Operations with Positive Fractions Section 1.3 Operations with Positive Fractions

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 _______________ .

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

Reduce each fraction to lowest terms. 2. 3.

Reduce each fraction to lowest terms. 4. 5.

Objective 2: Multiply and divide fractions. Verbally Algebraically Numerical Example To multiply two fractions, ____________ the numerators and multiply the denominators. for and .

Perform the indicated multiplication and write the answer in lowest terms. 6. 7.

Perform the indicated multiplication and write the answer in lowest terms. 8. 9.

Perform the indicated multiplication and write the answer in lowest terms. 10. 11. 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 .

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?

Perform the indicated division and write the answer in lowest terms. 13. 14.

Perform the indicated division and write the answer in lowest terms. 15. 16.

Perform the indicated division and write the answer in lowest terms. 17. 18. Divide 56 by .

Objective 3: Add and subtract fractions with the same denominator.

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 .

Perform the indicated additions and subtractions and express the result in lowest terms. 19. 20.

Perform the indicated additions and subtractions and express the result in lowest terms. 21. 22.

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.

Perform the indicated additions and subtractions and express the result in lowest terms. 25. 26.

Perform the indicated additions and subtractions and express the result in lowest terms. 27. 28.

Perform the indicated additions and subtractions and express the result in lowest terms. 29. 30.

Objective 5: Perform operations with mixed numbers. Perform the indicated operations and express the result as a mixed number in lowest terms. 31. 32.

Perform the indicated operations and express the result as a mixed number in lowest terms. 33. 34.

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)

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)