Page 105 - ArithBook5thEd ~ BCC

Both of the previous examples could have been done by first converting the mixed numbers into
improper fractions. For example,

2 35 17 18 3
7 − 3 = − = =3 .
5 5 5 5 5

Perhaps you find this easier. But here is an example that would involve much more work if we were to
use that method.

4
2
Example 123. Subtract 153 15 − 67 .
9
Solution. The LCD{15, 9} =45, and since 2 = 6 and 4 = 20 , we write, in vertical form,
15 45 9 45

6
153
45
20
− 67
45

The subtraction in the fractions column is not possible, so we borrow 1 from 153 (in the form 45 )and
45
add it to 6 ,obtaining
45
51
152
45
20
− 67
45

Now the subtraction in the fractions column is possible, and we obtain

51
152
45
20
− 67
45
31
85
45

The fractional part is in lowest terms, and we are done.

If we had done the previous example by first converting the mixed numbers into improper fractions, we
would have had to work with rather large numerators:

6891 3035
−
45 45
Not impossible, but the other method is easier!

Page 105