Page 89 - Basic College Mathematics with Early Integers

66 C HAPTE R 1 I THE WHOLE NUMBERS

Division Shown as Repeated Subtraction To further understand division, recall
from Section 1.6 that addition and multiplication are related in the following manner:

3 + 3 + 3 + 3 = 4 * 3 = 12
5
4 addends; each addend is 3
In other words, multiplication is repeated addition. Likewise, division is repeated
subtraction.
For example, let’s find
35 , 8

by repeated subtraction. Keep track of the number of times 8 is subtracted from 35.
We are through when we can subtract no more because the difference is less than 8.

35 , 8: Repeated Subtraction 8 dollars
1 time
35
f 1 time 8 dollars
-8 2 times
35 dollars 8 dollars
27 3 times
f 2 times 8 dollars
-8 4 times
19
f 3 times
-8 3 dollars
11 left over
f 4 times
-8
3 — Remainder
(We cannot subtract 8 again.)
Thus, 35 , 8 = 4 R 3.
To check, perform the same multiplication as usual, but finish by adding in the
remainder.

whole number part # divisor + remainder = dividend
of quotient
∂ ∂ ∂ ∂
4 # 8 + 3 = 35

Objective Solving Problems by Dividing

Below are some key words and phrases that may indicate the operation of division:

Division
Key Words or Phrases Examples Symbols
10
divide divide 10 by 5 10 , 5 or
5
64
quotient the quotient of 64 and 4 64 , 4 or
4
9
divided by 9 divided by 3 9 , 3 or
3
$100 divided equally 100 Copyright 2012 Pearson Education, Inc.
divided or shared equally among 100 , 5 or
among five people 5
100 miles
per 100 miles per 2 hours
2 hours