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Signed Rationals

Explore rounding decimals, comparing decimals using models, adding and subtracting decimals, multiplying and dividing decimals, reducing fractions, converting mixed numbers, and mastering basic fraction operations.

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Signed Rationals

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  1. Signed Rationals

  2. Place Value Let’s look at position after the decimal to help us do some rounding!

  3. Rounding and Estimating • When rounding a decimal you must look at the number to the RIGHT of the place value to which you are going to round. • If that number if 5 or greater, then you must raise the number by one in the position to which you are trying to round.

  4. Round 73.410 to the nearest whole number. Round 2145.721 to the nearest whole number. Example

  5. Round 36.480 to the nearest tenth. Round 9641.702 to the nearest hundredth. Example

  6. Whole Number Tenth Hundredth Thousandth Ten Thousandth You Try: Round 58.97360 to the nearest

  7. Comparing Decimals

  8. Using Models – A Graphical Approach • If you are comparing tenths to hundredths, you can use a tenths grid and a hundredths grid. Here, you can see that 0.4 is greater than 0.36.

  9. Another Way….. • Line up the numbers vertically by the decimal point. • Add “0” to fill in any missing spaces. • Compare from left to right.

  10. Let’s put these numbers in order:12.5, 12.24, 11.96, 12.36 Fill in the missing space with a zero.

  11. You Try: Arrange the following numbers from least to greatest. • 0.4, 0.38, 0.49, 0.472, 0.425

  12. Add and Subtract Decimals

  13. The Basic Steps to Adding or Subtracting Decimals: • Line up the numbers by the decimal point. • Fill in missing places with zeroes. • Add or subtract. • Be sure to put the larger number on top when subtracting.

  14. Example: 28.9 + 13.31

  15. 3.04 + 0.6 8 + 4.7 You Try

  16. 4 – 1.5 25.1 – 0.83 Ex: Subtract the following:

  17. Compute:

  18. Compute:

  19. Subtracting Across Zeroes • If you have several zeroes in a row, and you need to borrow, go to the first digit that is not zero, and borrow. • All middle zeroes become 9’s. • The final zero becomes 10.

  20. Example: 15 – 29.372

  21. Multiply and Divide Decimals

  22. To Multiply Decimals: • You do not line up the factors by the decimal. • Instead, place the number with more digits on top. • Line up the other number underneath, at the right. • Multiply • Count the number of decimal places (from the right) in each factor. • Use the total number of decimal places in your two factors to place the decimal in your product.

  23. Example:5.63 x 3.7

  24. Example: 0.53 x -2.61

  25. Try This: -6.5 x 15.3

  26. Example: 0.00325 2.5

  27. Example:

  28. You Try:

  29. Compute:

  30. Compute:

  31. Compute:

  32. Compute:

  33. You Try the following:

  34. Fractions

  35. Fractions • Top # is the numerator. • Bottom # is the denominator.

  36. Reducing Fractions • A fraction is said to be in its lowest terms (or reduced) when the numerator and denominator are relatively prime (have no common divisors other than 1).

  37. Reduce: • 6/10

  38. You Try… Reduce it:

  39. Mixed Numbers and Improper Fractions • The number 2¾ is an example of a mixed number. It is called a mixed number because it is made up of an integer and a fraction. • 2¾ means 2 + ¾ • An improper fraction is a fraction whose numerator is greater than its denominator.

  40. Example: Convert to Improper Fractions.

  41. Example: Convert to a mixed number.

  42. Example: Convert to a mixed number.

  43. Multiplication of Fractions • Multiply the numerators and multiply the denominators together then reduce if necessary.

  44. Examples

  45. Reciprocal • The reciprocal of any number is 1 divided by that number. • The product of a number and its reciprocal must equal 1.

  46. Division of Fractions • To find the quotient of two fractions, multiply the first fraction by the reciprocal of the second fraction.

  47. Evaluate:

  48. Addition and Subtraction of Fractions • Before we can add or subtract fractions, the fractions must have a lowest common denominator.

  49. Add/ Sub

  50. Adding or Subtracting Fractions with Unlike Denominators

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