Subtract negative numbers

As is well known, subtraction is the opposite of addition.

If a and b are positive numbers, then subtract the number b from the number a, then find the number c, which when added with the number b gives the number a.

a - b = c or c + b = a

The definition of subtraction is preserved for all rational numbers. That is, the subtraction of positive and negative numbers can be replaced by addition.

Or, in other words, it can be said that subtracting the number b is the same addition, but with the number opposite to the number b.

a - b = a + (- b)

Example.

6 - 8 = 6 + (- 8) = - 2

Example.

0 - 2 = 0 + (- 2) = - 2

Rules for subtracting negative numbers

As can be seen from the examples above, the subtraction of the number b is the addition with the number opposite to the number b.

This rule is preserved not only when subtracting a smaller number from a larger number, but also allows you to subtract a larger number from a smaller number, that is, you can always find the difference of two numbers.

The difference can be a positive number, a negative number, or a number zero.

Examples of subtracting negative and positive numbers .

• - 3 - (+ 4) = - 3 + (- 4) = - 7
• - 6 - (- 7) = - 6 + (+ 7) = 1
• 5 - (- 3) = 5 + (+ 3) = 8

It is convenient to remember the rule of characters , which allows to reduce the number of brackets.

The plus sign does not change the sign of the number, therefore, if there is a plus in front of the bracket, then the sign in brackets does not change.

+ (+ a) = + a

+ (- a) = - a

The minus sign in front of the brackets changes the sign of the number in brackets to the opposite.

- (+ a) = - a

- (- a) = + a

From the equalities it is clear that if there are identical signs in front of and inside the brackets, then we get “+”, and if the signs are different, then we get “-”.

(- 6) + (+ 2) - (- 10) - (- 1) + (- 7) = - 6 + 2 + 10 + 1 - 7 = - 13 + 13 = 0

The rule of signs is also preserved if there is not one number in brackets, but an algebraic sum of numbers.

a - (- b + c) + (d - k + n) = a + b - c + d - k + n

Please note that if there are several numbers in parentheses and the minus sign is in front of the parentheses, then the characters in front of all numbers in these parentheses should change.

To memorize the rule of signs, you can create a table of definitions of signs of a number.

Number Rule for Numbers

+ (+) = +	+ (-) = -
- (-) = +	- (+) = -

Or learn a simple rule.