Simplify special fraction forms.
Recall from Section 1.5 that a fraction bar indicates division. This fact helps us simplify
four special fraction forms.- Fractions that have the same numerator and denominator:In this case, we
have a number divided by itself. The result is 1 (provided the numerator and
denominator are not 0). We call each of the following fractions a form of 1.
...
- Fractions that have a denominator of 1:In this case, we have a number
divided by 1. The result is simply the numerator. - Fractions that have a numerator of 0:In this case, we have division of 0.
The result is 0 (provided the denominator is not 0). - Fractions that have a denominator of 0:In this case, we have division by 0.
The division is undefined.
is undefined is undefined18
0
7
0
0
11
0
0
56
0
0
8
0
7
1
7
24
1
24
5
1
5
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
2210 Chapter 3 Fractions and Mixed Numbers
The Language of Mathematics Perhaps you are wondering about the
fraction form It is said to be undetermined. This form is important inadvanced mathematics courses.0
0
.
EXAMPLE 3
Simplify, if possible: a. b. c. d.
StrategyTo simplify each fraction, we will divide the numerator by the
denominator, if possible.
WHYA fraction bar indicates division.
Solutiona. This corresponds to dividing a quantity into 12 equal parts, and then
considering all 12 of them. We would get 1 whole quantity.b. This corresponds to dividing a quantity into 24 equal parts, and then
considering 0 (none) of them. We would get 0.c. is undefined This corresponds to dividing a quantity into 0 equal parts, and then
considering 18 of them. That is not possible.d. This corresponds to "dividing" a quantity into 1 equal part, and then considering
9 of them. We would get 9 of those quantities.9
1
9
18
0
0
24
0
12
12
1
9
1
18
0
0
24
12
12
Self Check 3
Simplify, if possible:a. b. c. d.Now TryProblem 33