Subtraction: Step-by-Step Guide
Subtraction means taking one number away from another to find the difference. The number you start with is on top, and the number you take away is on the bottom. We subtract one column at a time, starting on the right. If the top digit is too small, we borrow 10 from the column next to it.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Line up the numbers by place value. Write the number you start with on top and the number you take away underneath. Line up ones with ones, tens with tens, and so on. If there are decimal points, line those up too.\[\begin{array}{r} a_n\,a_{n-1}\,\dots\,a_0 \\ -\;b_n\,b_{n-1}\,\dots\,b_0 \\ \hline \end{array}\]
- Subtract the ones column. If the top digit is bigger than or equal to the bottom digit, just subtract. If the top digit is smaller, borrow 1 ten from the next column. That gives your column 10 more ones.\[a_0 - b_0 = c_0 \quad\text{or}\quad (a_0+10) - b_0 = c_0\;(\text{borrow})\]
- Move left, remembering what you borrowed. If you borrowed from a column, that column's top digit is now 1 smaller. Subtract it, borrowing again if needed, and keep going until you finish all the columns.\[(a_i - 1) - b_i \quad\text{after lending to column } i-1\]
- Check by adding back. Add your answer to the number you took away. You should get the number you started with.\[(a - b) + b = a\]
Worked example
Find the difference: 503 - 178
Step 1: Line up the numbers: 5 0 3 - 1 7 8
Step 2: Ones column: 3 is smaller than 8, so we need to borrow. The tens digit is 0, so we borrow from the hundreds first: the 5 becomes 4, and the 0 becomes 10. Then we borrow from that 10: the tens digit becomes 9, and the 3 becomes 13. Now 13 - 8 = 5.
Step 3: Tens column: 9 - 7 = 2.
Step 4: Hundreds column: 4 - 1 = 3.
Step 5: Read the answer: 503 - 178 = 325.
Check: 325 + 178 = 503. That is the number we started with, so the answer is right.
Tips and common mistakes
- Start with the ones column and move left, just like addition.
- If the top digit is smaller, borrow 1 from the next column to the left. That adds 10 to your column.
- If the next column is 0, you have to borrow from farther left first. Numbers like 500 - 1 work this way.
- Always check by adding. Your answer plus the number you took away should equal the number you started with.
- For decimals, line up the decimal points and add zeros so both numbers have the same number of places.
- Order matters in subtraction. 9 - 4 is not the same as 4 - 9.
- Estimate first by rounding. It helps you see if your answer is about the right size.