Subtraction is one of the basic math operations. It is the process of taking away a number from another. This arithmetic operation is denoted by a subtraction symbol (-). Read on to learn all about calculating the difference between two or more numbers.
Here’s what we’ll cover:
- What is subtraction?
- Subtraction formula
- Properties of subtraction
- How to subtract numbers?
- Subtraction without regrouping
- Subtraction with regrouping
- Word problems on subtraction
- Verifying subtraction results
- How to subtract fractions?
- How to subtract decimals?
- Practice problems
What is Subtraction?
Subtraction is an arithmetic operation of taking the difference between two numbers. For instance, if x= a-b, then a is called the minuend, b is the subtrahend, and the symbol between the a and b is called the minus sign. The final result after subtracting subtrahend from minuend is called the difference of the two numbers. The expression “a-b” is read “a minus b.”
Subtraction Formula: Minuend – Subtrahend = Difference
Properties of Subtraction
The properties of subtraction are as follows:
- It is the reverse of addition.
- If we subtract a number from itself, it gives 0.
- For any two whole numbers, x and y, if x > y then x – y is a whole number and if x < y, then x – y is never a whole number. The subtraction of a bigger real number from a smaller number gives a negative real number. For example, 110 – 100 = 10, is a whole number but 100 – 110 = -10 is not a whole number.
- For any two whole numbers, x and y, x – y ≠ y – x. Hence, unlike addition, subtraction of the whole number is not commutative. For example, 15 – 7 = 8 but 7 – 15 ≠ 9.
- For any three whole numbers say x, y, and z (x – y) – z ≠ x – (y – z). So, the subtraction of whole numbers isn’t associative.
- The subtraction property of equality means balancing an equation by using the same mathematical operation on the two sides of the equation. Suppose there are 15 stars in two boxes. So, if we take away 2 stars from box 1 then, to balance this equation in both the boxes we need to take away 2 stars from the other box also.
- We can also extend the subtraction of real numbers to complex numbers.
How to Subtract Numbers?
To solve subtraction problems, we can easily subtract one-digit numbers, but for larger numbers, we use the place value method and split the numbers into columns like Ones, Tens, Hundreds, Thousands, and more. Subtracting numbers often have cases where we will have to borrow one number from the next.
Subtraction involving borrowing is also called subtraction with regrouping. We borrow one number from the preceding column when the minuend is smaller than the subtrahend. This borrowing makes the minuend bigger than the subtrahend. The following example will help to understand this method.
Note: While subtracting, we always subtract the smaller number from the larger number.
Subtraction Without Regrouping
Example: Subtract 2532 from 4856.
Solution: Follow the steps given below to get the right answer.
Step 1: Begin with the digit at ones place. (6 – 2 = 4)
Step 2: Next, we will solve the tens place. (5 – 3 = 2)
Step 3: Subtract the digits at hundreds place. (8 – 5 = 3)
Step 5: Finally, solve the digits at thousands place. (4 – 2 = 2)
Step 6: So, the difference between the two given numbers is: 4856 – 2532 = 2324.
Subtraction With Regrouping
Example: Subtract 3278 from 4462.
Solution: The following steps will help you solve subtraction problems with regrouping.
Step 1: We will begin subtracting the digits at ones place. Since 8 is greater than 2, we will borrow 1 from the tens column and 2 will become 12. Now we will subtract, 12 – 8 = 4 ones.
Step 2: As 6 donated 1 to the ones column in the previous step, it will become 5. Here, 7 is greater than 5, so we will borrow 1 from the preceding column. Now, it will become 15 and 15 – 7 will be 8 at tens place.
Step 3: Since in the previous step 4 donated 1 to the tens column, we are left with 3 at the hundreds place. Now, we will subtract the digits in the hundreds place, i.e., (3 – 2) and we will get 1.
Step 4: Now, we will subtract the digits at the thousands place. So, 4-3 will be 1 at the thousands place.
