Division of Whole Numbers

The operation by means of which a factor is obtained when the product and the other factor are given is called division. The arithmetic operation is performed on the number, which we take as the given product. In division this number is called the dividend. The given factor is known as the number by which the dividend or the product is to be divided. This number is called the divisor. The result of the division of the dividend by the divisor is called the quotient. The sign of division is “:” or “/“ in England.

Fractions

A fraction is a part of a unit, such as ½; ¼; etc. A fraction has a numerator and a denominator. 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.

Subtraction of Fractions

More than two numbers may be added at the same time. In subtraction, however, only two numbers are involved. In subtraction, as in addition, the denominators must be the same. One must be careful to determine which term is the first. The second term is always subtracted from the first, which should be of a larger quantity.

To subtract fractions you must:

a) change the mixed numbers, if any, to improper fractions;

b) find the L.C.D.;

c) change both fractions to fractions having the L.C.D. as the denominator;

d) subtract the numerator of the second fraction from the numerator of the first, and place this difference over the L.C.D.;

e) reduce if possible.

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