Section 1.3

Operations with Positive Fractions

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 _______________ .

1. Write a fraction in lowest terms to represent the shaded portion of each figure.

(a) (b) (c)

2. 3.2416

1575

Reduce each fraction to lowest terms.

4. 5.3696

2284

Reduce each fraction to lowest terms.

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

Perform the indicated multiplication and write the answer in lowest terms.

6. 7.2 53 7

3 64 7

Perform the indicated multiplication and write the answer in lowest terms.

8. 9.5 28 15 3

205

10. 11.

Perform the indicated multiplication and write the answer in lowest terms.

1 10 262 13 35 3

8 Determine of 56.

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

(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?

13. 14.

Perform the indicated division and write the answer in lowest terms.

2 33 5

12 45 3

15. 16.

Perform the indicated division and write the answer in lowest terms.

35

4 3

45

17. 18. Divide 56 by .

Perform the indicated division and write the answer in lowest terms.

7 18 2 7

8

Objective 3: Add and subtract fractions with the samedenominator.

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

Perform the indicated additions and subtractions and express the result in lowest terms.

19. 20. 3 411 11

1 38 8

21. 22. 8 315 15

11 724 24

Perform the indicated additions and subtractions and express the result in lowest terms.

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.

Perform the indicated additions and subtractions and express the result in lowest terms.

23. 24. 3 ?5 20

7 ?12 36

Perform the indicated additions and subtractions and express the result in lowest terms.

25. 26. 1 45 15 5 1

8 2

Perform the indicated additions and subtractions and express the result in lowest terms.

27. 28. 5 312 8

7 515 18

Perform the indicated additions and subtractions and express the result in lowest terms.

29. 30. 11 720 30

13 516 24

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

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

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:

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: