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½ - one half
¼ - one quarter
1/3 - one third
1/8 - one over eight
3/16 - three over sixtheen
FRACTIONS
Every fraction has a numerator and denominator. The denominator tells you the number of parts of equal size
into which some quantity is divided. The numerator tells you how many of these parts are to be taken.
Fractions representing values less than 1, like 2/3 for example, are called proper fractions. Fractions which
name a number equal to or greater than 1, like 2/2 or 3/2 , are called improper fractions. There are numerals
like 1×1/2 , which name a whole number and a fractional number. Such numerals are called mixed fractions.
Fractions which represent the same fractional number like ½, 2/4 ,3/6 , 4/8 and so on, are called equivalent
fractions. We have already seen that if we multiply a whole number by 1 we leave the number unchanged.
The same is true of fractions when we multiply both integers in a fraction by the same number. For example,
1× ½= ½. We can also use the idea that 1 can be expressed as a fraction in various ways
2/2 , 3/3, 4/4 and so on. Now see what happens when you multiply 1/2 by 2/2. You will have
1/2=1 ×1/2 = 2/2 ×1/2 = 2×1/ 2×2 = 2/4 . As a matter of fact in the above operation you have changed the
fraction to its higher terms. Now look at this: 6/8:1 = 6/8:2/2 = 6:2/8:2 = 3/4. In both of the above operations
the number you have chosen for 1 is 2/2. In the second example you have used division to change
6/8 to lower terms, that is to 3/4. The numerator and denominator in this fraction are prime and accordingly
we call such a fraction the simplest fraction for the given rational number.
A fraction is a number that can represent part of a whole.
Equivalent fractions are fractions that have the same value or represent the same part of an object
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.
The Greatest Common Factor (GCF) is the largest number that is a common factor of two or more
numbers.
The Least Common Denominator (LCD) is the Least Common Multiple of two or more denominators.
The Least Common Multiple (LCM) is the smallest number that two or more numbers will divide into
evenly.
Fractions consist of two numbers. The top number is called the numerator. The bottom
number is called the denominator.
numerator
denominator
fraction bar
To add two fractions with the same denominator, add the numerators and place that sum
over the common denominator.
To Divide Fractions:
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Invert (i.e. turn over) the denominator fraction and multiply the fractions
Multiply the numerators of the fractions
Multiply the denominators of the fractions
Place the product of the numerators over the product of the denominators
Simplify the Fraction
To Multiply Fractions:
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Multiply the numerators of the fractions
Multiply the denominators of the fractions
Place the product of the numerators over the product of the denominators
Simplify the Fraction
To Subtract Fractions
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Make sure the bottom numbers (the denominators) are the same
Subtract the top numbers (the numerators). Put the answer over the the same
denominator.
Simplify the fraction.
Improper fraction is just a fraction where the top number (numerator) is greater than or equal to the bottom
number (denominator).
Proper fraction is just a fraction where the numerator (the top number) is less than the denominator (the
bottom number
Mixed fraction is just a whole number and a fraction combined into one "mixed" number