2.2 Positive and negative numbers
Numbers which have a plus sign attached to them, such as + 7, are referred to as positive numbers. Numbers which have a minus sign attached to them, such as –5, are referred to as negative numbers. Similarly, the symbols used in algebra can also be positive or negative.
When carrying out operations with positive and negative numbers you need to remember these general rules.
Addition of numbers with the same sign
When adding numbers with the same sign, the sign of the sum is the same as the sign on each of the numbers.
– 5 + (–4) = –9
+ 5 + (+ 9) = + 14
When adding numbers with the same sign, you can omit the brackets and the + sign for the addition. When the first number is positive, it is usual to omit its + sign.
+ 5 + (+9) = + 14 can be written as 5 + 9 = 14
– 5 + (–4) = –9 can be written as –5 – 4 = –9
Addition of numbers with different signs
To add numbers whose signs are different, subtract the numerically smaller from the larger. The sign of the result is the same as the sign of the numerically larger number.
–12 + 6 = –6
11 – 16 = –5
When dealing with several numbers of different signs, separately add the positive and negative numbers together. The set of numbers then becomes two numbers, one positive and one negative, which you can add in the usual way.
Subtraction
To subtract numbers, change the sign of the number being subtracted and add the resulting number.
Multiplication
The product of two numbers with the same signs is positive, while the product of two numbers with different signs is negative.
Negative × negative = positive
Positive × negative = negative
If you multiply any number by zero, the answer is always zero.
Division
When dividing numbers with the same signs this gives a positive answer and numbers with different signs give a negative answer.
For example,
If you divide a number by zero, you will always get an error, as this is impossible.
Bear these rules in mind as you turn your attention to handling brackets in algebra in the next section.