Step 5: Therefore, the difference between the two numbers: 4462 – 3278 = 1184
Word Problems on Subtraction
|Example: A cricket match had a total of 4233 spectators. After the first innings, 2800 spectators left the stadium. Find the number of spectators remaining. |
Solution: Given: The total number of spectators present = 4233
The number of spectators who left the stadium after the first innings = 2800
Here, 4233 is the minuend and 2800 is the subtrahend.
Th H T O
4 2 3 3
-2 8 0 0
1 4 3 3
Therefore, the number of remaining spectators = 1433.
Verifying Subtraction Results
We can verify the answer as follows:
- Add the difference and the subtrahend. If you obtain the minuend as the sum, then your answer is correct.
- For example, 2233- 1000 = 1233. Here, 1000 is subtrahend and 2233 is minuend. The difference is 1233.
Now adding difference + subtrahend = minuend.
So, 1233 + 1000 = 2233. Hence, the answer is correct as the sum equals the minuend.
How to Find Missing Minuends?
Often subtraction problems require you to find a missing minuend in the given question. Consider the following example to understand this better.
|Example 1: Find the missing minuend in the given statement.___ – 567 = 343|
Solution: Given: The subtrahend is 567. The difference is 343.
We can calculate the minuend from the formula:
difference + subtrahend = minuend
So, 343 + 567
=910 is the minuend.
Example 2: Find the missing minuend (x) in the given equation.x – 2/3= 4/3
Solution: Firstly, we will keep x on the left-hand side and take the subtrahend to the right-hand side.
x = 4/3 + 2/3
Since the denominators are the same, we will add the numerators keeping the denominator as 3.
x = 4+2/3
x = 6/3
We can simplify the above fraction, so the answer will be x = 2.
How to Subtract Fractions?
Adding and subtracting fractions is one of the most common arithmetic operations. The following steps will help you subtract fractions:
Step 1. Firstly, we will ensure that the denominators of both the fractions are the same.
Step 2. If the denominators are the same, subtract the numerators. Next, we will place the answer over the same denominator.
Step 3. Lastly, simplify the fraction if required.
|Example 1: Solve 11/5 – 2/5|
Solution: Since the denominators are the same, we will subtract the numerators and place the numerator on the same denominator.
So, 11-2 = 9.
The answer will be 9/5. As it is an improper fraction, we will convert it into the mixed fraction form: 1 4/5.
|Example 2: Solve 11/4 – 2/3|
Solution: Since the denominators are different, we will first take the LCM of the denominators/ The LCM of 4 and 3 will be 12. Multiply the denominators by numbers such that they become 12. Now, we will multiply numerators with that number.
33 -8/12 =25/12
The answer will be 25/12. As it is an improper fraction, we will convert it into the mixed fraction form: 2 1/12.
How to Subtract Decimals?
Follow the steps given below to subtract decimals:
- Firstly, we will write down the two numbers, one below the other and ensure the decimal points are lined up.
- We add zeros to make the numbers of the same length.
- Then. We will subtract normally. We must keep in mind the place of the decimal point and put the decimal point in the answer.
|Example: Subtract 0.05 from 1.1|
Firstly, line the decimals up:
Now add zeros:
|Example: Calculate 7.005-0.10|
Line the decimals up:
|Practice ProblemsQuestion 1: |
Solve the following fractions
a. 2 1/9 – 5 4/7
c. 141/9 -131/9
d. 4/9-6/3 + 4/7
Question 2: Subtract the following decimal numbers
a. 23.56 – 12.4
b. 267.6 – 11.5
c. 67.1 – 23.3
Question 3: Riya has 676 sheets of plain paper. She uses 451 sheets to write a book. How many plain sheets are left with her now?
Question 4: There are 98 houses on a street. 35 houses have been painted blue. How many houses have not been painted yet?
Question 5: A basket holds 192 oranges. The shopkeeper has 345 oranges. How many oranges cannot be put in the basket?
Question 6: Out of 9578 children of the town, 6999 go to school. How many children do not attend school?
Question 7: John has 567 chocolates. He gives 97 to Emma and 56 to Isha. How many chocolates are left with him?
Question 8: Sara had $451.45. She bought a book for $34 and $45. How much money does she have now?