Difference between revisions of "Multiply Using the Russian Peasant Method"
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| − | Russian peasant multiplication is an interesting way to multiply numbers that uses a process of halving and doubling.<ref>http://scimath.unl.edu/MIM/files/MATExamFiles/WestLynn_Final_070411_LA.pdf</ref> Like standard multiplication and division, Russian peasant multiplication is an algorithm; however, it allows you to multiply any two whole numbers using only multiplication and division by 2.<ref> Gimmestad, Beverly J.. “The Russian Peasant Multiplication Algorithm: A Generalization”. The Mathematical Gazette 75.472 (1991): 169–171.</ref> Although Russian peasant multiplication is not as quick as the multiplication method that is now standard, it's still fun to try. | + | Russian peasant multiplication is an interesting way to multiply numbers that uses a process of halving and doubling.<ref name="rf1">http://scimath.unl.edu/MIM/files/MATExamFiles/WestLynn_Final_070411_LA.pdf</ref> Like standard multiplication and division, Russian peasant multiplication is an algorithm; however, it allows you to multiply any two whole numbers using only multiplication and division by 2.<ref name="rf2"> Gimmestad, Beverly J.. “The Russian Peasant Multiplication Algorithm: A Generalization”. The Mathematical Gazette 75.472 (1991): 169–171.</ref> Although Russian peasant multiplication is not as quick as the multiplication method that is now standard, it's still fun to try. |
[[Category:Multiplication and Division]] | [[Category:Multiplication and Division]] | ||
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#Think of the numbers you want to multiply. Choose two numbers that you want to multiply, whether to solve a particular problem or just to try out the Russian peasant method of multiplication. | #Think of the numbers you want to multiply. Choose two numbers that you want to multiply, whether to solve a particular problem or just to try out the Russian peasant method of multiplication. | ||
#*For example, try multiplying 146 x 37. | #*For example, try multiplying 146 x 37. | ||
| − | #Make two columns. Using a piece of paper and pen, divide the piece of paper into two columns by drawing a line down the middle of the paper. Write one of the numbers you want to multiply at the top the each column.<ref>http://scimath.unl.edu/MIM/files/MATExamFiles/WestLynn_Final_070411_LA.pdf </ref> | + | #Make two columns. Using a piece of paper and pen, divide the piece of paper into two columns by drawing a line down the middle of the paper. Write one of the numbers you want to multiply at the top the each column.<ref name="rf3">http://scimath.unl.edu/MIM/files/MATExamFiles/WestLynn_Final_070411_LA.pdf </ref> |
#*In this example, write “146” at the top of the left column, and “37” at the top of the right column. | #*In this example, write “146” at the top of the left column, and “37” at the top of the right column. | ||
| − | #Halve the number in the left column repeatedly.<ref | + | #Halve the number in the left column repeatedly.<ref name="rf1" /> [[Multiply and Divide Integers| Divide]] the number at the top of the left column by 2 continually until you get to 1. Ignore any remainder each time you halve the number. Write each halved number down in the left column, in order. In this example: |
#*Start by halving 146 (146 ÷ 2 = 73). Write “73” in the left column below “146.” | #*Start by halving 146 (146 ÷ 2 = 73). Write “73” in the left column below “146.” | ||
#*Next, halve 73 (73 ÷ 2 = 36 with a remainder of 1). Write “36” in the left column below “73,” ignoring the remainder. | #*Next, halve 73 (73 ÷ 2 = 36 with a remainder of 1). Write “36” in the left column below “73,” ignoring the remainder. | ||
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#*Next, halve 4 (4 ÷ 2 = 2). Write “2” in the left column below “4.” | #*Next, halve 4 (4 ÷ 2 = 2). Write “2” in the left column below “4.” | ||
#*Finally, halve 2 (2÷ 2 = 1). Write “1” in the left column below “2.” | #*Finally, halve 2 (2÷ 2 = 1). Write “1” in the left column below “2.” | ||
| − | #Double the number in the right column until the columns are the same length.<ref | + | #Double the number in the right column until the columns are the same length.<ref name="rf1" /> [[Multiply|Multiply]] the number in the second column by 2 until there are the same amount of numbers here as there are in the first column. In this example: |
#*Each column should have 8 numbers in it. This is because it took seven steps of dividing the original number in the right column to reach 1. | #*Each column should have 8 numbers in it. This is because it took seven steps of dividing the original number in the right column to reach 1. | ||
#*In the right column, start by doubling 37 (37 x 2 = 74). Write “74” in the right column below “37.” | #*In the right column, start by doubling 37 (37 x 2 = 74). Write “74” in the right column below “37.” | ||
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#*Next, double 1184 (1184 x 2 = 2368). Write “2368” in the right column below “1184.” | #*Next, double 1184 (1184 x 2 = 2368). Write “2368” in the right column below “1184.” | ||
#*Finally, double 2368 (2368 x 2 = 4736). Write “4736” in the right column below “2368.” | #*Finally, double 2368 (2368 x 2 = 4736). Write “4736” in the right column below “2368.” | ||
| − | #Cross out rows with an even number in the left column.<ref | + | #Cross out rows with an even number in the left column.<ref name="rf1" /> Using your pen, strike through those horizontal rows which begin with an even number in the left column. In this example: |
#*There are 8 rows. You will strike through 5 of them. | #*There are 8 rows. You will strike through 5 of them. | ||
