Page 220 - Basic College Mathematics with Early Integers

S E C T I O N 3.3 I MULTIPLYING AND DIVIDING FRACTIONS 197

Remember that the shortcut procedure above is the same as removing factors of
1 in the product.
# # #
#
#
6 14 2 3 2 7 7 3 2 2 = 1 1 4 4
# #
# #
# # #
#
#
7 27 = 7 3 3 3 = 7 3 3 3 9 = 9
23 4
Example 4 Multiply and simplify: # PRACTICE 4
32 7
4 3
Solution: Notice that 4 and 32 have a common factor of 4. Multiply and simplify: #
27 8
1
#
#
23 4 23 4 23 4 23 23
# = = = =
# #
#
#
32 7 32 7 4 8 7 8 7 56
1 Don’t forget that
we may identify common
Work Practice 4
factors that are not prime
After multiplying two fractions, always check to see whether the product can be numbers.
simplified.
1 1
Example 5 Multiply: - # PRACTICE 5
4 2
Multiply.
Solution: Recall that the product of a negative number and a positive number is
1 11
a negative number. # a- b
2 28
#
1 1 1 1 1
- # =- =-
#
4 2 4 2 8
Work Practice 5
Examples Multiply. PRACTICE 6–7
1 1 Multiply.
#
#
#
6 26 6 26 6 13 2 2
6. a- ba- b = = = The product of two negative 4 33
#
# #
13 30 13 30 13 6 5 5 numbers is a positive number. 6. a- ba- b
1 1 11 16
1 1 1 3 25
# # #
# #
1 2 9 1 2 9 1 2 3 3 3 7. # #
7. # # = = = 6 10 16
# # #
# #
3 5 16 3 5 16 3 5 2 8 40
1 1
Work Practice 6–7
Objective Evaluating Expressions with Fractional Bases
The base of an exponential expression can also be a fraction.
# # #
1 4 1 1 1 1 1 1 1 1 1
a b = # # # = =
# # #
3 3 3 3 3 3 3 3 3 81
('')''*
1
is a factor 4 times.
3 PRACTICE 8
Evaluate.
Example 8 Evaluate. 3 2
3 4
a. a b b. a- b
# # #
2 4 2 2 2 2 2 2 2 2 16 4 5
a. a b = # # # = =
# # #
5 5 5 5 5 5 5 5 5 625 Answers
#
1 2 1 1 1 1 1 The product of two negative numbers 4. 1 11 6. 3 7. 5
#
b. a - b = a - b a - b = = is a positive number. 18 5. - 56 4 64
#
4 4 4 4 4 16 27 16
8. a. b.
Work Practice 8 64 25