rational numbers
TRANSCRIPT
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Rational Numbers
Summary
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Definition of Rational Numbers
• Any number that can be made by dividing one integer by another. The word comes from "ratio".
• This means that rational numbers include positive and negative numbers, whole numbers, fractions and decimals.
a
b
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• Two fractions that stand for the same number
What is an equivalent fraction?
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Vs.Mixed
NumbersImproper Fractions
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What is a mixed number?
The sum of a whole number and a fraction
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&
These are examples of mixed numbers
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What is an improper fraction
A fraction with a numerator greater then the denominator
NUMERATOR denominator
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These are examples of improper fractions
&
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Changing an improper fraction to a mixed number
= =
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Notice how the denominator stays the same when converting to an improper fraction to a mixed number
=
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Changing a mixed number into an improper fraction
= =
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Notice how the denominators stay the same when converting from a mixed number to an improper fraction
= =
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Fractions are FUNNY!
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Were here to show you the rules!
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
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Adding Fractions
Adding fractions requires a common denominator
To find the common denominator between fractions simply multiply the
denominators and this is the common denominator.
this number may be large so try and find a number that all denominators will divide into
evenly.
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Adding Fractions• However this number may be large so try
and find a number that all denominators will divide into evenly. Adding fractions requires a common
denominatorTo find the common denominator
between fractions simply multiply the denominators and this is the common
denominator.
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Example
• We need to find a C.D. in order to add these fractions.
• If we multiply the denominators
that is a big number…but both 6 and 12 divide evenly (without a remainder) into 12.
• The first fraction already has a denominator of 12 so we leave it alone but what do we have to multiple the second denominator by in order to change it to 12?
• If you said 2…you are right!
2 4
12 6
12 6 72
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Example continued…• If you multiply the
denominator by 2 you MUST multiply the numerator by two also!
• Remember: whatever you do to the bottom you must do to the top.
• Once you have common denominators…add the numerator and KEEP the Common Denominator.
2 4
12 62 4 2
12 6 22 8
12 1210
12
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Subtracting Fractions
Same rule…you have to get a common denominator before you
subtract the numerators!
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Example of Subtraction
3 2
4 53 5 2 4
4 5 5 415 8
20 2015 8
207
20
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Multiplying Fractions
Multiplying fractions is easy
Multiple the numeratorsMultiple the denominators
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Example of Multiplying
1 2
3 51 2
3 52
15
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Dividing Fractions
Dividing fractions requires one more step
Keep the first fraction the sameChange the multiple to divide And FLIP the second fraction
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Example of Dividing 2 6
5 72 7
5 62 7
5 614
30
When the fraction is “flipped” it is called the INVERSE