Chapter 6.3, Problem 25P

When you divide whole numbers using an ordinary calculator, the answer is displayed as a decimal. But what if you want the answer as a whole number with a remainder? Here's a method to determine the remainder with an ordinary calculator, illustrated with the example of $236÷7$ .
Use the calculator to divide the whole numbers:
   $236÷7=\mathrm{33.71428...}$
Subtract the whole number part of the answer:
   $\mathrm{33.71428...}-33=\mathrm{0.71428...}$
Multiply the resulting decimal by the divisor (which was 7):
   $\mathrm{0.71428...}\cdot 7=4.99999(or5)$
Round the resulting number to the nearest whole number. This is your remainder. In this example the remainder is 5. So $236÷7=33,$ remainder 5.

1. Using a calculator, solve at least two more division problems with whole numbers, and use the preceding method to find the answer as a whole number with a remainder. Check that your answers are correct.
2. Now solve the same division problems you did in part (a), except this time give your answers as mixed numbers instead of as decimals.
3. Use the mixed number version to help you explain why the calculator method for determining the remainder works.