Division on Number Line

Division on a number line refers to the arithmetic operation of division being performed on numbers using a number line. A number line helps us to perform different arithmetic operations such as addition, subtraction, multiplication, and division. We will be learning about division on a number line by understanding the rules and examples in this article.

A number line is a visual representation of the set of real numbers that include integers, fractions, whole numbers, etc. The division is an arithmetic operation that can be performed with the help of a number line. We know that division is also known as repeated subtraction. We will use this fact and understand the representation of division operation on a number line.

Steps for Division on Number Line

Consider a number 'x' is being divided by 'y'. We will now represent x ÷ y on the number line. Since division operation is also known as repeated subtraction, therefore we will perform the subtraction operation by moving towards the left on the number line. Let's understand the steps of showing division on the number line given below to perform this.

• Step 1: Draw a number line, plotting the multiples of y starting from 0 and mark the dividend x on the number line. We will take x as the reference.
• Step 2: Starting from x, we keep subtracting groups of y units each until we reach the number 0. Each time we do the subtraction, we move by y units towards the left of x until we reach 0. The alternate method to do this is starting from 0 as the reference point, we can move towards the right by groups of y units each until we reach the number x.
• Step 3: The number of steps of y units each that we moved towards the left of x to reach 0 or the number of steps of y units each that we moved towards the right of 0 to reach x will give us the quotient.

Let's take an example to understand the representation of division on a number line.

Example: Divide 14 by 7 by representing the division on a number line.

Let us follow the steps that we discussed above to perform the division 14 ÷ 7.

• To perform 14 ÷ 7, we will make a number line and plot the first few multiples of 7 starting from 0 which includes the dividend 14. Encircle the dividend 14.
• Starting from 14, move towards the left by 7 units and keep repeating these moves of 7 units each until we reach 0.
• The number of moves made to reach 0 from 14 will be the quotient. As we see that, we had to move by 2 jumps to reach 0. Therefore, the quotient is 2.

Alternate Approach:

The same division operation can be shown on a number line by taking 0 as the reference and moving towards the right of 0 by groups of 7 to reach 14. The number of jumps made towards the right to reach 14 gives the quotient. Hence, we see that there are a total of 2 jumps made to reach 14 and therefore, 2 is the quotient.

Therefore, the value of 14 ÷ 7 = 2 is shown on the number line.

Division of Negative Numbers on a Number Line

We will now look into the representation of the division of negative numbers on a number line. The steps to show the division will be very similar as discussed in the above section. Let's take two cases with examples.

Case I: Negative number divided by a positive number

Example: (- 42) ÷ 6

As per the rules of integers operation, when a negative number is divided by a positive number or vice-versa the result is always a negative number. We plot the negative multiples of 6 on the number line starting from 0 to - 42 as the dividend is - 42. We see that there are a total of 7 jumps made each consisting of 6 units to reach - 42. Since the jumps are made towards the left of 0 on the number line, hence the result is - 7.

Therefore, (- 42) ÷ 6 = - 7 is shown using a number line.

Case II: Negative number divided by a negative number

Example: (- 42) ÷ (- 6)

As per the rules of integers operation, when a negative number is divided by a negative number, the result is always a positive number. We plot the positive multiples of 6 till 42 as shown in the diagram. Now, to reach 42, starting from 0, we make a jump of 7 moves of 6 units each. Since the jumps are towards the right-hand side of 0 on the number line, the result is positive and the quotient is 7.

Therefore, (- 42) ÷ (- 6) = 7 is shown using a number line.

While dividing numbers, we come across a lot of situations wherein the dividend is not completely divisible by the divisor. This happens when the dividend is not a multiple of the divisor or in other words, the divisor is not a factor of the dividend. When this situation arises, we get a non-zero remainder. We will now understand how to represent the division on a number line with remainders by taking an example.

Let's divide the number 12 by 5 and represent it on a number line.

• We start by drawing a number line marking all numbers starting from 0 at least up to 12.
• Since the divisor is 5, we start making groups of 5 units and start moving towards the right of 0 starting from 0 to reach the number 12.
• We see that the first group is 0 to 5 and the second group is 5 to 10. Thus, we have two groups of 5 from 0 to 10. Note that, for the third group we need a minimum of 5 more units but we have only 2 more units that are from 10 to 12. Hence, we can say that the remainder is 2 as these 2 units are not forming a group of 5.

Therefore, the quotient is 2 since there are two groups of 5 and the remainder is 2. Hence, we can represent this division as 12 ÷ 5 = 2r2 where r represents the remainder.

Related Articles

Check out the following links related to division on a number line.

• Addition on Number Line
• Subtraction on Number Line
• Multiplication on Number Line

What is Division on a Number Line?

Division on a number line is defined as the representation of the division operation using the number line for integers, fractions, whole numbers, etc.

How to show Division on a Number Line?

Division on a number line can be shown by plotting the multiples of the divisor starting from 0 at least up to the dividend. We then count the number of steps to reach the dividend counting from 0. The number of jumps or steps moved gives the result. The sign of the result depends on the direction of movement. For example, to show 4 ÷ 2 on the number line, we first plot the multiples of 2 starting from 0 up to 4. Now, starting from 0, we will have to move towards the right by 2 steps to reach 4. Therefore, the result is 2.

How to show Division of Integers on a Number Line?

The division of integers on a number line is very similar to the division of whole numbers wherein we graph the multiples of the divisor starting from 0 up to the dividend. Starting from 0, we check the number of jumps made to reach the dividend that gives us the final answer. If both dividend and divisors are positive or if both are negative, the multiples will lie towards the right-hand side of 0 and we get a positive result. In integers, we may have negative integers also being divided. If a negative integer is being divided by a positive integer or if a positive integer is being divided by a negative integer, the multiples will be graphed towards the left of 0. For example, to show (- 12) ÷ 3 we will plot the negative multiples of 3 towards the left-hand side of 0 up to - 12. Now, starting from 0, we will move by 4 steps to reach - 12. Since the jumps are made towards the left of 0 therefore the result is - 4.

Can you Divide on Number Line?

Yes, we can divide on a number line by plotting the multiples of the divisor and counting the jumps that will be done starting from 0 up to the dividend. The sign of the result depends on the direction of movement. If the jumps are made towards the left of 0 then the result is negative and if it is towards the right of 0 then the result is positive.

How do you Divide Negative Numbers on a Number Line?

Negative numbers can be divided on a number line by plotting the numbers towards the left-hand side of 0 if either of dividend or divisor is negative, But, if both dividend and divisor are negative then according to the rules of integers, they turn out to give a positive result and all the plottings will be done towards the right-hand side of 0 on the number line. For example, let's perform - 8 ÷ 2 on the number line. Since the dividend is negative, we will plot the negative multiples of 2 starting from 0 to - 8. Now, we start from 0 and move towards the left till - 8. To do so, we will have to move by four jumps. Since the jumps are made towards the left of 0 on the number line, therefore, the result will be - 4.