Rational Numbers. Numbers that can be written as a ratio (a fraction) All Integers are Rational Numbers because they can be written as a fraction: 7 =

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Presentation transcript:

Rational Numbers

Numbers that can be written as a ratio (a fraction) All Integers are Rational Numbers because they can be written as a fraction: 7 = Write three numbers that are rational, but not integers

3 What is a number between: 1)0 and 1 2)⅛ and ¼ 3)-3 and -4 4)-1⅞ and -2 5)5 and 5.5

Decimals Some decimals are rational numbers..5 = Decimals that are “terminating” or “repeating” are rational numbers.

Terminating Decimals A decimal that has an end For example: –These can be turned into a fraction.

Repeating Decimals Decimal that repeats the same sequence of numbers forever. Usually signified by a bar above the number.

Types of Numbers Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real numbers Imaginary numbers 1,2,3,4,5,6,7,8,9,10,11… 0,1,2,3,4,5,6,7,8,9,10… …-3, -2, -1, 0, 1, 2, 3… -2.2, -1, 0, ½, 4.77

8 Examples of Types of Numbers What is an example of a whole number that is also an integer? What is an example of a number that is not a ‘natural number’ but is an integer? What is an example of a rational number that is also an integer? What is an example of an irrational number? What is an example of a rational number that is not an integer.

9 Group Work: On the back of your paper 1) What is an example of a rational number that is an integer? Justify. 2) What is an example of a rational number that is not a whole number? Why? 3) What is an example of a natural number that that is not a rational number? Explain.

Operations with Rational Numbers Section 1.6

11 Adding Unlike Denominator The bottom numbers are different. See how the slices are different sizes? =

12 Adding Unlike Denominator Find a multiple for both denominators. Multiply both the top and bottom of your fraction Add the numerators; denominators stay the same. + = = 62 =

13 Variable Problems: Subtract Fractions When a = and b = Replace the variables with given fractions. Change the denominators so they are the same. =

Multiplying Fractions: Two Ways 1) Multiply Across and Reduce 1 2 2) Cross-Cancel and Multiply Across You get the same answer either way!

Dividing Fractions Multiply by the reciprocal (flipped-over fraction)

Dividing Fractions Multiply by the reciprocal (flipped-over fraction)