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**Operations with Positive Fractions**

Section 1.3 Operations with Positive Fractions

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**1.3 Lecture Guide: Operations with Positive Fractions**

Objective 1 : Reduce fractions to lowest terms. 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.**

(b) (c)

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**Reduce each fraction to lowest terms.**

2. 3.

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**Reduce each fraction to lowest terms.**

4. 5.

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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

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

6. 7.

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

8. 9.

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

10. 11. 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

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12. (a) Why is it important that we require that , , and In the rule for dividing fractions? (b) Can integers like 4 be written as fractions?

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

13. 14.

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

15. 16.

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

17. 18. Divide 56 by .

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**Objective 3: Add and subtract fractions with the same**

denominator.

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**Addition and Subtraction of Fractions**

Verbally Algebraically Numerical Example To 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

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**Perform the indicated additions and subtractions and express**

the result in lowest terms. 19. 20.

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**Perform the indicated additions and subtractions and express**

the result in lowest terms. 21. 22.

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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.

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

25. 26.

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

27. 28.

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

29. 30.

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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.

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**Perform the indicated operations and express the result as**

a mixed number in lowest terms. 33. 34.

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**Adding Fractions vs. Multiplying Fractions:**

35. Add the fractions in the first column and multiply the fractions in the second column. Adding (a) Multiplying (b)

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**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)

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