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A R I T H M E T I C

SUBTRACTING MIXED NUMBERS

Lesson 24 Section 2

First, let us subtract mixed units.

To add, subtract, or divide, the units must be the same. We subtract hours from hours and minutes from minutes. Now, we cannot take 40 minutes from 10 minutes. To get more minutes, we will break off 1 of the 7 hours, and decompose it into 60 minutes. We then regroup them with 10 minutes.

60 minutes + 10 minutes = 70 minutes:

2 hours from 6 hours is 4 hours. 40 minutes from 70 minutes is 30 minutes.

Solution. We cannot take 11 inches from no inches. To make inches, then, from 8 feet we will take 1 foot -- which is 12 inches:

5 feet from 7 feet is 2 feet. 11 inches from 12 inches is 1 inch.

We are now ready to subtract mixed numbers. We will treat them just like mixed units. First:

5.	How do we subtract a mixed number from a whole number?

	Break off 1 from the whole number and express it with the same denominator, then group the fractions.

Example 3. 8 − 2

3
4

To subtract 3-fourths from 8, we must make fourths. To do this,

break off 1 from 8, and decompose it into

4
4

8 = 7 + 1 = 7

4
4

(Lesson 20, Example 4.) Therefore,

"2 from 7 is 5.

3
4

from

4
4

1
4

Compare this with Example 2 in which there were no inches. There, we had to create inches from 8 feet. Here, we had to create fourths from the whole number 8.

Example 4.	6 − 1	2 3	=	5	3 3	− 1	2 3

			=	4	1 3	.

3
3

2
3

3
3

1
3

Example 5. Subtracting mixed numbers. Let us compare this problem

1
3

− 1

2
3

with the previous one. We cannot take

2
3

from

1
3

. We need more thirds.

And we will get them from 6. Again, we will decompose 6 into 5

3
3

but here we will add the

3
3

to the original

1
3

, making 5

4
3

6	1 3	=	5	3 3	+	1 3

		=	5	4 3	.

Therefore,

1
3

2
3

4
3

2
3

2
3

2
3

4
3

2
3

Compare this with Example 1, in which to get more minutes, we had to decompose 7 hours. Here, to get more thirds, we had to decompose the whole number 6.