unit 3.2  adding rational numbers
what do we need to know?
 Rational numbers: Any number that can be written as a fraction
 Fractions, terminating and repeating decimals, integers and mixed numbers are rational numbers.
 Pi is an irrational number because it is a decimal that is neither terminal nor repeating and therefore can't be written as a fraction
 Parts of a fraction
 Fractions, terminating and repeating decimals, integers and mixed numbers are rational numbers.
 Pi is an irrational number because it is a decimal that is neither terminal nor repeating and therefore can't be written as a fraction
 Parts of a fraction
class notes
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quick tips when placing rational numbers on a number line
 Positive numbers are always greater than any negative number.
 On the negative side of the number line, the bigger numbers are closer to zero.
 On the positive side of the number liner, the bigger numbers are further away from zero
.
 On the negative side of the number line, the bigger numbers are closer to zero.
 On the positive side of the number liner, the bigger numbers are further away from zero
.
the rule of signs for the addition of integers
adding decimals
When adding decimals:
 Write them vertically, that is, one on top of the other.
 Line up the decimal point.
 If the decimal numbers have a different amount of decimal places, add as many zeros as needed to one so that both end up with the same amount.
 Then, add from left to right, making sure you put the decimal point in the same place.
 Write them vertically, that is, one on top of the other.
 Line up the decimal point.
 If the decimal numbers have a different amount of decimal places, add as many zeros as needed to one so that both end up with the same amount.
 Then, add from left to right, making sure you put the decimal point in the same place.
when dealing with mixed numbers...
Always make them into improper fractions!
adding fractions with the same denominator
To add fractions of EQUAL DENOMINATORS:
 The denominator remains the same (it does not change).
 The numerators are then added.
 The denominator remains the same (it does not change).
 The numerators are then added.
adding fractions with different denominators
The FIRST thing you must do: take a look at the denominators:
If one of the denominators is a multiple of the other:
_ The objective is STILL to end up with fractions of equal denominators.
 Find the number by which you can multiply the fraction with the smallest denominator so that such denominator becomes equal to the other one.
 Remember that you must multiply BOTH the numerator and the denominator when multiplying to equate denominators.
 Find the number by which you can multiply the fraction with the smallest denominator so that such denominator becomes equal to the other one.
 Remember that you must multiply BOTH the numerator and the denominator when multiplying to equate denominators.
If the denominators are not multiples of the each other:
An alternate method is called "the butterfly methoD."
Although it is a very useful method for adding and subtracting fractions of different denominators, DO NOT USE IT IF YOU HAVE A DENOMINATOR THAT (BY BEING MULTIPLIED) IS A FACTOR OF THE OTHER.
ALSO: Be aware that you may have to simplify the resulting fraction.
ALSO: Be aware that you may have to simplify the resulting fraction.
adding mixed numbers
When working with mixed numbers, CONVERT THEM TO FRACTIONS, and use any of the methods previously described.
solutions to inclass worksheets
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interactive online activities
WORKSHEETS







REVIEW  workbook
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