Integers are a fundamental part of mathematics, and they are used to represent a wide variety of quantities, from the number of apples in a basket to the distance between two cities. But what exactly are integers, and how do we perform operations on them?
In this blog post, we will explore the four basic operations on integers: addition, subtraction, multiplication, and division. We will also look at some interesting examples of how these operations can be used in everyday life.
Adding Integers
Adding integers is like combining numbers to find their total. When you add integers with the same sign (both positive or both negative), you can think of it as moving in the same direction. The numbers are working together, and their values are increasing.
- For example, 3 + 5 = 8. This is because 3 and 5 are both positive, so they add up to 8.
- Similarly, (-4) + (-2) = -6. This is because -4 and -2 are both negative, so they combine to -6.
However, if you’re adding integers with different signs, it’s like moving in opposite directions. Think of it as a tug-of-war between positive and negative. The bigger value’s sign wins, and the result takes the sign of the larger number.
- For example, 5 + (-3) = 2. (The difference between these two number is 2 and its sign will be positive due to larger number between 5 & 3 is number 5 and its Positive sign wins)
Similarly, (-7) + 9 = 2. (The difference is 2 and larger number between 7 and 9 is number 9 and its positive sign win so result is positive)
Similarly, 10+(-15)= -5 (The difference is 5 and its sign will be negative due larger number between 10 and 15 is 15 then its negative sign wins)
We can also understand through another type of explanation :
Example 1
5 + (-3) = 2 + 3 + (-3)
= 2 + 0
= 2
Example 2
(-7)+9 = (-7) + 7 + 2
= 0 + 2
= 2
Example 3
10+(-15) = 10+ (-10)+ (-5)
= 0 +(-5)
= (-5) = -5
Subtracting Integers
Subtraction is about finding the difference between numbers. When you subtract a positive number, it’s like moving backward. When you subtract a negative number, it’s like moving forward, which might seem odd. It’s because subtracting a negative is like adding a positive.
- For example, 7 – 3 = 4. This is because 7 is larger than 3, so we are moving forward by 4.
- Similarly, 7 – (-3) = 10. This is because subtracting a negative is like adding a positive, so we are moving forward by 10.
Multiplying Integers
Multiplication is about repeated addition. When you multiply two integers with the same sign, the result is positive because you’re dealing with “groups” of the same direction. When you multiply numbers with different signs, the result is negative because you have an odd number of negative factors.
- For example, 4 * 2 = 8. This is because we are adding 4 to itself 2 times, which gives us 8.
- Similarly, (-4) * 3 = -12. This is because we are adding (-4) to itself 3 times, which gives us -12.
Dividing Integers
Division is about sharing equally. When you divide two integers with the same sign, the result is positive. When you divide numbers with different signs, the result is negative. Dividing by zero is undefined.
- For example, 12 / 3 = 4. This is because we are dividing 12 into 3 equal groups, which gives us 4 in each group.
- Similarly, (-12) / 3 = -4. This is because we are dividing (-12) into 3 equal groups, which gives us -4 in each group.
Key Takeaway
Operations on integers are like following rules in a number world. Adding is about combining values, subtracting is finding the difference, multiplying is repeated addition, and dividing is about sharing. Understanding these operations helps you solve various problems, from calculating expenses to interpreting temperature changes. These concepts are like tools that make working with numbers more manageable and meaningful.
Here are some interesting examples of how operations on integers are used in everyday life:
- When you buy groceries, you are adding the price of each item to find the total cost.
- When you track your weight loss, you are subtracting the current weight from your goal weight to find the difference.
- When you calculate the distance between two cities, you are multiplying the speed of the car by the time to find the total distance.
- When you divide your monthly income by the number of people in your household, you are finding the amount of money each person can spend each month.
I hope this blog post has given you a better understanding of operations on integers