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Simplification And Types Of Fraction
Simplifying fractions:
There are two methods for simplifying fractions.
The first method is to divide the numerator and denominator until you can't simplify any further. It's very important when you are dividing that at each step you divide the numerator and denominator by the same number. This will keep the fraction equivalent.
The second method is to divide each number by the greatest common factor (GCF). The GCF is the largest number that will divide into both numbers evenly. It is calculated by listing the factors of each number and determining which is the greatest.
Example: Simplify $\frac{140}{210}$.
Divide both the numerator and denominator by 2 to get $\frac{70}{105}$.
Divide both the numerator and denominator of $\frac{70}{105}$ by 5 to get $\frac{14}{21}$.
Divide both the numerator and denominator of $\frac{14}{21}$ by 7 to get $\frac{2}{3}$.
The fraction $\frac{2}{3}$ is in its simplest form.
2. Find the GCF of 36 and 54.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The common factors of 36 and 54 are 1, 2, 3, 6, 9, and 18.
HCF is 18
Types of Fractions
A fraction represents part of a whole number. The numerator or top number tells you how many parts you are talking about, and the denominator the bottom number is how many pieces make up the whole. If you ate 3 pieces out of 5 pieces of a pizza, the fraction has the numerator as 3, and the denominator as 5.
There are three types of fractions:
Proper fractions, where the numerator is less than the denominator
eg. $\frac{1}{2}$
Improper fractions, where the numerator is higher than (or equal to) the denominator eg $$\frac{2}{1}
Mixed fractions, a whole number and proper fraction combined.
eg $2\frac{1}{2}$
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