1 fractions
DESCRIPTION
for studyTRANSCRIPT
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Numerator Denominator
2
Fractions
I. Fractions a. Definition: A fraction (also called a rational number) is a number
that represents the quotient (or division) of two integers.
b. =ba
c. The denominator tells how many equal parts there are. d. The numerator tells how many of these parts are taken or used. e. Simplest form: A fraction is said to be written in simplest form
when there are no common factors in the numerator and denominator. The fraction has been reduced completely.
II. Zero In other words, zero in the numerator of a fraction yields zero for an answer as long as the denominator does not equal zero.
a. 00 =c where . 0c
b. =0c
undefined. In other words, division by zero is impossible!
=00
undefined.
III. Mixed Numbers & Improper Fractions a. You can change a mixed number to an improper fraction: b.
+ Steps:
1. Multiply the denominator by the whole number.
2. Add to the numerator. 3. The product becomes the
new numerator. 4. Denominator remains the
same.
=
83=
83
819
83)28( =+2
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IV. Multiplication and Division of Fractions
a. 1. 1514
57
32 = Multiply across the numerator and across the
denominator.
You may cancel before multiplying.
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2.
2
1 54
56
32 =
b. 1. 2110
75
32
57
32 == To divide, multiply by the reciprocal. DO NOT
cancel before inverting!!!
2
1 19462
2.
V. Equivalent Fractions a. You may multiply of divide both numerator and denominator of a
fraction by the same non-zero number without changing the fraction.
1. 2114
77
32 = and 3
22114=
2. 1510
55
32
55
32 == and 3
21510=
b. Your answer to a problem may be 52
, by the selection of answers
may look like:
A. 305
B. 3013
C. 3010
D. 3012
E. 3018
The correct answer is D because 52
3012= .
193==
619
32
These are Equivalent Fractions.
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VI. Addition and Subtraction of Fractions a. You may add or subtract fractions with the same denominator by
adding (or subtracting) the numerators and putting this answer over the common denominator.
Ex) 53
51
52 =+ Ex) 5
3106
101
107 ==
b. To add (or subtract) fractions with different denominators you
must first find the Least Common Denominator (LCD) and convert each fraction to an equivalent fraction whose denominator is the LCD.
1. Definition: The LCD is the smallest number that each denominator will divide into evenly. (The LCD is the smallest multiple that the given denominators have in common.)
Example Finding Common Denominators:
487
65
81 +
Examine each of the given denominators and break them down into their prime factors:
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3222248326
2228
==
=
The LCD is equal to every factor of the first denominator multiplied by any new factor that appears in a subsequent denominator.
LCD = 23222 There are 4 twos in the last denominator and only 3 so far in the LCD so we need one more factor of two. The factor of 3 in the last denominator does not need to be repeated.
We begin with every factor of the first denominator. 3 is a new factor from the 2nd
denominator. (The 2 of the 2nd denominator does not have to be be repeated since there are already 3 factors of 2.
so our LCD is 48.
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Now that we have our LCD, lets finish the problem: Change each of the given fractions to an equivalent fraction whose denominator is the LCD.
487
4840
486
487
65
81 +=+ Add the equivalent fractions and reduce the answer.
1613
4839
487
4840
486 ==+
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Practice Problems:
1. =)20(43
13. =8413
2. =+81
85
14. =94
32
3. =81
85
15. = 432
4. =+31
21
16. =43
1615
5. =+652
52
17. =421
1211
6. =+43
85
18. =217
7. =21
43
19. =0
14
8. =312
654 20. =
140
9. =187
16153 21. =0
131
10. =353
79
22. =1310
11. =83
32
23. =+65
103
34
12. =85
31
53
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Answers to Fractions: 1. 13. 26 15
2. 43
14. 211
3. 15. 561
4. 65
16. 45
or 411
5. 3073 17.
6311
6. 811
or 831 18. 14
7. 41
19. Undefined.
8. 212 20. 0
9. 144793 21. Undefined.
10. 56
or 511 22.
131
11. 41
23. 54
3024 =
12. 81
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