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Addition of Whole Numbers

The addition of two or more numbers is an arithmetic operation by means of which a new number is obtained. This new number contains as many units as are contained in all added numbers taken together. The numbers that are added are known as the addends. The number resulting from addition of two or more numbers is known as the sum. The sign for addition is + (plus).

Addition is best performed when the numbers are written in columns so that units, tens, hundreds, and so forth are written vertically. For example, the sum of 1,562 and 1,891 is obtained, as follows:

1,562

+1,891

3,453

Addition is performed from right to left. We can easily observe that addition of 8 to 35 gives the same result when 35 is added to 8. In either of the operations of addition the sum is 43. So the sum of two or more numbers does not change when the order, in which the numbers are added, is changed.

Subtraction of Whole Numbers

Subtraction is an arithmetic operation by means of which one of the addends is obtained, when the sum and another addend are given. The result is known as the difference of the two given numbers. The number from which another number is to be subtracted is known as the minuend. The number that is subtracted is known as the subtrahend. Subtraction is an operation opposite to addition. The sign is - (minus).

Subtraction of many-place numbers is performed as follows:

986

-354

632

We begin subtraction from the right and we subtract the numbers in the same column. Thus: 6 – 4 = 2; 8 – 5 = 3, etc.

Multiplication of Whole Numbers

Multiplication is an arithmetic operation by means of which one number is repeated as an addend until it occurs as many times as it is indicated by another number. There are two numbers involved in multiplication. The result of the operation of multiplication is known as the product. The number which is repeated is known as the multiplicand. The number by which the multiplicand is multiplied is known as the multiplier. The sign is “x“or “”.

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 .