Rational Numbers. An Introduction to the Unit & Math 8 Review. Math 9 Mrs. Feldes

Transcription

1 Rational Numbers An Introduction to the Unit & Math 8 Review Math 9 Mrs. Feldes

2 In this Unit, we will: Compare & order numbers using a variety of strategies. Strategies include: drawing pictures & number lines estimation changing forms: improper mixed numbers fractions decimals equivalent fractions

3 In this Unit, we will: Examine the relationships between different types of numbers. Fractions Proper & Improper Decimals Terminating & Repeating Rational & Irrational Square Roots Perfect Squares & Non Perfect Squares

4 In this Unit, we will: Add, subtract, multiply, & divide fractions. FOCUS: Using improper fractions, mixed numbers, larger common denominators Solve simple problems involving rational numbers. BEDMAS with rational numbers.

5 Fraction Review

6 Fractions: Fractions represent a portion of a whole.

7 Fractions: Fractions can be represented pictorially! 1 represents the # of slices eaten 8 represents the # of slices in a whole pizza

8 Fractions: Fractions can also be represented as a number on a number line. * 1 interval out of 8 intervals

9 Another example: Notice: This circle has 4 equal parts. And, this number line has 4 equal intervals between 0 & 1.

10 Number Lines: The denominator describes the number of intervals between each whole number. A number line must have consistent intervals between every whole number.

11 Number Lines: When you read a positive value on a number line, start from 0 and move to the right. When you read a negative value on a number line, start from 0 and move to the left.

12 Connect: A ruler is a good example to describe a portion of a whole when measuring a linear distance. Notice: A metric ruler has intervals of 10!

13 Connect: Being able to read values on a number line is similar to using various measuring devices. Many jobs and hobbies require reading measurements accurately.

14 Opposite Fractions: Are fractions equal distance from zero on the number line. Negative values Positive values

15 Negative Fractions: Typically, we write the negative sign out in front or in the numerator of the fraction.

16 Proper Fractions: The numerator is smaller than the denominator.

17 Improper Fractions: The numerator is larger than the denominator.

18 Proper & Improper Fractions on a number line: 1 2 PROPER FRACTION IMPROPER FRACTION

19 Connect: Pictorially, the improper fraction means 5 one quarter pieces!

20 Connect: On a number line, represents 5 one quarter intervals. 1 2

21 Connect: The improper fraction consists of a whole amount. Therefore, on a number line is past the value 1.

22 Mixed Numbers: A number that consists of a whole number & a fraction. = 1

23 Changing Forms: Improper Fraction to a Mixed Number: 7 Ask yourself how many groups of 5 go into 37. This number is your whole number. The remaining amount is the value of the numerator of the fraction.

24 Changing Forms: Sometimes, the mixed number can be reduced! REDUCE

25 Changing Forms: Mixed Number to an Improper Fraction: Multiply the denominator & the whole number together. Add the result with the numerator. This number is the value of the numerator in improper form.

26 Changing Forms: BE CAREFUL, if the mixed number is negative. Apply the negative AFTER the multiplication & addition step! Notice,

27 Equivalent Fractions: Fractions in different forms can equal each other.

28 Equivalent Fractions: Notice: the red portion in each rectangle is the same. The numerator & denominator have different values.

29 Equivalent Fractions: To make equivalent fractions, multiply the numerator & denominator by the same number.

30 Equivalent Fractions: To reduce fractions, divide the numerator & denominator by the same number. This number is called a common factor

31 Notice: Equivalent fractions also exist on a number line!

32 Estimation: Being aware of common fractions can help you estimate. Ie.,

33 Estimation: When comparing fractions, using the reference of greater than 1 can be very helpful! Math Antics: Types of Fractions

34 Percentage Review

35 Percent: A percent is another way of writing a fraction out of one hundred.

36 Connect: A discount is an example of the use of percentages. $ % off x 0.40 = = $6.00

37 Connect: Taxes paid are related to a percentage earned or value of goods purchased. Income Tax City Tax School Tax Sales Tax Gas Tax Liquor Tax Corporate Tax Capital Gains Tax

38 Connect: A test score is another example of a percentage that shows how many questions you scored correctly out of the total number of questions.

39 Connect: Percentages can help compare or show the breakdown of parts.

40 Decimal Review

41 Decimals: A decimal can represent a whole value & a portion of a whole.

42 Decimals: The values to the right of the decimal point represent the portion of a whole. This type of decimal can be converted to a proper fraction.

43 Decimals: When decimals have values to the left of the decimal point, the number can represent an integer, a mixed number, or an improper fraction.

44 Decimals Fractions: Notice: The denominators are powers of ten.

45 Terminating Decimals: A decimal that can be written as a fraction with a denominator as a power of 10.

46 Decimals Fractions: The number of place values determines the power of 10 in the denominator. REDUCE

47 Decimals Fractions: The denominator represents the place value. The number of zeros = The number of decimal places

48 Decimals Fractions: If a fraction does NOT have a power of 10 as the denominator, try to make an equivalent fraction NO! 5 2 A fraction CANNOT have a decimal in the numerator or the denominator.

49 Decimals Fractions: To convert an improper fraction to a decimal, the order of the steps does NOT matter. For example, OR,

50 Connect: Coins are another example that represents a portion of a whole. = quarters of a dollar

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53 Connect: A percent can also represent a decimal to the hundredth.

54 Repeating Decimals: Not all decimals end or terminate. And, not all fractions can have a power of 10 as the denominator!

55 Compare: 0.3 & 0.3 = = 0.3 = = 0.3 Terminating Decimal Repeating Decimal

56 Repeating Decimals: Rule: A fraction with denominator 9 & a single digit numerator, will have the single digit number repeat. = = 0.3

57 Repeating Decimals: Rule: A fraction with denominator 99 & a two digit numerator, will have the two digit number repeat. = = 0.40

58 Repeating Decimals: There are lots of repeating decimals.

59 Other Decimals: For example, the number pi is a decimal that does not terminate nor has a repeating pattern.