Negative numbers are fundamental and useful mathematical ideas. They may be difficult to understand at first. Problems with negative numbers are common among school math learners. Students must know the basic facts about negative numbers. It is also equally important to practice math problems involving negative numbers.

Notion of opposites is very common to our experience. Word pairs like up and down, forward and backward, increase and decrease etc. are used to express opposites. In math + and – signs are used with numbers to express opposites. Any two exact opposites nullify each other to give a zero sum.

–3 + 3 = 0

–8 + 8 = 0

A number line is a geometric representation of positive numbers and their opposite negative numbers. It begins at zero and extends indefinitely either way. See that negative numbers are only to the left of zero and positive numbers only to the right of it.

Numbers increase towards right on a number line. Note that negative numbers increase as their numerical size decrease towards zero on the right. This seems unnatural but holds sense as they are opposites. Positive numbers start to the right of zero. They increase naturally towards right with an increase in their numerical size.

Zero is the separator between negative and positive numbers. It is greater than the largest negative number to its immediate left. It is also smaller than the smallest positive number to its immediate right.

**Using Negative Numbers**

Numbers and their opposites are useful for representing two sides of many real world situations. Zero works as a fixed point between two sides. One side of zero represents positive measurements while the opposite side represents negative measurements.

**Example 1 **

Calendars measure time of history. They cannot have a zero as their starting point. Some important event in history is fixed as the zero time. For Gregorian Calendar, the event is the approximate birth date of Jesus. So time before Jesus is considered negative and time after his birth as positive. Tenth year before Jesus is 10BCE which is same as –10.

**Example 2**

For measuring temperature, freezing temperature of water works as a zero as it is the best choice. Temperatures higher than the zero are positive while those lower than it are negative. The scale of a thermometer is like a number line.

**Example 3**

For a bank account, the fixed point is a zero balance i.e. no money in either deposit or debt. Money deposited is positive. It increases the balance by a number equal to the number of dollars deposited. Money withdrawn is negative and lowers the balance by a number equal to the number of dollars withdrawn.

Think of more examples where negative numbers are useful. Try to answer the question that why for a long time after their discovery negative numbers continued to be regarded as meaningless, mysterious and of no use.

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