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Calculator Use
Multiplication of positive or negative whole numbers or decimal numbers as the multiplicand and multiplier to calculate the product using long multiplication. The solution shows the work for the Standard Algorithm.
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How To Do Long Multiplication
Long multiplication means you're doing multiplication by hand. The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. These are the steps to do long multiplication by hand:
- Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
- Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number
- Write the answer below the equals line
- If that answer is greater than nine, write the ones place as the answer and carry the tens digit
- Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
- When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
- Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
- When you finish multiplying, draw another answer line below your last row of answer numbers.
- Use long addition to add your number columns from right to left, carrying as you normally do for long addition.
Long Multiplication with Decimals
Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow.
- Count the total number of decimal places contained in both the multiplicand and the multiplier.
- Ignore the decimals and right align the numbers one on top of the other as if they were integers
- Multiply the numbers using long multiplication.
- Insert a decimal point in the product so it has the same number of decimal places equal to the total from step 1.
Example Long Multiplication with Decimals
Multiply 45.2 by 0.21
There's 3 total decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.
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Rewrite the product with 3 total decimal places.
Answer = 9.492
Therefore: 45.2 × 0.21 = 9.492
Long Multiplication with Negative Numbers
When performing long multiplication you can ignore the signs until you have completed the standard algorithm for multiplication. Once you complete the multiplication follow these two rules:
- If one number is positive and one number is negative make the product negative.
- If both numbers are negative or both numbers are positive make the product positive.
Long Multiplication Example: Multiply 234 by 56
Long Multiplication Steps:
Stack the numbers with the larger number on top. Align the numbers by place value columns.
Stack the numbers with the larger number on top. Align the numbers by place value columns.
Marvelous designer 6 enterprise v2 5 92 23021 download free. Multiply the ones digit in the bottom number by each digit in the top number
6 × 4 = 24
Put the 4 in Ones place
Carry the 2 to Tens place
6 × 4 = 24
Put the 4 in Ones place
Carry the 2 to Tens place
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6 × 3 = 18
Add the 2 that you carried = 20
Put the 0 in the Tens place
Carry the 2 to the Hundreds place
Add the 2 that you carried = 20
Put the 0 in the Tens place
Carry the 2 to the Hundreds place
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6 × 2 = 12
Add the 2 that you carried = 14
This is the last number to multiply so write the whole number answer. No need to carry the 1.
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Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number.
5 × 4 = 20
Add a row to your multiplication answer
When you write your answer, shift one column to the left
Put the 0 in Ones place
Carry the 2 to Tens place
5 × 4 = 20
Add a row to your multiplication answer
When you write your answer, shift one column to the left
Put the 0 in Ones place
Carry the 2 to Tens place
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5 × 3 = 15
Add the 2 that you carried = 17
Put the 7 in the Tens place
Carry the 1 to the Hundreds place
Add the 2 that you carried = 17
Put the 7 in the Tens place
Carry the 1 to the Hundreds place
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5 × 2 = 10
Add the 1 that you carried = 11
This is the last number to multiply so write the whole number answer. No need to carry the 1.
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Add the numbers in the columns using long addition
4 + 0 = 4
0 + 0 = 0
4 + 7 = 11
write the 1 and carry 1
1 + 1 + 1 = 3
Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.
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Related Calculators
If you need help with long addition see our Long Addition Calculator to add numbers by long addition and see the work.
For long division see the Long Division Calculator to divide numbers by using long division with remainders. This calculator also shows the work.
![2do 2do](https://files.liveworksheets.com/def_files/2021/5/25/10525102704351399/10525102704351399001.jpg)
If you need to multiply fractions visit our Fractions Calculator. Adobe acrobat reader installer for windows 7. You can do fraction multiplication, addition, subtraction and division here.
References
Math is Fun shows examples of Long Multiplication in an animated video.
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Long multiplication is an algorithm and you can find examples of multiplication algorithms at Wikipedia.
Goodman, Len. 'Long Multiplication.' From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. Long Multiplication
Release Date: March 18, 2010
Python 2.6.5 was a maintenance release for Python 2.6.4, fixingdozens of issues in the core, builtin modules, libraries, and documentation.Python 2.6.5 final was released on March 19, 2010.
Python 2.6 is now in bugfix-only mode; no new features are being added. Chrome 32 bit. TheNEWS file lists every change in each alpha, beta, and releasecandidate of Python 2.6.
- What's New in Python 2.6.
- Report bugs at http://bugs.python.org.
- Read the Python license.
- PEP 361 set out the development schedule for 2.6.
Help fund Python and its community by donating to the Python Software Foundation.
This is a production release; we currently support these formats:
MD5 checksums and sizes of the released files:
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The signatures for the source tarballs above were generated withGnuPG using release managerBarry Warsaw'spublic keywhich has a key id of A74B06BF.The Windows installers were signed by Martin von Löwis'public keywhich has a key id of 7D9DC8D2.The Mac disk image was signed byRonald Oussoren's public key which has a key id of E6DF025C.
The documentation has also been updated. You can browse the HTML on-line or download the HTML.
[1] | The binaries for AMD64 will also work on processors that implement the Intel 64architecture (formerly EM64T), i.e. the architecture that Microsoft calls x64,and AMD called x86-64 before calling it AMD64. They will not work on IntelItanium Processors (formerly IA-64). |
Version | Operating System | Description | MD5 Sum | File Size | GPG |
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bzip2 compressed source tarball | Source release | 6bef0417e71a1a1737ccf5750420fdb3 | 11095581 | SIG | |
Gzipped source tarball | Source release | c83cf77f32463c3949b85c94f661c090 | 58071040 | SIG | |
Mac OS X installer | macOS | 84489bba813fdbb6041b69d4310a86da | 20348693 | ||
Windows x86-64 MSI installer | Windows | for AMD64/EM64T/x64 | 9cd2c4d23dea7dfcd964449c3008f042 | 15430656 | SIG |
Windows x86 MSI installer | Windows | 0b6bc43c45fb2e3195ecdab3fad59fc2 | 15103488 | SIG |