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3.01 Reducing Fractions from Basic Algebra: One Step at a Time © 2002 P. 241-246 Dr. Robert J. Rapalje Seminole State College of Florida
ANSWERS TO ALL EXERCISES ARE INCLUDED AT THE END OF THIS PAGE
Before beginning Chapter 3 on FRACTIONS be sure to have both of your calculators turned on--that is, the calculator in your hand, and the calculator between your ears! This chapter on fractions provides an excellent opportunity to use the hand-held calculator to solve problems and check your answers, especially if you have a calculator that works with fractions and converts decimals to fractions. It also gives you the opportunity to develop and sharpen your mental skills by using your "head-calculator." It is not a question of whether or not to use the hand-held calculator, or of which calculator to use. You really need to use both! In this chapter there will be five types of fractions problems: reducing fractions, multiplying and dividing fractions, adding and subtracting fractions, solving fractional equations, and a few easy applications that (believe it or not!) you will really like.
A fraction can be “reduced” whenever a factor can be found that divides evenly into both the numerator and denominator of the fraction. For example, the fraction 8/12 can be reduced because 4 is a factor of the numerator and also the denominator. Dividing the numerator and denominator by 4 reduces the fraction to 2/3.
EXAMPLE 1.
Reduce the fraction
Solution: Notice
that both numerator and denominator are even numbers, and therefore
divisible by 2. Dividing 126 and 216 each by 2, you get
EXAMPLE 2.
Reduce the fraction
Solution
#1: First,
enter the numerator 126 divided by the denominator, and press [ENTER] or
[=]. This changes the fraction to a decimal 0.583333333 . . . Most
calculators can convert this decimal to a fraction, and the fraction will
be reduced to lowest terms. For a TI 85/86, press [CUSTOM] [Frac]
[ENTER]. For a TI 30, press [2nd] [F«D].
The calculator should give you for a final answer,
Solution
#2: If
your calculator has an [a b/c] button (TI 30 and several other
brands and models of calculators), then press [126] [a b/c] [216] [=].
The calculator will give you 7
ű
12, which
means EXERCISES. In each of the following, reduce the fractions completely. As in the examples above, you reduce the fractions with or without a calculator, or use both methods. If you use a calculator, of course you will not need the hints nor the extra blanks that are provided.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
= _________ is reduced completely. [Hint: one to three steps!] = _________
12.
= _________ is reduced completely. [Hint: one to three steps!] = _________
13.
= _________ is reduced completely. [Hint: one to three steps!] = _________
14.
= _________ is reduced completely. [Hint: one to three steps!] = _________
15.
[Remember: when you divide with variables, you subtract exponents!]
16.
17.
Divide out 14, X2, and Y6. Avoid negative exponents!
19.
21.
23.
24.
25.
26.
[Notice that in these exercises, only FACTORS (not TERMS!) can be divided out!]
27.
29.
In the next exercises, remember you must factor the numerator and denominator (if possible!) first. Divide out only factors that are common to the numerator and denominator.
31.
= ________________ = _________________
33.
= ________________ = _________________
35.
= ________________ = _________________
37.
= ______________ = ______________
39.
= ______________ = ______________
41.
= ______________ = ______________
43.
45a) The negative of x is _______. b) The negative of y is ________. c) The negative of x - y is - (x - y) or ________ or ________. d) The negative of y - x is - (y - x) or ________ or ________. e) The negative of a - b is - (a - b) or ________ or ________. f) The negative of b - a is - (b - a) or ________ or ________. g) If you take the negative of 6 - 3 (which is +3), you could say 3 - 6 or ________.
46a) When any number is divided by its negative, what is the result? ________
Examples:
b)
47.
50.
ANSWERS 3.01 p. 242 - 246:
1.
3/4; 2. 7/15; 3. 2/3; 4.
2/9; 5. 2/5; 6. 2/3; 7. 4/5; 8. 5/4 or 1
1/4; 9. 5/2 or 2 1/2; 10. 26/43; 11. 2/9; 12.
9/37; 13. 2/7; 14. 2/5; 15. 45a) -x; b) -y; c) -x+y or y-x; d) -y+x or x-y; 45e) -a+b or b-a; f) -b+a or a-b; g) -3; 46a) -1; b) -1; c) -1; d) -1; e) -1; 47. -1; 48. -1; 49. 1; 50. -1; 51. -1; 52. 1. Return to main page Math in Living C O L O R !! Return to Basic Algebra page Return to Intermediate Algebra page Return to College Algebra page
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