Download - Operations with rational numbers
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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
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Mixed Numbers
Improper Fractions
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The sum of a whole number and a fraction
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These are examples of mixed numbers
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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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Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
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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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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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We need to find a C.D. in order to add these fractions.
If we multiply the denominatorsthat 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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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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Same rule…you have to get a common denominator before you
subtract the numerators!
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3 2
4 53 5 2 4
4 5 5 415 8
20 2015 8
207
20
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Multiplying fractions is easy
Multiple the numeratorsMultiple the denominators
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1 2
3 51 2
3 52
15
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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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2 6
5 72 7
5 62 7
5 614
30
When the fraction is “flipped” it is called the INVERSE
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