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May 2012

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The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Subtract mixed numbers: renaming
Free lesson plan from HomeschoolMath.net

Strategy 3: Rename the mixed number. In this method you break up one whole pie into slices, and join the "slices" from the whole pie with the existing slices. After that, you subtract. Examples will make this strategy clear.
3 2 6  is renamed as 2 8 6 , and then we subtract 1 5 6 .     At first we have three uncut pies and 2/6. Then one of the whole pies is cut into 6th parts. Now we have only two whole (uncut) pies and 8 sixth parts. We say that 3 2/6 is renamed as 2 8/6. Then we can subtract 1 5/6 easily. 3 2 6  − 1  5 6   =   2 8 6  − 1  5 6   =  1 3 6	Borrow 1 whole pie. Borrow 1 whole pie from the whole pies' column into the fractional parts' column. The one whole pie is 6 sixths. There were already two sixths in the fractional parts' column, so that is why it now has 8/6. Now you can subtract 5/6.
2 1 8  is renamed as 1 9 8 , and then we subtract 5 8 .   At first we have two uncut pies and 1/8. Then one of the whole pies is cut into 8th parts. Now we have only one whole (uncut) pie and 8 eighth parts. We say that 2 1/8 is renamed as 1 9/8. Then we can subtract 5/8 easily. 2 1 8  −  5 8   =   1 9 8  −  5 8   = 1 4 8	Borrow 1 whole pie. Borrow 1 whole pie from the whole pies' column into the fractional parts' column. The one whole pie is 8 eighths. There was already one eighth in the fractional parts' column, so that is why it now has 9/8. Now you can subtract 5/8.

1. Do not subtract anything. Just cut up one whole pie into fractional parts, and rename the mixed number.

a.  2 1 6  is renamed as

b. (available in the book)

c.  (available in the book)

2. Do not subtract anything. Just cut up one whole pie into fractional parts, and rename the mixed number.

a.  2 3 5  is renamed as

c.  2 1 4  is renamed as

3. Subtract. First rename. Be careful. Check your calculation with the help of the pie pictures.

a. 3 4 9  −  8 9     ↓       = 2 13 9  −  8 9  =	b. (available in the book)
c. (available in the book)	2 3 8 −  1 7 8 d. 2 3 8  −  1 7 8     ↓       =        −  1 7 8  =

4. Subtract. You can draw a picture to help.

5. Rename if needed and subtract.

a.        3  1 7 −  1  3 7	b.        7  4 9 −  2  7 9	c. (available in the book)
			h.        10  3 20 −  5  7 20

6. Figure out what was subtracted. You can use the pictures to help you. 

a.   3  −            = 1 1 4		c. (available in the book)
	e.   5  −            = 1 1 8

7. Subtract. 

Next lesson: A fractional part of a group 2

The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.