Thursday, October 6, 2016 2.1 Rational Numbers.

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Thursday, October 6, 2016 2.1 Rational Numbers

rational number - a number that can be expressed as a fraction; a terminating or repeating decimal irrational number – a number that can’t be written as a fraction; a non-terminating, non-repeating decimal terminate – to stop

Just listen and learn... Irrational Numbers Real Numbers Whole 0 ½, -½, 7¾, 4.9, -6.27 Irrational Numbers Natural 1,2, 3, ... Whole 0 Integers ...-3, -2, -1, ...

Number Groups natural (N): 1, 2, 3, 4, ... (counting numbers) Resume writing… Number Groups natural (N): 1, 2, 3, 4, ... (counting numbers) whole (W): 0, 1, 2, 3, ... (counting numbers and 0) integer (Z): ..., –2, –1, 0, 1, 2, ...( + and ‒ wholes) rational (Q): fractions irrational (I): non-terminating and non-repeating real (R): rationals and irrationals

A) Which, if any, of the following are equal? Write in these forms only.

B) Order from least to greatest. Methods to consider: Common sense (be careful!) . Change all numbers to decimals (usually the best). Change all numbers to fractions with com denoms. Strategies: All negatives are less than all positives. Numbers that are more negative are smaller. Arrange negatives first, then positives, then together.

B) Order from least to greatest.

Let’s categorize some numbers…

Least Common Denominator (LCD) – the LCM of two or more denominators. Least Common Multiple (LCM) – the smallest common product of a group of numbers ► LCM is  given numbers Least Common Denominator (LCD) – the LCM of two or more denominators. Do not just multiply denominators. This does not always give LCD. C) Find the LCD of . . 3 6 15 2 5 Use side and bottom numbers. LCD= 3(2)(5) = 30

D) Find the LCD of . 2 8 14 42 7 4 7 21 4 1 3 LCM: 2(7)(4)(1)(3) = 168 8 14 42 If factor divides only 2 of 3 numbers, proceed and bring down 3rd number. 7 4 7 21 4 1 3 LCM: 2(7)(4)(1)(3) = 168

3 3 12 5 1 4 5 LCD: 3(1)(4)(5) = 60 E) Simplify. 40 55 36 To add fractions, you must have an LCD. An LCD can be found mentally, but use this process if you can’t. 40 55 36 3 3 12 5 1 4 5 LCD: 3(1)(4)(5) = 60