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Solving Equations with Multiplication and Division: Techniques and Examples

This lesson focuses on solving equations using multiplication and division. You'll learn how to isolate variables effectively, such as making '1x' from equations involving fractions and numbers. Through practical examples, like determining Ciro’s mowing earnings and the altitude of a descending plane, we’ll explore how to set up and solve equations accurately. This method will enhance your skills in manipulating equations to find unknown variables, providing a solid foundation in algebraic problem-solving.

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Solving Equations with Multiplication and Division: Techniques and Examples

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  1. Solving Equations Using Multiplication and Division

  2. Solve for 1x • If there is more than 1x, divide both sides by the number to make 1.

  3. EXAMPLE 3 3

  4. EX 2

  5. EX 3

  6. EX 4

  7. EX5Write the equation and solve: • Negative six times a number is the same as negative forty-eight.

  8. Solve for 1x • If x is a fraction, multiply to cancel the denominator.

  9. EXAMPLE (5) (5)

  10. EX 2

  11. EX 3

  12. EX 4

  13. EX 5Write the equation and solve: • One-fourth of a number is twelve.

  14. Solve for 1x • If x is a fraction with a numerator other than 1 • 1st multiply to cancel the denominator • 2nd divide to make 1

  15. (3) EX 1 (3) 2 2

  16. EX 2

  17. EX 3

  18. EX 4

  19. EX 5Write the equation and solve: • Three-fifths of a number is negative nine.

  20. Other Uses Of Multiplication • Multiplication can be used to cancel all fractions from an equation, even if x is not a fraction. • If there is more than one fraction with different denominators, multiply by a common denominator.

  21. EX 1

  22. EX 2

  23. EX 3Write the equation and solve: • Negative six times a number is equal to one and a half.

  24. 1 Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year. 4 Example 4: Application one-fourth times earnings equals college fund Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. Ciro earned $1140 mowing lawns. m = $1140

  25. Check it Out! Example 4 The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began. Distance divided by 3 equals height in thousands of feet Write an equation to represent the relationship. Substitute 45 for d. 15 = h The plane was flying at 15,000 ft when the descent began.

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