Page 210 - Basic College Mathematics with Early Integers

S E C T I O N 3.2 I FACTORS AND SIMPLEST FORM 187

The method for simplifying negative fractions is the same as for positive fractions.

10
Example 6 Write in simplest form: - PRACTICE 6
27
9
Solution: Write in simplest form: -
50
#
10 2 5
- =- Prime factorizations of 10 and 27
# #
27 3 3 3
10
Since 10 and 27 have no common factors, - is already in simplest form.
27
Work Practice 6

30
Example 7 Write in simplest form: PRACTICE 7
108
49
Solution: Write in simplest form: 112
# #
30 2 3 5 2 3 5 5 5
# #
= = # # = 1 1 =
# # # #
# #
108 2 2 3 3 3 2 3 2 3 3 18 18
Work Practice 7
We can use a shortcut procedure with common factors when simplifying.
1
#
#
4 2 2 1 2 2 Divide out the common factor of 2 in the
= = =
#
#
6 2 3 1 3 3 numerator and denominator.
1
This procedure is possible because dividing out a common factor in the numerator
and denominator is the same as removing a factor of 1 in the product.
Writing a Fraction in Simplest Form

To write a fraction in simplest form,write the prime factorization of the numerator
and the denominator and then divide both by all common factors.

72
Example 8 Write in simplest form: - PRACTICE 8
26
64
Solution: Write in simplest form: - 20
1
# # # #
# # # #
72 2 2 2 3 3 1 2 2 3 3 36
- =- =- =-
#
#
26 2 13 1 13 13
1
Work Practice 8
15
Concept Check Which is the correct way to simplify the fraction ?
25
Or are both correct? Explain.
1 1 Answers
#
15 3 5 3 1 5 11
a. = = b. = 9 7 16
#
25 5 5 5 2 5 21 6. - 50 7. 16 8. - 5
1 1
Concept Check Answers
a. correct b. incorrect