Subtraction is one of the fundamental operations in mathematics. It involves taking away one number from another to find the difference. Whether you’re counting objects, managing money, or solving problems, mastering subtraction is essential for everyday math and more complex mathematical concepts.
What is Subtraction?
Subtraction is a mathematical process where you remove one quantity (the subtrahend) from another quantity (the minuend) to determine how much is left (the difference). The symbol used for subtraction is “−”.
Basic Subtraction Example
For example, if you have 10 apples and eat 3, you can represent this as:
Here, 10 is the minuend, 3 is the subtrahend, and 7 is the difference.
Subtraction on Number Line
Subtraction on a number line is a simple and effective way to visualize the process of taking away. To use a number line for subtraction, you begin at the minuend (the number you start with) and move to the left to find the difference. Each space you move represents a single unit being subtracted. For example, if you want to subtract 5 from 12, you start at 12 on the number line and make five jumps to the left. After making these jumps, you land on 7, which is the result of the subtraction (12 – 5 = 7). This method not only helps in finding the answer but also reinforces the concept of subtraction as “taking away.” It provides a clear visual representation of how numbers relate to one another.
Properties of Subtraction
Understanding the properties of subtraction can help you solve problems more easily:
Non-Commutative Property: Unlike addition, changing the order of the numbers in subtraction changes the result. For example:
The first equation equals 2, while the second equals -2.
Identity Property: Subtracting zero from any number leaves the original number unchanged. For example:
Subtracting from Itself: If you subtract a number from itself, the result is always zero. For example:
Methods of Subtraction
There are various methods to perform subtraction, which can be useful for different situations:
Column Subtraction: Aligning numbers vertically and subtracting each column, starting from the right. This method is helpful for larger numbers.
7 9 -
2 5
---
5 4Mental Math: Techniques that allow you to subtract numbers in your head without writing them down. For instance, if you need to find , you can think of it as .
Using Visual Aids: Objects like counters, fingers, or drawings can help visualize subtraction, making it easier for younger learners.
Subtraction with Borrow (Regrouping)
When we subtract numbers and the top number is smaller than the bottom number in any place value, we need to borrow. Borrowing helps us figure out the answer without getting confused. It’s like asking a friend for help when we don’t have enough of something.
Let’s say we want to subtract 29 from 73. First, we look at the ones place, which is the last number (3 in this case). We can’t take away 9 from 3 because 9 is bigger, so we need to borrow from the next number. We look at the 7 in the tens place. We take away 1 from the 7, which makes it a 6. Then, we add 10 to the 3, making it 13. Now, we can subtract!
So, we do 13 minus 9, which equals 4. Now we look at the tens place: we have 6 minus 2, which equals 4. So, when we put it together, 73 minus 29 equals 44! Borrowing and regrouping help us when we can’t take away a bigger number from a smaller number.
Regrouping Explained with Tens and Ones
When we subtract and need to borrow, we can think about the numbers in terms of tens and ones, which makes it easier. Let’s look at the problem 95 minus 48.
Start with the Numbers: In 95, we have 9 tens (which is 90) and 5 ones. In 48, we have 4 tens (which is 40) and 8 ones.
Look at the Ones Place: We want to subtract 8 ones from 5 ones. But we can’t do that because 8 is bigger than 5! So, we need to regroup.
Borrowing: We’ll borrow 1 ten from the 9 tens in 95. That makes 9 tens become 8 tens, and we add 10 to the 5 ones. Now we have:
- 8 tens (which is 80)
- 15 ones (5 + 10 = 15)
Now Subtract the Ones: We can subtract now! We take away 8 ones from 15 ones.
- 15 – 8 = 7 ones.
Subtract the Tens: Next, we subtract the tens. We have 8 tens and we need to subtract 4 tens.
- 8 – 4 = 4 tens.
Put It All Together: Now we combine our results:
- We have 4 tens (which is 40) and 7 ones.
So, when we put it all together, 95 – 48 equals 47!
This way of using tens and ones helps us solve subtraction problems, especially when we need to borrow.
Word Problems
Subtraction word problems are a fun way to practice our math skills in real-life situations! These problems typically tell a story and involve taking away a certain number from a total. For example, if a farmer has 30 apples and sells 12, we can figure out how many apples are left by using subtraction. We start with the total number of apples (30) and subtract the number sold (12), which helps us find the answer:
30 – 12 = 18.
Word problems encourage critical thinking and help children understand how subtraction is used in everyday life, from counting toys to managing money.
Toy Collection: Sarah has 25 toy cars in her collection. She gives 7 toy cars to her friend. How many toy cars does Sarah have left?
Books Read: John started with 48 books to read this summer. After finishing 19 books, how many books does he still need to read?
Party Balloons: At a birthday party, there were 50 balloons. During the party, 15 balloons popped. How many balloons are left at the party?
Practice Problems
Try these subtraction problems to test your skills!
- What is ?
- Calculate .
- If you have 12 candies and give away 4, how many candies do you have left?
FAQs on Subtraction
- No, subtraction is not commutative. Changing the order of the numbers changes the result.
- Example: 5−2≠2−5.
- No, subtraction is not associative. Changing the grouping of numbers affects the result.
- Example: (10−5)−3≠10−(5−3).
- Yes, start at the minuend and move left by the value of the subtrahend.
- Example: To subtract 7−4, start at 7 on the number line and move 4 spaces to the left to reach 3.
- Repeated subtraction is subtracting the same number multiple times. It’s a foundational concept for division.
- Example: 20−4−4−4−4−4=0 (equivalent to 20÷4=5).
- Subtraction is the operation, while the difference is the result of subtracting one number from another.
- Example: The difference between 9 and 6 is 3.