Fractions

A fraction is a part of a unit, such as ½; ¼; etc. A fraction has a numerator and a denominato r. For example in the fraction ¾ - 3 is the numerator, and 4 is the denominator. In the fraction the numerator is divided by the denominator. The fraction 2/7; indicates that 2 is being divided by 7.

A mixed number is an integer together with a fraction, such as 2 3/5; 7 3/8 etc. An integer is the integral part and a fraction is the fractional part. An improper fraction is one in which the numerator is greater than the denominator, such as 19/6; 23/4 etc.

To change a mixed number to an improper fraction you must:

a) multiply the denominator of the fraction by the integer;

b) add the numerator to this product;

c) place the sum over the denominator of the fraction.

For example let’s change 3 4/7 to a fraction.

The solution is: 7 x 3 = 21; 21 + 4 = 25; 3 4/7 = 25/7.

Addition of Fractions

Fractions cannot be added unless the denominators are all the same. If they are, add all the numerators and place this sum over the common denominator. Add up the integers, if any.

If the denominators are not the same, the fractions in order to be added must be converted into fractions having the same denominators. In order to do this; it is first necessary to find the Lowest Common Denominator (L.C.D.). The L.C.D. is the lowest number, which can be divided by all the given denominators.

For example L.C.D. of ½, 1/3, and 1/5 is 2 x 3 x 5 = 30.