Addition is a concept that entails combining or adding things together. It is a mathematical operation in which we add numbers together.
In math, to subtract is to take something away from a group or a number of things. When we subtract from a group, the number of things in the group decreases or becomes smaller.
A bar model is a pictorial representation of a number in the form of bars or boxes that is used to solve numerical problems in mathematics. Bar models assist us in understanding how a problem should be solved and what should be done to proceed with the calculation.
The term “length” refers to the measurement of something from one end to the other, or the distance between two specific points.
For example, the length of the pencil in the image is 5 cm.
A number line is a diagram that depicts numbers on multiple, equally spaced points on a straight line. This line is used to compare numbers that are spaced at equal intervals on an infinite line that runs horizontally or vertically on both sides. The numbers increase as we move to the right side of a number line, and decrease as we move to the left. Similarly, on a vertical number line, the numbers increase towards the top and decrease as we follow the numbers towards the bottom.
Using visual interpretations to add measurements on a number line is a great way to learn how to add numbers. When we add measurements, we move to the right of the number line.
Example:
You take a break after swimming 10 meters. After that, you swim a distance of six meters. What is the total distance that you have covered while swimming?
Solution:
First, you swim for 10 meters and then for 6 meters, so the total swimming distance can be written as 10 + 6 = 16. Let’s represent this on a number line. First, we draw a number line, start from 10, and add 6. We reach 16.
Hence, the swimming distance is 16 meters.
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Subtraction reduces a number. We know that numbers decrease when moving left on a number line. Hence, to subtract measurements, we need to move to the left.
Example:
The length of a ribbon is 14 yards. You cut six yards off. What is the length of the ribbon now?
Solution:
It is given that the initial length of the ribbon is 14 yards and the length of the ribbon cut off is 6 yards. So the current length of the ribbon can be written as, 14 – 6 = 8.
Let’s represent this on a number line. First, we draw a number line, start from 14, and subtract 6. We reach 8.
Hence, the current length of the ribbon is 8 yards.
Example 1:
The length of a piece of paper is 8 inches. You cut 4 inches off. What is the current length of the paper?
Solution:
It is given that the initial length of the piece of paper is 8 inches and you cut off 4 inches from it. So the current length of the paper can be written as, 8 – 4 = 4.
Let’s represent this on a number line. First, we draw a number line, start from 8, and cut off 4. We reach 4.
Hence, the current length of the paper is 4 inches.
Example 2:
You want to make a woollen chain with a length of 10 inches. Before lunch, you make 7 inches. After lunch, you make another 3 inches. Have you completed the woolen chain?
Solution:
7 + 3 = 10 inches
First, you make 7 inches of the chain before lunch, and after lunch you make 3 inches more, so the total length of the chain can be written as 7 + 3 = 10.
Let’s represent this on a number line. First, we draw a number line, start from 7, and add 3. We reach 10.
Hence, the woolen chain is now complete.
Example 3:
A blue boat sails a distance of 34 feet, and a white boat sails 14 feet. By how much does the distance covered by the white boat and blue boat differ?
Solution:
It is given that the blue boat covers 34 feet and the white boat covers 14 feet. So, subtract the distance of the white boat from the distance of the blue boat to get the desired result.
The white boat travels 20 feet less than the blue boat.
Example 4:
Your pet turtle was 12 centimeters long last year. It is now 27 centimeters in length. How big did the turtle get in one year?
Solution:
It is given that the turtle was 12 centimeters long last year and now its length is 27 centimeters.
To get the increment in length of the turtle, subtract the last year’s length from the present length of the turtle.
Here, 12 can be written as 10 + 2 to make subtraction easier. First, subtract 10 from 27. We will get 17. Post that, on subtracting 2, we get 15 as the final result.
Hence, the turtle has grown 15 centimeters in one year.
Example 5:
Four students made paper models of the Statue of Liberty. The length of their models is given below in inches. How much taller is student 4’s model than the shortest model?
Solution:
In the given question, we can see that the shortest model belongs to student 2.
To find how much taller student 4’s model is than student 2’s model, we need to subtract the height of student 2’s model from that of student 4’s model.
Hence, student 4’s model of the Statue of Liberty is 4 inches taller than the shortest model.
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Adding and subtracting numbers on a number line is an engaging and easy way to visualize the manner in which numbers are added and subtracted. They act as visual interpretations of these mathematical operations.
A number line is a diagram that depicts numbers on a straight line. It serves as a tool for comparing and placing numbers in order.
To measure length, we use various units of measurement. For example, miles, feet, yards, inches, decimeters, centimeters, and millimeters are all units of measurement.