Addition on Number line: The number line is a horizontal line with equal spacing of numbers that extends infinitely to either side. It is the visual representation of numbers on a horizontal line that is straight. On a number line, we can represent the numbers in a pattern.

The number zero is in the midst of the number line, with positive numbers to the right of it and negative numbers to the left. We will move to the right of the number line to add a number and to the left of the number line to subtract a number.

Continue reading this article to know more about addition on number line.

Number Line

A number line can be described as a straight line with numbers placed at equal intervals or segments along its length. It can be extended infinitely in any direction and represented horizontally, and is used as a reference for comparing and ordering numbers. A number line is a way to describe any real number that includes every whole number and natural number.

Representation of Numbers on Number Line

We can explain all arithmetic operations such as the addition, subtraction, multiplication, and division of numbers on a number line. Firstly, one must learn to locate numbers on a number line, the middle point of a number line is Zero. Therefore, all positive numbers will be on the right side of the zero, whereas negative numbers will be on the left side of zero on the number line. In other words, if we move to the left side of zero, the value of the number decreases, and if we move to the right side of zero, the value of the number increases.

Addition

Addition generally indicated by \(+ \) sign is a method of finding the sum of two or more numbers, or objects is known as an addition.
For example, to find the sum of \(5\) and \(7,\) we will write it as \(5 + 7.\)

Addition on Number Line

As discussed earlier, the number line is the visual representation of numbers on a straight horizontal line.

The numbers on the number line shown below, with zero in the middle, positive numbers to the right of the zero and negative numbers to the left side of zero.

The addition on the number line is the way to find the sum of numbers using a horizontal line with the numbers placed in equal distance.

There are two steps to be followed to add numbers on a number line.

1. Move right to add the positive numbers.
2. Move left to add the negative numbers.

Addition of Positive Numbers

When we find the sum of two positive numbers, the result will always be a positive number. Therefore, when we find the sum of positive numbers direction of movement will always be to the right side.
For example, let us do the addition of \(2\) and \(3.\)
\(2 + 3 = 5\)
Here the first number is \(2,\) and the second number is \(3;\) both are positive. So first, locate \(2\) on the number line. Then move \(3\) places to the right to get the answer.

Addition of Negative Numbers

When we find the sum of two negative numbers, the result will always be a negative number. Therefore, while adding negative numbers direction of movement will always be to the left side.
For example, let us do the addition of \( – 6\) and \( – 3.\)
Now, let us add \( – 6\) and \( – 3\) using a number line. Since both are negative numbers, mark the point \( – 6\) to the left of zero. Because \( – 6\) lies left to zero in a number line.
Now, move \( 3\) points to the left of \( – 6\) on the number line as \( – 3\) is a negative number. We get \( – 9.\)

Representation of Fractions on Number Line

The term used to represent the part of the whole is called a fraction. There are two parts in a fraction, namely, numerator and denominator.

The fractions can be classified as

1. Proper Fractions
2. Improper Fractions
3. Mixed Fractions

We know how to represent integers numbers on the number line. Now, let us try to represent fractions, for example \(\frac{1}{2}\) on a number line.
It is clear that \(\frac{1}{2}\) is greater than \(0\) and less than \(1.\) So, it must lie in between \(0\) and \(1.\) Since the denominator of the given fraction is \(2,\) divide the space between \(1.\) and \(2\) into two equal parts.

Addition of Fractions on Number Line

When we need to add two fractions, the denominator should be the same. If the denominators are not the same, you have to use equivalent fractions with a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators. To add the given fractions with unlike denominators, write the fractions with a common denominator. Then add and simplify.

For example, if we need to add \(\frac{4}{{10}} + \frac{3}{{10}},\) first, make ten equal space between \(0\) and \(1.\) Then mark \(\frac{4}{{10}}\) on the number line, then move \(3\) places right to \(\frac{4}{{10}}\) to get the required answer. From the above number line, \(\frac{4}{{10}} + \frac{3}{{10}} + \frac{7}{{10}}\)

Solved Examples

Q.1. Add \(5\) and \(7\) using a number line.
Ans: Draw a number line and mark the equal spaces on the right side of zero since both the given numbers are positive. Then mark \(5\) on the number line and move \(7\) places right to \(5\) to get the required answer.

So, from the above number line, we can conclude that \(5 + 7 = 12.\)

Q.2. Add \(6\) and \(3\) using a number line.
Ans: Draw a number line and mark the equal spaces on the right side of zero since both the given numbers are positive. Then mark \(6\) on the number line and move \(3\) places right to \(6\) to get the required answer.

So, from the above number line, we can conclude that \(6 + 3 = 9.\)

Q.3. Add \( – 1\) and \( – 10\) using the number line.
Ans: Draw a number line and mark the equal spaces on the left side of zero since both the given numbers are negative. Then mark \( – 1\) on the number line and move \( 10\) places left to \( – 1\) to get the required answer.

So, from the above number line, we can conclude that \( – 1 – 10 = – 11.\)

Q.4. Find the sum of \( – 8\) and \( – 12\) using the number line.
Ans: Draw a number line and mark the equal spaces on the left side of zero since both the given numbers are negative. Then mark \( – 8\) on the number line and move \( 12\) places left to \( – 8\) to get the required answer.

So, from the above number line, we can conclude that \({\rm{ – 8 – 12 = }}\,{\rm{ – 20}}{\rm{.}}\)

Q.5. Add \(\frac{3}{6}\) and \(\frac{5}{6}\) using the number line.
Ans: We know that the value of \(\frac{3}{6}\) is \(0.5\) and \(0.5\) lies between \(0\) and \(1.\) So, draw a number line and make six equal space between \(0\) and \(1\) and \(1\) and \(2.\) Then mark \(\frac{3}{6}\) on the number line, then move \(5\) places right to \(\frac{8}{6}\) to get the required answer.

So, from the above number line, we can conclude that \(\frac{3}{6} + \frac{5}{6} + \frac{8}{6}.\)

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Summary

In the above article, we have learned the meaning of the number line, the definition of addition of numbers, the example of addition, how to add the integers on the number line, facts on the addition of number line, and addition of fractions on the number line.

Frequently Asked Questions

We have provided some frequently asked question here:

Q.1. What is addition on the number line?
Ans: The addition on number line is the way to find the sum of numbers using a horizontal line with the numbers placed in equal distance.

Q.2. How do you add three numbers on a number line?
Ans: When we have \(3\) numbers to add, for example, \(3 + 5 + 2,\) first mark the given addend \(3\) on the number line and move \(5\) points to the right of \(3.\) We will get the sum of \(3 + 5.\) Then move \(2\) points to the right from the sum to get the required answer.

Q.3. How do you add large numbers on a number line?
Ans: If we want to add large numbers on a number line, for example, \(42 + 12,\) we need to draw the number line so that the points must be equal to multiples of \(10.\) The space between \(40\) and \(50\) will contain \(10\) points. Mark \(42\) on it and move \(12\) points to the right of \(42\) to get the required answer.

Q.4. How do you teach addition on a number line?
Ans: When we find the sum of two positive numbers, the result will always be a positive number. Therefore, when we find the sum of positive numbers direction of movement will always be to the right side.
When we find the sum of two negative numbers, the result will always be a negative number. Therefore, while adding negative numbers direction of movement will always be to the left side.

Q.5. How do you do addition and subtraction on a number line?
Ans: When we add two positive numbers on the number line, mark the first addend and move to the right according to the value of the second addend. When we subtract two numbers, for example, \(8 – 6,\) mark \(8\) on the number line and then move \(6\) points to the left from \(8\) to get the required answer.

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