Simplification of Fractions and Operations on Fractions
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The document discusses various operations involving fractions, including simplifying, converting between mixed and improper fractions, multiplying, dividing, adding, and subtracting fractions. It provides examples of performing each operation step-by-step and simplifying the resulting fraction. Rules for working with fractions are reviewed and examples of applying the rules are shown.
Simplification of Fractions and Operations on Fractions
- 1. Review on FRactions Simplification of Fractions/ Operations on Fractions
- 2. 40 Simplifying 10 Reduce 4 ⋅ 10 4 = = = 4 1 ⋅ 10 1 10 = Greatest Common Factor Write the numerator and denominator as a product of factors, then cancel common factors and obtain the result.
- 3. 16 Simplifying 72 4⋅4 4 2⋅2 2 = = = = 4 ⋅ 18 18 2⋅9 9 Write the numerator and denominator as a product of common factors then cancel the common factors and obtain the result. Repeat the simplification process until all common factors are removed.
- 4. Converting Mixed Numbers 1 5 3 • + 16 = 3 Multiply the whole number by the denominator Add the numerator to the result Place over the initial denominator Compute the final result
- 5. Converting Mixed Numbers 2 6 9 • + 56 = 9 Multiply the whole number by the denominator Add the numerator to the result Place over the initial denominator Compute the final result
- 6. Multiplying 3 10 ⋅ 3 10⋅ 3 2 5 15 ⋅ ⋅ 8 11 = 8 11⋅= = 4 2 11 44 ⋅⋅ a c ac ⋅ = Fraction Multiplication b d bd Fraction Simplification
- 7. Multiplying 2 15 ⋅ 2 15⋅ 2 3 5 5 ⋅ ⋅ 3 4 = 3 4 ⋅= 3 2 2 = 2 ⋅⋅ a c ac ⋅ = Fraction Multiplication b d bd Fraction Simplification
- 8. Dividing 12 3 12 3•4 7 28 ÷ = • = • 3 = 5 7 5 5 5 a c a d ÷ = ⋅ Fraction Division b d b c Fraction Simplification and Multiplication
- 9. 4 8 Dividing 4 5 ÷ 15 = 24 8 24 3•8 3•5 ÷ = • = • 8 5 15 5 5 9 = = 9 1 a c a d ÷ = ⋅ Fraction Division b d b c Fraction Simplification Fraction Multiplication Mixed Number Conversion
- 10. Adding/Subtracting Fraction Simplification 3 - 1 2 = 1 = = 8 8 8 4 8 a b a±b ± = Fraction Addition/Subtraction c c c
- 11. Adding/Subtracting 11 2 = 11 + 2 •??? 11 + 8 11 2 4 + 7 28 + 7 • 4 = 28 28 28 28 + 7 = 11 + 8 = 19 28 28 28 a b a±b Common = ± Denominator = ?????? Fraction Addition/Subtraction c c c
- 12. Rules of Fractions Review • Fraction Simplification • Mixed Number Conversion • Fraction Multiplication • Fraction Division • Fraction Addition/Subtraction
- 13. 21 YOU TRY IT 13 8 45 3 1 5 4 2 + − 8 4 9 15 3 12 5 4 ⋅ ÷ 2 15 12 3 6 5 5 16
- 14. Fractions: Steps for Success 1. Know the fraction rules and how to apply them 2. Show your work and write out each step 3. Check your work for errors or careless mistakes
- 15. 3 1 19 + 1 2 + = Mixed Number Conversion 8 4 8 4 19 + 2 Fraction Addition = 8 8 21 = Fraction Addition 8
- 16. 5 4 25 - 12 − = Fraction Subtraction 9 15 45 45 13 = Fraction Subtraction 45
- 17. 3 12 3 3 • 4 Fraction Simplification ⋅ = 2 • 2 15 3•5 3 4 = • Fraction Simplification 2 5 3 2 • 2 Fraction Simplification = • 2 5 3 2 Fraction Simplification = 1 • 5 6 = 5 Fraction Multiplication
- 18. 5 4 5 3 ÷ = • Fraction Division 12 3 12 4 5 3 = 3•4 • 4 Fraction Simplification 5 • 1 = Fraction Simplification 4 4 5 = Fraction Multiplication 16
Editor's Notes
- #2: The animation on this slide is intended to create a sense of being overwhelmed with fractions. It will play automatically on click and then the titles will appear. The rest of this presentation is intended to emphasize solving fraction problems by showing steps and applying rules. The accompanying handout (Rules of Fractions) contains the specific rules that are referenced and applied. Each slide has animation of some type. Some of it is automatic and some requires the click of a mouse. To get a feel for how each slide is set up, watching the show all the way through will help. As you are watching the show, give a little time (1 – 2 seconds) for an animation to occur. If it does not occur, then click the mouse to advance. If you click too soon, you will miss some of the animations.
- #13: The links above will take you back to the first of each problem type shown. Click the “one way” arrow icon to return to this page.
- #14: Clicking on the red button in each problem cell will cause the answer to appear. Each problem itself is linked to a page that shows the problem solution. The one way arrows on the bottom of the problem pages will bring you back to this page. Animation is automatic on all problem pages so after you click to reach the page, the solution will appear with no clicks.
- #15: Each list item animates separately on the click of the mouse.