Long Multiplication Calculator
Column multiplication with partial products, step by step
Long Multiplication Calculator
Long Multiplication: How It Works
Multiply by each digit of the multiplier from the right, writing each partial product one place further left; then add the partial products.
Example: 75 × 12
75 × 12 in a column
| 7 | 5 | ||
| × | 1 | 2 | |
| 1 | 5 | 0 | |
| + | 7 | 5 | 0 |
| 9 | 0 | 0 |
In the column: product 900.
- Step 1Multiply the multiplicand by the last digit of the multiplier, 2: 75 × 2 = 150.
- 5 × 2 = 10. Write 0 and carry 1.
- 7 × 2 = 14, plus the carried 1 makes 15. Write 5 and carry 1.
- No digits are left, so the carried 1 is written in front: the partial product is 150.
- Step 2The next digit of the multiplier is 1, and it stands for 10: 75 × 10 = 750.
- 5 × 1 = 5. Write 5.
- 7 × 1 = 7. Write 7.
- Sum of the partial products150 + 750 = 900
See Also
- Times Table Chart - Any number from 1 to 100, rows from ×1 to ×12
- Long Division Calculator - Step-by-step long division with detailed explanation
- Multiplying Fractions Calculator - Multiply fractions, mixed numbers and whole numbers step by step
- Factors of a Number - List all Factors and Factor Pairs of a Number
- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers
- Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
Products of 75
FAQ
How does long multiplication work?
Write the multiplicand above the multiplier, right-aligned. Multiply the whole multiplicand by each digit of the multiplier in turn, carrying whenever a column passes nine, and shift each partial product one place further to the left. Adding the partial products gives the answer.
Why is each partial product shifted to the left?
Because the digit it came from is not a plain digit but a place value. In 12 × 15 the 1 of 15 stands for ten, so its partial product is 12 × 10 = 120, not 12 — the shift is what turns the digit into its place value.
Does the order of the two numbers matter?
Not for the answer: 16 × 3 and 3 × 16 are both 48, because multiplication is commutative. It does change the work — the number with fewer digits is easier to use as the multiplier, since it produces fewer partial products.
How do you check a multiplication result?
Divide the product back by one of the factors: if 16 × 3 = 48, then 48 ÷ 3 must give 16 exactly, with no remainder. The long division calculator on this site shows that check step by step.
Can this calculator multiply decimals or fractions?
It works with whole numbers only. Fractions and mixed numbers are handled by the fraction multiplication calculator; for a decimal, multiply without the point and then move the point back by as many places as both factors have together.