1 / 53

Adding & Subtracting Fractions, Mixed Numbers, and Rational Expressions

Adding & Subtracting Fractions, Mixed Numbers, and Rational Expressions. Preview. When you finish this unit, you will be able to:. Add and subtract fractions with the same denominator Add and subtract signed numbers with the same denominator. Preview.

truax
Download Presentation

Adding & Subtracting Fractions, Mixed Numbers, and Rational Expressions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Adding & Subtracting Fractions, Mixed Numbers, and Rational Expressions

  2. Preview When you finish this unit, you will be able to: • Add and subtract fractions with the same denominator • Add and subtract signed numbers with the same denominator

  3. Preview When you finish this unit, you will be able to: • Add and subtract rational expressions with the same denominator • Add and subtract fractions with different denominators

  4. ? 100 Adding Fractions with the Same Denominator how many .25’s =

  5. 10¢ + 10 ¢ = 20 ¢ Fractions/Same Denominator

  6. + = 3 2 + 5 = Fractions/Same Denominator Whole 6 slices

  7. = + 1 3 4 + = Fractions/Same Denominator Whole5 pieces

  8. numerators add keep deno min ator Fractions/Same Denominator D pieces

  9. Fractions/Same Denominator

  10. + = Fractions/Same Denominator 5total

  11. + = Fractions/Same Denominator 7total

  12. ? 100 Fractions/Same Denominator Subtracting Fractions with the Same Denominator how many .25’s =

  13. - = Fractions/Same Denominator 7 pieces

  14. An example Fractions/Same Denominator Jack gas gauge reads 7/8 of a tank at the beginning of the day. At 5 PM the gauge reads 1/8 full. How much of a tank-full of gas has he used that day? If he gets 240 miles on a full tank, how far has he driven? Jack gas gauge reads 7/8 of a tank at the beginning of the day. At 5 PM the gauge reads 1/8 full. How much of a tank-full of gas has he used that day? If he gets 240 miles on a full tank, how far has he driven?

  15. 7/8 full - start 1/8 full - end 240 miles - full tank 7 8 Full240 mi 1 8 how much of a tank-full? how far has he driven? Fractions/Same Denominator Given: Asked:

  16. Fractions/Same Denominator Asking for the difference between beginning and the the end of the day. Subtract - tankused Gas used is ¾ of 240 mi -

  17. Fractions/Same Denominator Check: Is 180 gal ¾ of 240 gal? OK

  18. subtract numerators keep deno min ator Fractions/Same Denominator Rule:

  19. ? 100 Signed numbers with the Same Denominator how many .25’s =

  20. Signed Numbers A flash from the past

  21. Signed Numbers

  22. Signed Numbers All operations of integer math apply!

  23. Signed Numbers

  24. Signed Numbers

  25. Signed Numbers

  26. 4x2 – x + 1 x – 3 - Rational Expressions with the Same Denominator 4 4 4x2 – x + 1 – x + 3 4 6x2 - 1x + 9 = 4

  27. Rational Expressions/Same Denominator Rational Number: Number expressed as a ratio of integers Like Terms:having the same variables, raised to the same powers.5x2 + 2x2 = 7x2 … 5x3 + 2x2 = ?

  28. Rational Expressions/Same Denominator

  29. Rational Expressions/Same Denominator

  30. Rational Expressions/Same Denominator

  31. Rational Expressions/Same Denominator

  32. .05 + .10 = .15 = 15 3 = 100 20 Fractions with Different Denominators

  33. + = Fractions/Different Denominator + = quarter dollar half dollar

  34. + = Fractions/Different Denominator + = quarter dollar half dollar

  35. Fractions/Different Denominator + = one quarter dollar two quarter dollars + =

  36. Fractions/Different Denominator + = + =

  37. Fractions/Different Denominator • Upscale fractions without changing value so that they all have the same denominator. • Do the math

  38. Fractions/Different Denominator At the end of the day, Chuck’s Diner has 2 pieces of an apple pie cut into 6 slices and one piece of an equal sized blueberry pie cut into 4 slices left over. How much pie remains? At the end of the day, Chuck’s Diner has 2 pieces of an apple pie cut into 6 slices and one piece of an equal sized blueberry pie cut into 4 slices left over. How much pie remains?

  39. Slices are different sizes for each pie Asked: How much pie remains? Fractions/Different Denominator Given: 2 pieces of 6 slices1 piece of 4 slices

  40. + Fractions/Different Denominator 2 pieces of 6 slices1 piece of 4 slices Need to represent 6th and 4th as same denominator.

  41. Fractions/Different Denominator Need to represent 6ths and 4ths with same (common) denominator. + 12 pieces

  42. + + = = Fractions/Different Denominator 12 pieces + =

  43. Fractions/Different Denominator Finding a common denominator

  44. 8 6 6 8 To get a common denominator: Multiply numerator and denominator of each term by the denominator of the other(s). Fractions/Different Denominator The easiest way… 6 8

  45. Fractions/Different Denominator The easiest way… 8 6 6 6 8 8

  46. Fractions/Different Denominator Example:

  47. Fractions/Different Denominator Example:

  48. Fractions/Different Denominator Example:

  49. Review We have seen how to: • Add fractions with the same denominator

  50. Review We have seen how to: • Add subtract with the same denominator

More Related