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Section 1.3
Operations with Positive Fractions
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Objective 1 : Reduce fractions to lowest terms.
1.3 Lecture Guide: Operations with Positive Fractions
A positive fraction is in lowest terms if the numerator and the denominator are positive and have no common factor greater than _____. To reduce a fraction to lowest terms _______________ both the numerator and the _______________ by their common _______________ .
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1. Write a fraction in lowest terms to represent the shaded portion of each figure.
(a) (b) (c)
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2. 3.2416
1575
Reduce each fraction to lowest terms.
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4. 5.3696
2284
Reduce each fraction to lowest terms.
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Objective 2: Multiply and divide fractions.
Verbally Algebraically Numerical Example
To multiply two fractions, ____________the numerators and multiply the denominators.
for
and .
a c acb d bd
0b
2 37 5
0d
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Perform the indicated multiplication and write the answer in lowest terms.
6. 7.2 53 7
3 64 7
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Perform the indicated multiplication and write the answer in lowest terms.
8. 9.5 28 15 3
205
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10. 11.
Perform the indicated multiplication and write the answer in lowest terms.
1 10 262 13 35 3
8 Determine of 56.
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Division of Fractions
Verbally Algebraically Numerical Example
To divide two fractions, multiply the first fraction by the _________ of the second fraction.
for , , and .
a c a d adb d b c bc
0b 0c 0d
2 53 7
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(a) Why is it important that we require that , , and . In the rule for dividing
fractions?
12. 0b0c 0d
(b) Can integers like 4 be written as fractions?
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13. 14.
Perform the indicated division and write the answer in lowest terms.
2 33 5
12 45 3
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15. 16.
Perform the indicated division and write the answer in lowest terms.
35
4 3
45
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17. 18. Divide 56 by .
Perform the indicated division and write the answer in lowest terms.
7 18 2 7
8
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Objective 3: Add and subtract fractions with the samedenominator.
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Verbally Algebraically Numerical ExampleTo add fractions with the same denominator , add the ____________ and use the common denominator.
for .
To add subtract fractions with the same denominator, subtract the ____________ and use the common denominator.
for .
a c a cb b b
0b
4 27 7
a c a cb b b
0b
4 27 7
Addition and Subtraction of Fractions
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Perform the indicated additions and subtractions and express the result in lowest terms.
19. 20. 3 411 11
1 38 8
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21. 22. 8 315 15
11 724 24
Perform the indicated additions and subtractions and express the result in lowest terms.
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Objective 4: Add and subtract fractions with different denominators.
To add or subtract fractions with different denominators, we must first convert each fraction to an equivalent form having the _______________ denominator.
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Perform the indicated additions and subtractions and express the result in lowest terms.
23. 24. 3 ?5 20
7 ?12 36
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Perform the indicated additions and subtractions and express the result in lowest terms.
25. 26. 1 45 15 5 1
8 2
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Perform the indicated additions and subtractions and express the result in lowest terms.
27. 28. 5 312 8
7 515 18
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Perform the indicated additions and subtractions and express the result in lowest terms.
29. 30. 11 720 30
13 516 24
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Objective 5: Perform operations with mixed numbers.
Perform the indicated operations and express the result as a mixed number in lowest terms.
31. 32. 1 16 4
2 5 1 1
6 42 5
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Perform the indicated operations and express the result as a mixed number in lowest terms.
33. 34. 1 2
5 24 3 1 2
5 24 3
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35. Add the fractions in the first column and multiply the fractions in the second column.
Adding
(a)
Multiplying
(b)
1 512 12
1 512 12
Adding Fractions vs. Multiplying Fractions:
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35. Add the fractions in the first column and multiply the fractions in the second column.
Adding
(c)
Multiplying
(d)2 13 4 2 1
3 4
Adding Fractions vs. Multiplying Fractions: