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Fractions
A fraction is part of an entire object. Fractions consist of two numbers. The
top number is called the numerator. The bottom number is called the
denominator.
numerator
denominator
1
4
2
4
One fourth is yellow
Two fourths are yellow.
One half is yellow.
3
4
Three fourths are yellow.
4
4
Four fourths are yellow.
Identifying Equivalent Fractions
Equivalent fractions are fractions that have the same value or represent the
same part of an object. If a pie is cut into two pieces, each piece is also onehalf of the pie. If a pie is cut into 4 pieces, then two pieces represent the
same amount of pie that 1/2 did. We say that 1/2 is equivalent to 2/4.
Fractions are determined to be equivalent by multiplying the numerator and
denominator of one fraction by the same number. This number should be
such that the numerators will be equal after the multiplication. For example
if we compare 1/2 and 2/4, we would multiply 1/2 by 2/2 which would result
in 2/4 so they are equivalent.
To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since
3/6 is not the same as 3/7, the fractions are not equivalent.
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Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ...
Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...
Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ...
Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...
Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...
Adding Fractions with the same Denominator
To add two fractions with the same denominator, add the numerators and
place that sum over the common denominator.
Adding Fractions with Different Denominators
How to Add Fractions with different denominators:
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Find the Least Common Denominator (LCD) of the fractions
Rename the fractions to have the LCD
Add the numerators of the fractions
Simplify the Fraction
Example: Find the Sum of 2/9 and 3/12
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Determine the Greatest Common Factor of 9 and 12 which is 3
Either multiply the denominators and divide by the GCF (9*12=108,
108/3=36)
OR - Divide one of the denominators by the GCF and multiply the
answer by the other denominator (9/3=3, 3*12=36)
Rename the fractions to use the Least Common
Denominator(2/9=8/36, 3/12=9/36)
The result is 8/36 + 9/36
Add the numerators and put the sum over the LCD = 17/36
Simplify the fraction if possible. In this case it is not possible
Adding Mixed Numbers with the same Denominator
Mixed numbers consist of an integer followed by a fraction.
How to add two mixed numbers whose fractions have the same
denominator:
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Add the numerators of the two fractions
Place that sum over the common denominator.
If this fraction is improper (numerator larger than or equal to the
denominator) then convert it to a mixed number
Add the integer portions of the two mixed numbers
If adding the fractional parts created a mixed number then add its
integer portion to the sum.
Example: 3 2/3 + 5 2/3 =
Add the fractional part of the mixed
numbers
Convert 4/3 to a mixed number
Add the integer portions of the mixed
numbers
Add the integer from the sum of the
fractions
State the final answer:
2/3 + 2/3 =
4/3
4/3 = 1 1/3
3+5=8
8+1=9
9 1/3