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# What is the Lowest Common Denominator (LCD)?

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1. 5.3 – Addition & Subtraction of Rational Expressions What is the Lowest Common Denominator (LCD)?

2. 5.3 – Addition & Subtraction of Rational Expressions What is the Lowest Common Denominator (LCD)?

3. 5.3 – Addition & Subtraction of Rational Expressions What is the Lowest Common Denominator (LCD)?

4. 5.3 – Addition & Subtraction of Rational Expressions Examples (Like Denominators):

5. 5.3 – Addition & Subtraction of Rational Expressions Examples (Like Denominators):

6. 5.3 – Addition & Subtraction of Rational Expressions Examples (Like Denominators):

7. 5.3 – Addition & Subtraction of Rational Expressions Examples: 15

8. 5.3 – Addition & Subtraction of Rational Expressions Examples: 40x2

9. 5.3 – Addition & Subtraction of Rational Expressions Examples: continued

10. 5.3 – Addition & Subtraction of Rational Expressions Examples: continued

11. 5.4 – Complex Fractions Complex Fractions Defn: A rational expression whose numerator, denominator, or both contain one or more rational expressions.

12. 5.4 – Complex Fractions LCD: 12, 8 24 LCD: 24 24 2 3

13. 5.4 – Complex Fractions LCD: y y–y

14. 5.4 – Complex Fractions LCD: 6xy 6xy 6xy

15. 5.4 – Complex Fractions Outersover Inners LCD: 63

16. 5.4 – Complex Fractions Outersover Inners

17. 5.5 – Equations with Rational Expressions Solve for a LCD: abx

18. 5.6 – Applications Problems about Numbers If one more than three times a number is divided by the number, the result is four thirds. Find the number. LCD = 3x

19. Time to sort one batch (hours) Fraction of the job completed in one hour 5.6 – Applications Ryan Mike Together Problems about Work Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort a batch in 3 hours. If they work together, how fast can they sort one batch? 2 3 x

20. Time to sort one batch (hours) Fraction of the job completed in one hour 5.6 – Applications Ryan Mike Together Problems about Work 2 3 x 6x LCD = hrs.

21. Time to mow one acre (hours) Fraction of the job completed in one hour 5.6 – Applications James Andy Together James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together? 2 8 x

22. Time to mow one acre (hours) 5.6 – Applications Fraction of the job completed in one hour James Andy Together 2 8 x LCD: 8x hrs.

23. Time to pump one basement (hours) Fraction of the job completed in one hour 5.6 – Applications 1st pump 2nd pump Together A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone? 12 x

24. Time to pump one basement (hours) Fraction of the job completed in one hour 5.6 – Applications 1st pump 2nd pump Together 12 x

25. 5.6 – Applications LCD: 60x hrs.

26. 5.6 – Applications Distance, Rate and Time Problems If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive?

27. 5.6 – Applications A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles. x t 450 mi t x + 15 600 mi

28. 5.6 – Applications 450 mi x t t x + 15 600 mi LCD: x(x + 15) x(x + 15) x(x + 15)

29. 5.6 – Applications x(x + 15) x(x + 15) Motorcycle Car

30. 5.6 – Applications A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water? boat speed = x t 22 mi x - 5 t 42 mi x + 5

31. 5.6 – Applications boat speed = x x - 5 t 22 mi 42 mi x + 5 t LCD: (x – 5)(x + 5) (x – 5)(x + 5) (x – 5)(x + 5)

32. 5.6 – Applications (x – 5)(x + 5) (x – 5)(x + 5) Boat Speed

33. 5.7 – Division of Polynomials Dividing by a Monomial

34. 5.7 – Division of Polynomials Dividing by a Monomial

35. 5.7 – Division of Polynomials Review of Long Division

36. 5.7 – Division of Polynomials Long Division

37. 5.7 – Division of Polynomials Long Division