Subtraction is simply taking one number from another. Subtracting one whole number from another is fairly straightforward, but subtraction can be a bit more complicated when working with fractions or decimals. Once you have mastered subtraction, you will be able to move on to more difficult math concepts and you will be able to add, multiply, and divide numbers with great ease.
Steps
Method 1 of 6: Subtract Large Whole Numbers by Borrowing
Step 1. Write the larger number
Suppose the problem is: 32 - 17. First write 32.
Step 2. Write the smallest number just below the first
Make sure to line up the tens and ones columns so that the 3 in "32" is just above the 1 in "17" and the 2 in "32" is on top of the "7" in 17.
Step 3. In the ones column, subtract the number at the bottom from the number at the top
This can be a bit tricky as the bottom number is higher than the top. In this case, 7 is greater than 2. This is what you need to do:
- You will need to "borrow" from the 3 into "32" (also known as regrouping) in order to turn that 2 into 12.
- Cross out the 3 into "32" and make it 2, while the 2 becomes 12.
- Now you have 12 - 7, the result of which is 5. Write a 5 under the two numbers you subtracted, so that it lines up with the ones column forming a new row.
Step 4. In the tens column, subtract the number at the bottom from the number at the top
Remember that the 3 is now a 2. Next, subtract the 1 in 17 from the 2 above to get (2-1) 1. Write 1 under the numbers in the tens column, to the left of the 5 that It is found in the units column in the subtraction or difference row. You should have written 15. This means that 32 - 17 = 15.
Step 5. Review the operation
If you want to make sure you have correctly subtracted both numbers, all you have to do is add the answer to the smaller number to get the larger number. In this case, add the answer (15) to the smallest number located in the subtrahend (17). 15 + 17 = 32, that means you have subtracted correctly. Well done!
Method 2 of 6: Subtract Small Whole Numbers
Step 1. Identify the largest number
A problem like 15 - 9 will require a different visualization technique than a problem like 2 - 30.
- In problem 15 - 9, the first number (15) is greater than the second (9).
- In problem 2 - 30, the second number (30) is greater than the first (2).
Step 2. Decide if the answer will be a positive or negative number
If the first number is greater, the answer will be positive. If the second number is greater, the answer will be negative.
- In the first problem (15 - 9) the answer will be positive because the first number is greater than the second.
- In the second problem (2 - 30) the answer will be negative because the second number is greater than the first.
Step 3. Find the difference between the two numbers
To subtract two numbers, you must visualize the difference between them and count the numbers in between.
- For problem 15 - 9, visualize a stack of 15 poker chips. Take away 9 and you will see that there are 6. So 15 - 9 = 6. You can also imagine a number line. Think of the numbers 1 through 15 and then subtract or go back 9 units to get 6.
- For problem 2 - 30, the easiest thing you can do is invert the numbers and then do the subtraction by giving the answer a negative sign. So 30 - 2 = 28, since 28 is just two numbers less than 30. Next, give the answer a negative sign, since you initially determined that it would be negative because the second number is greater than the first.. Therefore, 2 - 30 = -28.
Method 3 of 6: Subtract Decimals
Step 1. Write the larger number on top of the smaller number with the decimals aligned
Suppose you have the following problem: 10, 5 - 8, 3. Write 10, 5 on top of 8, 3 so that the decimal points of both numbers are aligned. The.5 in 10, 5 must be above the.3 in 8, 3, while the 0 in 10, 5 must be above the 8 in 8, 3.
- If you have a problem where both numbers do not have the same number of digits after the decimal point, write a zero in the empty spaces until they are equal. For example, if you have the problem 5, 32 - 4, 2, you can write it as 5, 32 = 4.2 0. This will not change the value of the second number, but it does make subtracting both numbers easier.
Step 2. In the decimal column, subtract the number at the bottom from the number at the top
You should follow the same procedure that you would when subtracting regular whole numbers, with the exception that you should not forget to align the decimals of both numbers to preserve the decimal in the answer. In this case, you need to subtract 3 from 5. 5 - 3 = 2, so you should write a 2 under the 3 in 8, 3.
