Multiplication: Step-by-Step Guide
Multiplication is a fast way to add the same number again and again. For example, 4 x 3 means 4 + 4 + 4. When the numbers are bigger, we multiply by each digit of the bottom number, one at a time. Then we add up the results.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Line up the numbers. Write one number on top and the other underneath, with the ones digits lined up. It is usually easiest to put the bigger number on top.\[\begin{array}{r} a \\ \times\; b \\ \hline \end{array}\]
- Multiply by the ones digit on the bottom. Multiply each digit of the top number by the ones digit of the bottom number. Start on the right and work left. If a product is 10 or more, write the ones digit and carry the rest.\[a \times b_0 = p_0\]
- Multiply by the next digit, one place to the left. For the tens digit, first write a 0 in the ones place, then multiply as before. For the hundreds digit, write two zeros first. Keep going for each digit.\[a \times b_i \times 10^{i} = p_i\]
- Add the rows. Add all the rows you made. The total is your answer.\[a \times b = \sum_{i=0}^{n} a \cdot b_i \cdot 10^{i}\]
Worked example
Compute: 47 x 23
Step 1: Line up the numbers: 4 7 x 2 3
Step 2: Multiply 47 by the ones digit, 3. First 7 x 3 = 21, so write 1 and carry 2. Then 4 x 3 = 12, and 12 + 2 = 14. The first row is 141.
Step 3: Multiply 47 by the tens digit, 2. Because it is the tens place, write a 0 first. Then 7 x 2 = 14, so write 4 and carry 1. Then 4 x 2 = 8, and 8 + 1 = 9. The second row is 940.
Step 4: Add the rows: 141 + 940 = 1081.
Step 5: So 47 x 23 = 1081.
Check: Round to 50 x 20 = 1000, which is close to 1081. You can also divide: 1081 / 23 = 47.
Tips and common mistakes
- Learn your times tables up to 12 x 12. Knowing them by heart makes everything faster.
- Do not forget the 0 on the second row. Multiplying by tens means the answer is ten times bigger.
- To multiply by 10, 100, or 1000, just add that many zeros to the end.
- You can break a hard problem into easy ones: 47 x 23 = 47 x 20 + 47 x 3.
- Write your carries small, above the next column, so you do not lose them.
- Estimate first by rounding both numbers. Your answer should be close.
- For decimals, multiply as if there were no decimal points. Then count the decimal places in both numbers and put that many in your answer.