# Directed Numbers

**Introduction**

Numbers are used in performing calculations by using operators like addition, subtraction, multiplication, division, and so on. The sign, added sometimes right before a number, plays a vital role in the number system. It can change the entire situation in our decision-making. The standard numbers which are greater than zero are described as positive numbers and a plus sign is $$(+)$$ placed before the number indicates the same. On the other hand, the numbers that are less than zero are known as negative numbers and are represented by placing a minus sign $$(-)$$ before them.

Positive and negative numbers generally are used to show the direction of a value. A positive sign represents the positive direction and a negative sign represents the negative direction. These numbers are called the directed numbers.

So, from the above explanation, it can be concluded that the directed numbers are the numbers that have both size and direction (positive or negative). Consider an example of a bag attached to the air-filled balloons and a few weights are added in the bag.

The balloon pulls the bag up in a positive direction and the weights in the bag pull it down in the negative direction. Adding more balloons will help pull the bag upwards and adding more weights in the bag will pull the bag downwards.

**E1.4: Use directed numbers in practical situations**

**Directed numbers**

Directed numbers are numbers which have both size (value of the number) and the direction (positive or negative). They can be visualised on the number line which has both positive and negative numbers separated by the $$0$$ number, as can be seen in the diagram below:

If the mathematical operations are performed on any two numbers, the resulting value will lie either on the right (positive) side or on the left (negative) side of $$0$$, depending on the operation applied and the nature of the two numbers. The value can be $$0$$ as well.

Now, consider a few examples where directed numbers are widely used in the real world situations.

The road on which people travel in their everyday lives can be considered a gigantic number line.

In banking, the amount deposited in an account is normally represented by a positive value and the amount that is withdrawn is represented by negative values.

In daily weather forecasts, negative numbers are used, to represent low temperatures, that is, below freezing point. The subtraction of the lowest temperature in a day from the highest temperature helps to determine the value of fluctuation and also calculate the average temperature of a particular region on any specific day.

In the field of medicine, to measure blood pressure levels, body weights and diabetes levels, the concept of negative and positive scales are used.

**Worked examples:**

**Example 1:** Use the number line to evaluate the expression $$-5-4$$.

Step 1: Apply the numerical operation.

Start at number $$-5$$ and add the number $$-4$$ to it, that is, move $$4$$ places to the left of $$-5$$.

It will arrive at the number $$-9$$.

Step 2: Point the values on the number line.

Point the given numbers on the number line and perform the operation that gives the required answer.

**Example 2:** Use the number line to evaluate the expression $$-3-(-6)$$.

Step 1: Apply the numerical operation.

Start at number $$-3$$ and subtract the number $$-6$$ from it, that is, move $$6$$ places to the right of $$-3$$. It will arrive at the number $$3$$.

Step 2: Point the values on the number line.

Point the given numbers on the number line and perform the operation that gives the required answer.