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Fraction Notes
Vocabulary
common factor – a number that is a factor of two or more numbers
common multiple – a whole number that is a multiple of two or more numbers.
fraction - number that represents part of a whole or part of a set
denominator – the bottom number in a fraction. It represents the number of parts in the
whole.
numerator – the top number in a fraction; the part of the fraction that tells the number of
parts you have.
Least Common Multiple (LCM) – the smallest whole number greater than 0 that is a
common multiple of each of two or more numbers.
least common denominator – the least common multiple of the denominators of two or
more fractions
Greatest Common Factor (GCF) – the greatest of the common factors of two or more
numbers.
mixed number - a fraction that has a whole number part and a fraction part
improper fraction – a fraction with a numerator that is greater than or equal to the
denominator.
simplest form - a fraction in which the GCF of the numerator and the denominator is 1.
Notes:
Reducing or Simplifying Fractions:
~When reducing a fraction first find the Greatest Common Factor (GCF) between the
numerator and the denominator
Example: Simplify
15
21
15 The factors of 15 are 1, 3, 5, and 15
21 The factors of 21 are 1, 3, 7, and 21
The Greatest Common Factor (GCF) between 15 and 21 is 3, so take the numerator and
denominator and divide both of them by 3. (What you do to the bottom you have to do to
the top)
15 ÷ 3 = 5
21 ÷ 3 = 7
5
7
is in simplest form, because the only common factor between 5 and 7 is 1.
Reducing or Simplifying and Improper Fraction
When you have an improper fraction you can divide the numerator by the denominator.
You will end up with a whole number. If you have a remainder, it becomes your numerator.
The divisor will be your denominator. (You have now created a mixed number (a whole
number with a fraction).
Example:
8
5
Take 8 ÷ 5 = 1 R 3, so your new number will be 1
3
5
*You may have to simply once you make your mixed number. In this case
3
5
is already
in simplest form.
Adding Fractions with LIKE Denominators:
When the denominators are the same you simply add or subtract the numerators. DO NOT
add the denominators). Then simplify if needed.
2
1
4
4
Examples: +
=
3
4
4
5
3
2
5
1
4
4
4
4
3 +1 =4 =5
3
1
5
5
− =
Adding Fractions with UNLIKE Denominators:
When adding and subtracting fractions with unlike denominators first you have to find the
least common denominator (use the Least Common Multiple (LCM) to find the least
common denominator). Once you have found a common denominator you carry out the
function. Finally, simplify if needed.
Adding:
1
2
1
1𝑥3
3
2𝑥3
+ =
+
1𝑥2
3𝑥2
=
Subtracting without barrowing:
3
6
7
8
+
2
6
=
5
6
1
7𝑥2
2
8𝑥2
− =
−
1𝑥8
2𝑥8
=
14
16
−
8
16
=
6 ÷2
16÷2
=
3
8
Subtracting with barrowing: There are two ways you can barrow when subtracting:
1) You can change the fractions back into improper fractions by multiplying the
whole number and the denominator and then add the numerator.
1
1 21 5 21 5𝑥2 21 10 11
3
5 −2 =
− =
−
=
−
=
=2
4
2
4 2
4 2𝑥2
4
4
4
4
2) Or you can first find a common denominator if needed and then barrow from the
whole number. When you are barrowing from the whole number your
numerator and denominator should be the same. Add that fraction to the
fraction that is already there (if there is one). Then carry out the function.
1
1
1
1𝑥2
1
2
4 1
2
5
2
3
5 −2 =5 −2
=5 −2 =4 ( + )−2 =4 −2 = 2
4
2
4
2𝑥2
4
4
4 4
4
4
4
4