3. Write the addition sentences that the pictures illustrate and add.

+ + a.

b.

4. Write the addition sentences that the pictures illustrate and add.

a.    +
c.   +
e.    +   +

5. Add.

6. Add.

a. 4 3 7       + 5 5 7                 9 8 7  →  10 1 7

b. 3 3 5   + 3 4 5              →

7. Find the missing addend. Imagine drawing more to the picture.

a.   1 1 2 +              = 3
c.   1 1 4 +              = 5

Sometimes the sum of the fractional parts can go over two or three whole pies. Figure out how many whole pies you can make from the fractional part, and add them to the whole number.     + +   = 1 5 6  +  1 3 6  +  1 5 6  =   3 13 6   →    5 1 6   1 5 6         1 3 6       +   1 5 6         3 13 6   →  5 1 6

8. Convert these mixed numbers so that the fractional part is less than one.

a.  3 13 5  →  5 3 5

b.  1 11 4

9. Add the mixed numbers.

10. (available in the book)

11. Add the mixed numbers.

a. 10 7 9     2 5 9   + 3 8 9         12 20 9  →

b. 1 5 11     3 9 11   + 2 8 11              →

12. Find the missing addends.

Next lesson: subtracting mixed numbers

The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book.

Math Mammoth Fractions 1 $4.50 A self-teaching printable worktext that teaches fractions and their operations with visual models. You don't need to just memorize fraction rules blindly - learn and understand! The book covers fractions, mixed numbers, equivalent fractions, adding and subtracting like fractions and unlike fractions, adding and subtracting mixed numbers, comparing fractions, and finding a fractional part of a group.