#*Strike through the rows beginning with 146, 36, 18, 4, and 2 in the left column, since these are even numbers. Working left to right, this means striking through the first row (146, 37), the third row (36, 148), the fourth row (18, 296), the sixth row (4, 1184), and the seventh row (2, 2368). | #*Strike through the rows beginning with 146, 36, 18, 4, and 2 in the left column, since these are even numbers. Working left to right, this means striking through the first row (146, 37), the third row (36, 148), the fourth row (18, 296), the sixth row (4, 1184), and the seventh row (2, 2368). | ||
#*Please note that you should strike through even numbers, even if they begin with an odd numeral. For example, you should strike through the row beginning with 146 since it is an even number, even though 146 begins with an odd numeral, 1. Likewise, you should strike though 36, since it is an even number, even though 36 begins with an odd numeral, 3. | #*Please note that you should strike through even numbers, even if they begin with an odd numeral. For example, you should strike through the row beginning with 146 since it is an even number, even though 146 begins with an odd numeral, 1. Likewise, you should strike though 36, since it is an even number, even though 36 begins with an odd numeral, 3. | ||
#*If you prefer, you can just strike through the numbers in the right side that fall into the rows that begin with an even number on the left side (as in the picture above). In this example, this means striking through the numbers on the right hand side of the first, third, fourth, sixth, and seventh rows: 37, 148, 296, 1184, and 2368. | #*If you prefer, you can just strike through the numbers in the right side that fall into the rows that begin with an even number on the left side (as in the picture above). In this example, this means striking through the numbers on the right hand side of the first, third, fourth, sixth, and seventh rows: 37, 148, 296, 1184, and 2368. | ||
| − | #Find the sum of the remaining numbers in the right column.<ref | + | #Find the sum of the remaining numbers in the right column.<ref name="rf1" /> [[Add|Add]] the numbers in the right column that you did not strike through. The sum of these numbers is equal to the product you would get from multiplying the original numbers using the standard method. In this example: |
#*The remaining numbers in the right column are 74, 592, 4736. | #*The remaining numbers in the right column are 74, 592, 4736. | ||
#*Add these numbers to get the sum of 5402 (74 + 592 + 4736 = 5402). | #*Add these numbers to get the sum of 5402 (74 + 592 + 4736 = 5402). | ||
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#*Check all of your work twice to make sure that you get the correct answer. | #*Check all of your work twice to make sure that you get the correct answer. | ||
#Ask someone for help if you are struggling. If you can’t seem to get the right answer, or if you aren’t sure how to check your work, ask some for help (such as a friend, sibling, parent, or teacher). Ask this person to try the problem out, too, and then you compare answers. The person might also be able to explain how to use the Russian peasant method. | #Ask someone for help if you are struggling. If you can’t seem to get the right answer, or if you aren’t sure how to check your work, ask some for help (such as a friend, sibling, parent, or teacher). Ask this person to try the problem out, too, and then you compare answers. The person might also be able to explain how to use the Russian peasant method. | ||
| − | #Understand why the method works.<ref>http://www.wolframalpha.com/input/?i=russian+multiplication</ref> The Russian peasant method works because it converts the problem into binary (base 2) multiplication, rather than base 10 (which standard multiplication uses). It does this by halving and doubling the numbers you are trying to multiply (since halving and doubling convert all numbers into multiples of 2, or into factors of numbers that are divisible by 2). | + | #Understand why the method works.<ref name="rf4">http://www.wolframalpha.com/input/?i=russian+multiplication</ref> The Russian peasant method works because it converts the problem into binary (base 2) multiplication, rather than base 10 (which standard multiplication uses). It does this by halving and doubling the numbers you are trying to multiply (since halving and doubling convert all numbers into multiples of 2, or into factors of numbers that are divisible by 2). |
#Know when the Russian peasant method of multiplication is useful. You might be asked to try the Russian peasant method of multiplication for a school assignment, or just try it out for fun. However, the method has advantages that might make it turn out to be a handy way to multiply in other situations. | #Know when the Russian peasant method of multiplication is useful. You might be asked to try the Russian peasant method of multiplication for a school assignment, or just try it out for fun. However, the method has advantages that might make it turn out to be a handy way to multiply in other situations. | ||
#*You don’t need to know or memorize multiplication tables in order to multiply using the Russian peasant method (like you do in order to use standard long multiplication). As long as you can double and halve, you can multiply any two numbers using the Russian peasant method. | #*You don’t need to know or memorize multiplication tables in order to multiply using the Russian peasant method (like you do in order to use standard long multiplication). As long as you can double and halve, you can multiply any two numbers using the Russian peasant method. | ||
