By ToolzHive · Published
Split one factor into place values
Multiplication becomes easier to follow when you split a number into hundreds, tens and ones. Calculate each partial product, then add them. For 23 × 14, rewrite 14 as 10 + 4. You now have 23 × 10 plus 23 × 4. This is the distributive property applied to an arithmetic problem.
Two-digit example: 23 times 14
First calculate 23 × 10 = 230. Then calculate 23 × 4 = 92. Add 230 + 92 = 322. The multiplication calculator can check the final product; the steps in this guide explain how to reach it by hand. If your answer is unexpectedly small, check whether you treated the tens digit as a single unit.
Three-digit example: 125 times 24
Split 24 into 20 + 4. Multiply 125 × 20 = 2500 and 125 × 4 = 500. Add the partial products for 3000. An estimate also helps: 125 × 25 is one quarter of 125 × 100, or 3125, so multiplying by 24 should be slightly smaller.
Multiply decimal values
For 2.5 × 1.2, first calculate 25 × 12 = 300. The original factors have two decimal places in total, so move the decimal point two places left to get 3.00, equivalent to 3. Use the original numbers in the calculator to check your answer. Keep track of units as well as digits when calculating prices or measurements.
Check the sign and the scale
One negative factor gives a negative product; two negative factors give a positive product. For example, -23 × 14 = -322 and -23 × -14 = 322. Estimate the size before trusting the final answer. For a list of partial products, Addition Calculator can check their sum. Division Calculator can help check a nonzero multiplication result by reversing the operation.
Put this guide into practice
- Addition Calculator — Add two or more numbers of any size exactly, including decimals and negatives.
- Multiplication Calculator — Multiply numbers of any size exactly, including decimals.
- Division Calculator — Divide numbers and see the exact decimal, repeating digits, fraction and remainder.