Make sure to put that decimal point in the answer. For now, the answer should be like this:, 2
Step 3. In the ones column, subtract the number at the bottom from the number at the top
Now you will need to subtract 8 from 0. Borrow the 1 next to the 0 to make it 10 and subtract 8 (10 - 8) from it to get 2. You can also subtract 8 from 10 without borrowing anything since there is no number in the subtrahend from the tens column. Write your answer below the 8, to the left of the decimal point.
Step 4. State the final answer
The final answer is 2, 2.
Step 5. Review the operation
If you want to make sure you've subtracted the decimals correctly, all you have to do is add the answer to the smaller number to get the larger number. 2, 2 + 8, 3 = 10, 5, done.
Method 4 of 6: Subtract Fractions
Step 1. Line up the denominators and numerators of the fractions
Suppose you have the following problem: 10/13 - 3/5. Write the problem such that both numerators (13 and 3) and both denominators (10 and 5) are directly opposite each other. A minus sign will separate the two numbers. This will help you visualize the problem and find a solution more easily.
Step 2. Find the lowest common denominator
The least common denominator is the smallest number divisible by both numbers. In this example, you will need to find the lowest common denominator of the numbers 10 and 5. You can see that 10 is the lowest common denominator of both numbers, because it is divisible by 10 and by 5.
Keep in mind that the lowest common denominator of two numbers is not always one of them. For example, the least common denominator of 3 and 2 is 6, because it is the smallest number divisible by both
Step 3. Rewrite the fractions with the same denominators
The fraction 13/10 can be written in the same way, since the denominator (10) is included in the lowest common denominator (10) exactly once. However, the fraction 3/5 must be rewritten because the denominator (5) is included in the least common denominator (10) twice. So the fraction 3/5 must be multiplied by 2/2 to have 10 in the denominator. Therefore, 3/5 x 2/2 = 6/10. You have created an equivalent fraction. 3/5 is equal to 6/10, although this fraction allows you to subtract 6/10 from 13/10.
The new problem is: 10/13 - 10/6
Step 4. Subtract the numerators of both fractions
Simply subtract 13 - 6 to get 7. You should not change the denominators of the fractions.
Step 5. Write the new numerator over the same denominator to get the final answer
The new numerator is 7 and both fractions have the denominator 10, therefore the final answer is 7/10.
Step 6. Review the operation
If you want to make sure you've subtracted the decimals correctly, all you have to do is add the answer to the smaller number to get the larger number. Therefore, 7/10 + 6/10 = 13/10. Ready.
Method 5 of 6: Subtract a fraction from a whole number
Step 1. Write the problem
Suppose the problem is as follows: 5 - 3/4. Write it.
Step 2. Convert the whole number into a fraction with the same denominator as the fraction
You must convert the 5 into a fraction that has a denominator of 4 in order to subtract both numbers. You can first consider 5 as a fraction (5/1). You can then multiply both the top and bottom numbers of the new fraction by 4 to create two fractions with the same denominator. Therefore, 5/1 x 4/4 = 20/4. This fraction is equal to 5, but it allows you to subtract both fractions.
Step 3. Rewrite the problem
You can rewrite the new problem as follows: 4/20 - 3/4.
Step 4. Subtract the numerators of the fractions and keep the same denominator
Then simply subtract 3 from 20 to get the final answer. 20 - 3 = 17, so 17 is the new numerator. You can leave the denominator as is.
Step 5. Write the final answer
The final answer is 4/17. If you want to formulate it as a mixed number, simply divide 17 by 4 to get 4, with a remainder of 1. This will make your final answer (17/4) equal 4 1/4.
Method 6 of 6: Subtract Variables
Step 1. Write the problem
Suppose the problem is as follows: 3x2 - 5x + 2y - z - (2x2 + 2x + y). Write the first set of terms on top of the second.
Step 2. Subtract the like terms
When working with variables, you can only add or subtract terms that have the same variable and that are written to the same degree. For example, you can subtract 4x2 of 7x2, but not 4x of 4y. This means that you can break down the problem like this:
- 3x2 - 2x2 = x2
- -5x - 2x = -7x
- 2y - y = y
- -z - 0 = -z
Step 3. State your final answer
Now that you have subtracted all possible like terms, all you can do is indicate the final answer, which will contain each of the terms you subtracted. This is the final answer:
- 3x2 - 5x + 2y - z - (2x2 + 2x + y) = x2 - 7x + y - z