College Algebra & Trigonometry, 2018a

116 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
2 30
38)87, 462
−76
114
−114
0006
0
00062
Now that we have included all the digits from our original number 87,462, the
last step is to divide 38 into 62. This goes one time with 24 left over.
2 301
38)87, 462
−76
114
−114
0006
−0
00062
−38
00024
So, now we have the solution to the original problem 87, 462 ÷ 38 = 2, 301 R24 or
2, 301 24
38 .
The WHY? of the long division algorithm is somewhat hidden by the HOW? In
the first step, we are determining which place value will hold the first digit of our
answer. When we determine that 38 does divide into 87, this indicates that the
first digit in our answer will be the thousands place. Dividing 38 into 87 tells us
how many thousands there will be. Then we subtract:
87, 462
−76, 000
11, 462