Addition: Step-by-Step Guide
Addition means putting numbers together to find the total. The numbers you add are called addends, and the answer is called the sum. When the numbers have more than one digit, we add one column at a time, starting on the right. If a column adds up to 10 or more, we carry to the next column.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Line up the numbers by place value. Write the numbers in a stack so the ones line up under the ones, the tens line up under the tens, and the hundreds line up under the hundreds. If the numbers have decimal points, line those up too.\[\begin{array}{r} a_n\,a_{n-1}\,\dots\,a_1\,a_0 \\ +\;b_n\,b_{n-1}\,\dots\,b_1\,b_0 \\ \hline \end{array}\]
- Add the ones column. Start on the far right and add the two digits. If the answer is 9 or less, write it under the line. If the answer is 10 or more, write only the ones digit under the line and carry the tens digit to the next column.\[a_0 + b_0 = c_0 \;\;(\text{carry } k_1 \text{ if sum} \geq 10)\]
- Add each column to the left, including any carry. Move left to the tens column, then the hundreds, and so on. In each column, add the two digits plus any number you carried. If the total is 10 or more, carry again.\[a_i + b_i + k_i = c_i + 10\,k_{i+1}\]
- Check your answer. Add the numbers again in the opposite order. You should get the same answer. You can also round each number to something easy and make sure your answer is close.\[a + b = b + a\]
Worked example
Find the sum: 487 + 256
Step 1: Line up the numbers by place value: 4 8 7 + 2 5 6
Step 2: Add the ones column: 7 + 6 = 13. Write 3 under the line and carry the 1 to the tens column.
Step 3: Add the tens column and the carried 1: 8 + 5 + 1 = 14. Write 4 and carry the 1 to the hundreds column.
Step 4: Add the hundreds column and the carried 1: 4 + 2 + 1 = 7. Write 7.
Step 5: Read the answer: the sum is 743.
Check: Add in the opposite order. 256 + 487 = 743, the same answer. Rounding gives 500 + 250 = 750, which is close to 743.
Tips and common mistakes
- Always start with the ones column on the right, then move left.
- Keep your columns neat. Graph paper helps you keep digits lined up.
- If a column adds up to 10 or more, write only the ones digit and carry the rest.
- Do not forget the last carry. 95 + 8 = 103, not 13.
- You can add numbers in any order and get the same sum, so 8 + 5 is the same as 5 + 8. Use this to make mental math easier.
- Estimate first. Rounding each number gives you a quick way to tell if your answer makes sense.
- When adding decimals, line up the decimal points. Add zeros if you need to, so 3.4 becomes 3.40 next to 1.27.