Long Multiplication Calculator
Perform long multiplication with comprehensive step-by-step breakdown and visual working area. Our arithmetic calculator supports educational learning, partial products analysis, and detailed multiplication algorithm demonstration.
Last updated: October 19, 2025
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Use this long multiplication calculator with steps to show the column method for any two numbers.
Enter a number (up to 10 digits, negative numbers allowed)
Enter a number (up to 10 digits, negative numbers allowed)
Expression:
234 × 45
Multiplication Analysis
Final Product:
10530
Method:
Step-by-step long multiplication
Working Area:
Partial Products:
Analysis:
Long multiplication breaks down 234 × 45 into partial products, then adds them together to get 10530.
Step-by-Step:
- 234 × 5 = 1170
- 234 × 4 = 936 (shifted 1 position)
Long Multiplication Tips:
- • Place Value: Each partial product shifts one position left
- • Distributive Property: Multiply each digit separately
- • Carries: Remember to add carry-over values
- • Signs: Positive × Positive = Positive, Negative × Positive = Negative
Quick Example Result
For 234 × 45 using long multiplication:
10,530
Partial products: 1170 (234×5) and 9360 (234×40)
Popular Long Multiplication Examples (with Steps)
These examples match common searches like "step-by-step multiplication calculator" and questions such as "45.2 times 45" or "37000 times 4 calculation".
45.2 times 45
- Write 45.2 and 45 using column multiplication.
- First ignore the decimal: 452 × 45.
- Compute 452 × 5 = 2,260.
- Compute 452 × 40 = 18,080 (shift one place left).
- Add partial products: 2,260 + 18,080 = 20,340.
- There is 1 decimal place in 45.2, so place the decimal: 2,034.0.
Answer: 2,034
12.6 times 5
- Ignore the decimal: 126 × 5 = 630.
- 12.6 has 1 decimal place, so move the decimal 1 place left.
Answer: 63.0
41.62 × 24
- Ignore decimals first: 4162 × 24.
- 4162 × 4 = 16,648.
- 4162 × 20 = 83,240 (shift one place left).
- Add: 16,648 + 83,240 = 99,888.
- 41.62 has 2 decimal places, so final answer has 2 decimal places.
Answer: 998.88
37000 times 4 calculation
- Multiply 37,000 × 4.
- 37 × 4 = 148.
- Attach the three zeros: 148,000.
Answer: 148,000
80.3 × 64.7
- Ignore decimals: 803 × 647.
- Use long multiplication (column method) to get 519, ... (calculator can show full steps).
- Total decimal places: 1 (80.3) + 1 (64.7) = 2.
- Place decimal 2 digits from the right.
Answer: ≈ 52, ... with 2 decimal places (exact value shown by the calculator).
8.288 × 19.299
- Count decimal places: 4 (8.288) + 3 (19.299) = 7 places.
- Multiply as whole numbers, then insert the decimal point 7 places from the right.
The calculator shows the full long multiplication and final decimal answer.
Multiplying Money and Large Numbers
Many people use a long multiplication calculator for salaries, payments or big quantities, for example "5.8 million times 60" or "what is $545.40 times 36".
Example: 5.8 million times 60
- Write 5.8 million as 5,800,000.
- Multiply 5,800,000 × 60.
- First multiply 58 × 6 = 348.
- Add the five zeros from 5,800,000 and the one zero from 60 → total six zeros.
Answer: 348,000,000.
Example: what is $545.40 times 36?
- Ignore the dollar sign and decimal: 54540 × 36.
- Use long multiplication to get the product.
- Since $545.40 has 2 decimal places, move the decimal 2 places back in the final answer.
The calculator shows the step-by-step working and exact dollar amount.
Example: 65 times 2080
- Multiply 65 × 2080.
- Think 2080 = 208 × 10.
- 65 × 208 = 13,520, then ×10 → 135,200.
Answer: 135,200.
How This Step-by-Step Long Multiplication Calculator Works
Our long multiplication calculator applies the traditional multiplication algorithm to break down complex multiplications into manageable steps. The calculator uses the distributive propertyand place value concepts to provide clear, educational demonstrations of the multiplication process.
Long Multiplication Algorithm
Write larger number on top, smaller belowMultiply top number by ones digit of bottomMultiply by tens digit, shift left one positionSum all partial products for final answerThe long multiplication algorithm systematically applies the distributive property: (a × 10 + b) × (c × 10 + d) = ac × 100 + ad × 10 + bc × 10 + bd. Each partial product represents one term of this expansion, with proper place value positioning.
Shows how partial products align with place values in the multiplication process
Mathematical Foundation
Long multiplication is built on fundamental arithmetic principles: the distributive property, place value system, and addition with carrying. This method demonstrates how complex multiplications can be broken down into simpler operations that students can perform mentally or with basic arithmetic skills. The algorithm's systematic approach ensures accuracy while building number sense and mathematical understanding.
- Demonstrates the distributive property in practice
- Reinforces place value concepts and decimal system understanding
- Builds foundation for polynomial multiplication in algebra
- Develops systematic problem-solving approaches
Sources & References
- Elementary Mathematics for Teachers - Thomas H. Parker and Scott J. BaldridgeComprehensive treatment of arithmetic algorithms and their mathematical foundations
- National Council of Teachers of Mathematics - Arithmetic Education StandardsProfessional guidelines for teaching multiplication algorithms
- Common Core State Standards - Mathematics Standards for ArithmeticEducational standards for multi-digit arithmetic operations
Using Long Multiplication Inside Bigger Expressions
Some searches include multi-step expressions like 4791.85/60*24or simple equations like 200 + 30x = 10x + 45000. Our long multiplication calculator focuses on the multiplication step itself: it helps you compute products such as 200 × 52 or 24 × 21.63using the standard algorithm with steps.
To evaluate multi-step expressions, break the problem into parts:
- First do any division, then use long multiplication for each "times" step.
- For simple linear equations, move all x-terms to one side, constants to the other, then divide.
Need help with other arithmetic calculations? Check out our division calculator and fraction calculator.
Get Custom Calculator for Your PlatformExample Analysis
Problem Setup:
- Multiplicand: 347 (3-digit number)
- Multiplier: 28 (2-digit number)
- Method: Long multiplication algorithm
- Goal: Find 347 × 28
Step-by-Step Solution:
Result: 347 × 28 = 9,716
This example demonstrates how long multiplication breaks down a complex problem into manageable steps. First, 347 × 8 = 2,776, then 347 × 20 = 6,940 (note the position shift for the tens digit). Adding these partial products: 2,776 + 6,940 = 9,716. This systematic approach ensures accuracy and helps students understand the underlying mathematical principles of multiplication and place value.
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