FRACTION REFERENCE SHEET
REDUCING FRACTIONS
xro reduce a fraction, first find a number that goes
evenly into both the
numerator and the denominator ftry to find the biggest number
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that both divide by).
*ln the example, the biggest number that 18
and 24 both divide by is 6,
so we divide 18 by 6 and also divide Z4by 6.
*check to make sure that the result
cannot be further simplified.
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WRITING A MIXED NUMBER AS AN IMPROPER FRACTION
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*A mixed number combines a whole
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*An improper fraction is a fraction
where the numerator is larger
than the denominator flike
xTo change a mixed number to
an improper fraction:
-multiply the denominator by the whole number
-add that to the numerator
-put that result over the denominator
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fln the example, we multiply the 7 by 3,giving us 21. Then we addZ,giving us 23. Finally, we put the
23 over the original denominator of 71.
Note: To make a whole number a fraction, put it over 1. Example:
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CHANGING AN IMPROPER FRACTION TO A MIXED NUMBER
To change an improper fraction to a mixed number:
*First, figure oufho* many of the denomlnator you
can fit into
numerator. 4...8...1,2... [16 would be too big), so 4 goes into ].5 three
This means 3 would be the whole number in the mixed
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number.
*whatever is leftover will be the fraction part of our
mixed number.
3 sets of 4 is L2 of the fourths. That means we have 3 of the fourths left over,
making l the fraction in our mixed number.
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FRACTION REFERENCE SHEET
ADDING AND SUBTRACTING FRACTIONS
*lf the denominators are the same,add or subtract the numerators
and keep the denominator the same.
[Do NOIadd the denominators... ever!]
xCheck to see ifthe result can be
reduced.
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...IF DENOMINATORS ARE DIFFERENT
*Find a common multiple
[preferably the lowest common multiple)
of the denominators (in the example, the least common multiple
would be 40).
*Multiply the top and the bottom of the fraction by whichever
number is necessary to get the denominator that you want.
*Add or subtract the numerators and reduce the result
if necessary.
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ADDING AND SUBTRACTING MIXED NUMBERS
There are different ways of doing this. I like the following set of steps, because they work for any set
of fractions or mixed numbers, positive or negative.
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1. change any mixed numbers into improper fractions ___>
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2. If necessary, rewrite one or both fractions so that you
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3. Add or subtract the numerators.
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4. If necessary, reduce the result. Also, convert it to a
mixed number if the numerator is bigger than the
denominator.
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