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Everyday Mathematics Alternative Algorithms

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Partial Sums An Addition Algorithm

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Add the hundreds ( ) 140 Add the tens (60 +80) Add the ones (8 + 3) Add the partial sums ( )

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Add the hundreds ( ) 120 Add the tens (80 +40) Add the ones (5 + 1) Add the partial sums ( )

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An alternative subtraction algorithm

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In order to subtract, the top number must be larger than the bottom number To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number become 12 and the top number in the tens column becomes To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 12 and the top number in the hundreds column becomes Now subtract column by column in any order 5 6 7

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Lets try another one together To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number become 15 and the top number in the tens column becomes To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 11 and the top number in the hundreds column becomes Now subtract column by column in any order 2 7 2

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Now, do this one on your own

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Last one! This one is tricky!

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Partial Products Algorithm for Multiplication

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Calculate 50 X x 53 Calculate 50 X 7 3, Calculate 3 X 60 Calculate 3 X 7 + Add the results 3,551 To find 67 x 53, think of 67 as and 53 as Then multiply each part of one sum by each part of the other, and add the results

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Calculate 10 X x 23 Calculate 20 X Calculate 3 X 10 Calculate 3 X 4 + Add the results 322 Lets try another one.

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Calculate 30 X x 79 Calculate 70 X 8 2, Calculate 9 X 30 Calculate 9 X 8 + Add the results Do this one on your own Lets see if youre right.

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Lattice Method of Multiplication Another Multiplication Algorithm

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Add the numbers along each diagonal. The lattice method of multiplication has been used for hundreds of years. It is very easy to use if you know basic multiplication facts. It becomes a favorite algorithm of students learning double digit multiplication Draw a box with squares and diagonals, this is called a lattice. Write 45 above the lattice. Write 3 on the right side of the lattice Multiply 3 x 5. Write the number as shown. Multiply 3 x 4. Write the number as shown x 3 = x

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Lets Try Another One! Multiply 7 x x 89 = 623

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2-Digit by 2-Digit Multiplication 34 x x 26 = 884

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Partial Quotients A Division Algorithm

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The Partial Quotients Algorithm uses a series of at least, but less than estimates of how many bs in a. You might begin with multiples of 10 – theyre easiest There are at least ten 12s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 10 – 1st guess Subtract There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 3 – 2 nd guess Sum of guesses Subtract Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses ( = 13) plus what is left over (remainder of 2 )

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Lets try another one 36 7, – 1st guess - 3,600 4,291 Subtract 100 – 2 nd guess - 3, R7 Sum of guesses Subtract – 3 rd guess – 4th guess - 324

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Now do this one on your own. 43 8, – 1st guess - 4,300 4,272 Subtract 90 – 2 nd guess -3, R 15 Sum of guesses Subtract – 3 rd guess – 4th guess - 86

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