About Addition of Numbers Using Number Lines
Addition on a Number Line using Number Lines
An open number line is a number line that does not have any numbers or markings.
It can be used to mark and map out what is thought about when a question is presented. Number lines are important and are required because it helps us to see and understand different mathematical operations like addition and subtraction. A number line never ends. It goes on for infinity as numbers never end. As you move towards the left of the number line, the value decreases and as you move towards the right, the value of the numbers increases.
Usually the number lines you are familiar with look like this:
Now, you could also represent a number line in units of tens or hundreds, or even thousands.
Now, if you are asked to add 20 and 32, this is what it would look like in a number line. First, you move from the marking that represents ‘20’. Next, we split 32 into tens and ones. 32 can be expressed as 3 tens and 2 ones hence it can be written as:
32 = 10 + 10 + 10 + 1 + 1
Now, add three more units on the number line where each unit is 10 greater than the unit to the immediate left. So, we have marked the number line with 30, 40 and 50 as ‘20 + 10 = 20’, ‘30 + 10 = 40’ and ‘40 + 10 = 50’. Now, we add another unit by adding ten to 50 and mark it as 60. The space between 50 and 60 is divided into ten equal parts. Each subdivision between 50 and 60 denotes 1.
So, the sum of 20 and 32 is equal to 52. And the dot represents 52.
As 32 is 3 tens and 2 ones, from 20 we have to jump by ten 3 times and then by one 2 times.
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Solved Examples of Addition on a Number Line
Fill in the blanks
Example 1. Complete the number line and the equation
Answer:
Take a look at the number line. we need to obtain 70 and we can make three jumps as per the diagram of which two of these jumps cover 10 units each. Ten is added to 46 and this gives 56. Write ‘56’ in the blank provided. Next, add ten again which gives us the answer to the next blank which is ‘66’. To obtain 70, subtract ‘66’ from ‘70’ which gives us ‘4’. We write ‘4’ in this blank.
Next, we need to fill in the equation:
The first blank is 46 and the second blank is the sum of 10+10+4 =24.
Therefore, 46 and 24 are placed in the blanks and that’s our answer.
Example 2. Represent the following sum on a number line.
20 + 23
Answer:
So, after drawing a number line, we mark ‘20’ as that’s the first number we need to add (we can also mark 23 and proceed with the addition the answer would be the same). Next, we need to add ‘23’.
23 = 10 + 10 + 3
Next, we add ‘10’ twice which gives us ‘40’. Finally, by adding three more ‘1’s, 43 is obtained which is the sum of 20 and 23.
Example 3. Tom climbed a flight of stairs which has 10 steps. Then he climbed two more flights of stairs and was about to climb the third flight of stairs but stopped at the seventh step. Represent the total number of stairs Tom climbed using a number line.
Answer:
Each flight of stairs comprises 10 steps. In total, Tom climbed three flights of stairs. This means,
10 + 10 + 10 = 30
Next, Tom was about to climb another flight of stairs but he stopped at ‘7’. So,
30 + 7 = 37
After drawing a number line, we mark ‘10’. The jump from 0 to 10 represents the first flight of stairs. Next, add two more flights of stairs so add two tens to 10 which gives us ‘30’ in total. Finally, seven more ones or subunits give us a total of 37 steps which is the total number of stairs.
Example 4. Sam distributed 25 chocolates to class A, 13 Chocolates to class B and 12 chocolates to class C. Find the total number of chocolates he distributed with the help of a number line.
Answer:
So, first, we will split the number of chocolates distributed to each class into tens and ones.
Class A: 25 = 10 + 10 + 5
Class B: 13 = 10 + 3
Class C: 12 = 10 + 2
We can see that there are four ‘10’s. Let’s draw a number line with six units. Each unit is equal to ten chocolates more than the unit to the immediate left. We also divide the space between 40 and 50 into ten units such that each unit is one.
Now we reach 40.
Next, we need to find 5 +3 + 2. So from 40, we count on the number line by 5 ones, 3 ones and 2 ones this gives us the answer as 50. Therefore, 50 chocolates were given away to the three classes.
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The phrase ‘count on’ means counting ahead from a particular number. In the context of the number line, you ‘count on’ from 30 to 40 by adding ten. Or we ‘count on’ from 10 to 40 by adding two tens.
- When adding on the number line, any number can be marked first. The answer remains the same. To add on a number line, first mark any number on the number line, then split the other addend into multiples of tens and ones. Count all the 10’s and plot them first, followed by the remaining ones to get the answer.