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Mastering Multiplication and Division Equations: A Step-by-Step Guide

hoyt-burgess avatar
hoyt-burgess
44 diapositives · 570 Views · Nov 19, 2014

This guide focuses on solving multiplication and division equations by isolating the variable. Learn the fundamental principle of performing the same operation on both sides of the equation to maintain balance. We will cover inverse operations, how to check solutions through substitution, and practice solving various types of equations. With clear examples, students can grasp the techniques needed to tackle multiplication equations like 8x = 56 and division equations such as x/3 = 15. Perfect for reinforcing fundamental math skills!

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  1. Solving Multiplication and Division Equations

  2. Multiply & Divide Equations 1) GOAL: Get the variable on one side of the equation. 2) You always perform the same operation to both sides of an equation. 3) To undo an operation you perform its opposite operation to both sides of the equation.

  3. Multiply & Divide Equations SUBTRACT • The inverse of add is The inverse of subtract is ADD The inverse of multiply is DIVIDE The inverse of divide is MULTIPLY

  4. What you do to one side of an equation, you must do to the other side to keep it balanced. Multiply & Divide Equations = 30 5 x 6

  5. To solve a multiplication equation Multiply & Divide Equations • Use the inverse operation for multiplication which is division. • Get the variable alone, by dividing the same number into both sides.

  6. Try to solve this multiplication equation. Multiply & Divide Equations How do you get x all by itself? = 8x 56

  7. Multiply & Divide Equations Divide 8 into both sides. = 8x 56 7 8 8

  8. Multiply & Divide Equations Divide 8 into both sides. Check your answer by substitution! = 8x •7 56

  9. Try to solve this multiplication equation Multiply & Divide Equations How do you get x all by itself? = 42 7x

  10. Multiply & Divide Equations Divide 7 into both sides. = 42 7x 6 7 7

  11. Multiply & Divide Equations Divide 7 into both sides. Check your answer by substitution! = 42 7x •6

  12. To Solve a Multiplication Equation Multiply & Divide Equations Dividethesame numberinto both sides • 8x = 32 Get the variable alone. 8 8 Divide 8 into both sides. x = 4 8 divided by 8 cancels out 8 •4 = 32 Show your check! 32 = 32 Finish your check!

  13. Multiply & Divide Equations 1) 3) 2) 4)

  14. To solve a division equation Multiply & Divide Equations • Use the inverse operation for division which is multiplication. • Get the variable alone, by multiplying the same number to both sides.

  15. Try to solve this division equation Multiply & Divide Equations How do you get x all by itself? x 3 = 15

  16. Multiply & Divide Equations Multiply both sides by 3 x 3 = •3 45 •3 15

  17. Multiply & Divide Equations Multiply both sides by 3 Check your answer by substitution! 45 x 3 = 15

  18. Try to solve this division equation Multiply & Divide Equations How do you get x all by itself? x 6 = 4

  19. Multiply & Divide Equations Multiply both sides by 6 x 6 = •6 24 4 •6

  20. Multiply & Divide Equations Multiply both sides by 6 Check your answer by substitution! 24 x 6 = 4

  21. Try to solve this division equation Multiply & Divide Equations How do you get x all by itself? x 7 = -7

  22. Multiply & Divide Equations Multiply both sides by 7 x 7 = •7 -49 -7 •7

  23. Multiply & Divide Equations Multiply both sides by 7 Check your answer by substitution! -49 x 7 = -7

  24. To Solve a Division Equation Multiply & Divide Equations Multiply the same number to both sides. x 3 = 25 Get the variable alone. 3••3 x 3 Multiply both sides by 3. = 25 3 divided by 3 cancels out to 1. x = 75 Show your check! Finish your check! 25 = 25

  25. m (-2) (-2) = 8 -2 Multiply & Divide Equations Try These Equations Show your check! -3x = 21 -3 -3 m = -16 x = -7 -3(-7) = 21 21 = 21 8 = 8

  26. Multiply & Divide Equations Try These Equations 1) 2)

  27. Multiply & Divide Equations Try These Equations 3) 4)

  28. Multiply & Divide Equations That's all Folks! Take Out Your Study Guide!!!

  29. #5 To Solve a Multiplication Equation Divide the same number into both sides • 5x = 40 Get the variable alone. 5 5 Divide 5 into both sides. x = 8 5 divided by 5 cancels out to 1. 5 • 8 = 40 Show your check! 40 = 40 Finish your check!

  30. #6 To Solve a Division Equation Multiply the same number to both sides x 2 Get the variable alone. • = 20 2• •2 x 2 Multiply both sides by 2. = 20 2 divided by 2 cancels out to 1. x = 40 Show your check! Finish your check! 20 = 20

  31. Teacher Note: The following slides may be inserted at the beginning of the lesson if the lesson is also teaching writing expressions and/or equations.

  32. twice Multiply & Divide Equations Add Subtract Multiply Divide minus times quotient plus difference sum product of increased by decreased by less total more than less than subtracted from added to Flip Flop Numbers

  33. Placement Rule Multiply & Divide Equations • Always write the variable afterthe number! a 4WRITE IT AS4a

  34. Using Parentheses Multiply & Divide Equations • 8 x is written as • 8(x) • (8)x • (8x) • 8x Parentheses mean multiply!

  35. Translate the following into equations. 1) Eleven more than a number t is 23. 2) Eight times a number k is equal to 56. 3) Thirteen less m equals 6. 4) The quotient of x and 3 is 18. Multiply & Divide Equations

  36. Multiply & Divide Equations Write a phrase that describes each variable expression below. Four times the sum of m and 5 minus 3 Five minus twice the quotient of x and 8 The quotient of a and 7 minus 3

  37. Teacher Note: The following slides may be inserted at the end of the lesson if the lesson is also teaching solving equations with fractions.

  38. Multiply & Divide Equations Short Way Long Way Easier to multiply by the reciprocal!

  39. Multiply & Divide Equations Solve the division bymultiplying by the reciprocal.

  40. Multiply & Divide Equations Solve the division bymultiplying by the reciprocal.

  41. Multiply & Divide Equations Solve the division bymultiplying by the reciprocal.

  42. To Solve a Fraction Equation #7 Multiply both sides by thereciprocal of the fraction. Multiply thenumerators.Multiply thedenominators. Simplify

  43. If you have trouble viewing you need MathType software: To see all math formulas correctly you need to install MathType software, similar to equation editor and is available for free at Design Science website.

  44. For more information on Math Slideshows visit:http://www.mathslideshows.com/