Page 104 - ArithBook5thEd ~ BCC

Then we add the columns separately.

2
2
4
3
+ 6
4
5
8
4
1
5
The resulting mixed number, 8 , is not in proper form, because 5 4 =1 . So we leave the proper fractional
4
4
1
part, , in the fractions column, and carry the whole number part, 1, over to the whole number column.
4
(We indicate the carrying by writing {1} above the whole number column.) Then we recompute the
whole number sum, obtaining the final answer in proper form:
{1}
2
2
4
3
+ 6
4
1
9
4

To subtract mixed numbers, we sometimes need a “borrowing” procedure, analogous to the proce-
dure we use when subtracting whole numbers.
2
Example 122. Subtract 7 − 3 .
5
Solution. Note that the whole number 7 is a mixed number with 0 fractional part, and we can represent
0
0 as a fraction using any convenient denominator. Here the convenient choice is 5. So we write 7 = 7 .
5
Aligning whole number parts vertically, we have
0
7
5
2
− 3
5

Now we see that the subtraction in the fractions place is not possible (we can’t take 2 fifths from 0
fifths), so we need to borrow 1 from the whole numbers column. 1 = n n for any convenient n (except
5
0), and in this example, it is convenient to write 1 = . Borrowing 1 = 5 5 from 7 (reducing it to 6),
5
and adding 1 = 5 to 0 at the top of the fractions column, we have
5 5
5
6
5
2
− 3
5
3
3
5

Page 104