1 / 48

Solving Equations

Solving Equations. MA.6.A.2.2. Solving Addition Equations Using Algebra Tiles. Use algebra tiles to solve x + 2 = 4. Solving Equations Using Algebra Tiles. Use algebra tiles to solve x + 2 = 4 + = . Solving Equations Using Algebra Tiles.

xanti
Télécharger la présentation

Solving Equations

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. Solving Equations MA.6.A.2.2

  2. Solving Addition Equations Using Algebra Tiles Use algebra tiles to solve x + 2 = 4

  3. Solving Equations Using Algebra Tiles Use algebra tiles to solve x + 2 = 4 + =

  4. Solving Equations Using Algebra Tiles Use algebra tiles to solve x + 2 = 4 + = = x = 2

  5. Solving Addition Equations • To solve an addition equation, subtract the same number from each side so that the variable is by itself on one side (isolated). • This process is called using the inverse operation (subtraction is the inverse or opposite operation of addition).

  6. Solving Addition Equations Using Inverse Operations Use inverse operations to solve y + 25 = 140

  7. Solving Equations Using Inverse Operations Use inverse operations to solve y + 25 = 140 y + 25 = 140 - 25-25 y = 115

  8. Solving Equations Using Inverse Operations Check your answer: y + 25 = 140 115 + 25 = 140 140 = 140

  9. Using an Addition Equation You buy an outfit at a vintage shop that costs $17.45. You pay with a $20 bill. What is the amount of change c that the clerk should give you?

  10. Using an Addition Equation SOLUTION: Cost + Change = Amount paid Write a verbal model

  11. Using an Addition Equation SOLUTION: Cost + Change = Amount paid Write a verbal model 17.45 + c = 20.00 Write an equation

  12. Using an Addition Equation SOLUTION: Cost + Change = Amount paid Write a verbal model 17.45 + c = 20.00 Write an equation - 17.45-17.45 c = 2.55 Simplify

  13. Using an Addition Equation Check your answer: 17.45 + c = 20.00

  14. Using an Addition Equation Check your answer: 17.45 + c = 20.00 17.45 + 2.55 = 20.00

  15. Using an Addition Equation Check your answer: 17.45 + c = 20.00 17.45 + 2.55 = 20.00 20.00 = 20.00

  16. Solving Subtraction Equations

  17. Solving Subtraction EquationsWorking Backwards Collecting Example: You gave away 2 conch shells from your collection and now you have 5 conch shells left. How many conch shells did you have at the start? An equation that represents this situation is x – 2 = 5, where x is the number of conch shells you had in your collection at the start.

  18. Solving Subtraction EquationsWorking Backwards After giving away 2 conch shells, you have 5 conch shells. x – 2 = 5 To find the value x you had before subtracting 2, you can add 2 to undo the subtraction. 5 + 2 = x x = 7 Check: x – 2 = 5 7 -2 = 5 5 = 5

  19. Solving Subtraction Equations • To solve a subtraction equation, add the same number to each side so that the variable is by itself on one side (isolated). • This process is called using the inverse operation (addition is the inverse or opposite operation of subtraction).

  20. Solving Subtraction Equations Using Inverse Operations Solve the equation: 14 = n - 6

  21. Solving Subtraction Equations Using Inverse Operations Solve the equation: 14 = n - 6 14 = n - 6 + 6+ 6

  22. Solving Subtraction Equations Using Inverse Operations Solve the equation: 14 = n - 6 14 = n - 6 + 6+ 6 20 = n

  23. Solving Subtraction Equations Using Inverse Operations Check your answer: 14 = n - 6 14 = n - 6 14 = 20 – 6

  24. Solving Subtraction Equations Using Inverse Operations Check your answer: 14 = n - 6 14 = n - 6 14 = 20 – 6 14 = 14

  25. Solving Subtraction Equations Using Inverse Operations Solve the equation: m – 3.1 = 11.95

  26. Solving Subtraction Equations Using Inverse Operations Solve the equation: m – 3.1 = 11.95 m – 3.1 = 11.95 + 3.1 + 3.1 m = 15.05

  27. Solving Subtraction Equations Using Inverse Operations Check your answer: m – 3.1 = 11.95 m – 3.1 = 11.95 15.05 – 3.1 = 11.95 11.95 = 11.95

  28. Using a Subtraction Equation Elevator Example: You are riding an elevator. You go down 14 floors and exit on the 23rd floor. On what floor did you enter the elevator?

  29. Using a Subtraction Equation Let f represent the number of the floor on which you entered the elevator. f – 14 = 23

  30. Using a Subtraction Equation Let f represent the number of the floor on which you entered the elevator. f – 14 = 23 + 14+14 f = 37

  31. Using a Subtraction Equation Check your answer: f – 14 = 23

  32. Using a Subtraction Equation Check your answer: f – 14 = 23 37 – 14 = 23

  33. Using a Subtraction Equation Check your answer: f – 14 = 23 37 – 14 = 23 23 = 23

  34. Solving Multiplication and Division Equations

  35. Solving Multiplication and Division Equations • To solve an equation, try to get the variable by itself on one side of the equation. You can use inverse operations to undo the process in order to isolate the variable. • To solve a multiplication equation, divide each side by the number that the variable is multiplied by. • To solve a division equation, multiply each side by the divisor.

  36. Algebra Tiles Activity Draw a model of the equation: 2x = 6

  37. Solve using Algebra Tiles = Divide the x-tiles into 2 equal = groups. Divide the 1-tiles into the same number of equal groups. = Match a group on the left with a group on the right.

  38. Solving a Multiplication Equation Solve and check the equation 5x = 20

  39. Solve 5x = 20 Write the original equation = Divide each side by 5 x = 4 Simplify

  40. Check: 5x = 20 5 · 4 = 20 20 = 20

  41. Solving Division Equations

  42. Solving a Division Equation Solve the equation = 3

  43. Solving a Division Equation Solve the equation: = 3 7 · = 3 · 7 x = 21

  44. Check the Division Equation Check the solution: = 3 = 3 3 = 3

  45. Using an Equation Cheerleading:In a local cheerleading competition, a team is awarded points in 3 categories. The mean of the team’s scores for the 3 categories is 21. Write and solve a division equation to find t, the total number of points the team earns.

  46. Setup and Solve the Equation = 21 3 · = 21 · 3 t = 63

  47. Check your Answer Estimate: 3 · 21 = 63

  48. Solve the Two-Step Equation Which operation(s) would you use to solve the equation below? 2x + 4 = 26

More Related