1. Step-by-Step Everyday Mathematics Review Partial Sums AdditionPartial Sums Addition Trade-First SubtractionTrade-First Subtraction Partial Products MultiplicationPartial Products Multiplication Partial Quotients DivisionPartial Quotients Division

2. Partial Sums An Addition Algorithm

3. 268+ 483 600 Add the hundreds ( 200 + 400) Add the tens (60 +80) 140 Add the ones (8 + 3) Add the partial sums (600 + 140 + 11) + 11 751

4. 785+ 641 1300 Add the hundreds ( 700 + 600) Add the tens (80 +40) 120 Add the ones (5 + 1) Add the partial sums (1300 + 120 + 6) + 6 1426

5. 329+ 989 1200 100 + 18 1318

6. An alternative subtraction algorithm

7. In order to subtract, the top number must be larger than the bottom number 9 3 2 - 3 5 6 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 2. 12 2 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 8. 12 8 Now subtract column by column in any order 5 6 7

8. Let’s try another one together 7 2 5 - 4 9 8 15 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 1. 15 1 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 6. 11 6 Now subtract column by column in any order 2 7 2

9. Now, do this one on your own. 9 4 2 - 2 8 7 12 3 13 8 6 5 5

10. Last one! This one is tricky! 7 0 3 - 4 6 9 13 9 6 2 4 3 10

11. Partial Products Algorithm for Multiplication

12. Calculate 50 X 60 67 X 53 Calculate 50 X 7 3,000 350 180 21 Calculate 3 X 60 Calculate 3 X 7 + Add the results 3,551 To find 67 x 53, think of 67 as 60 + 7 and 53 as 50 + 3. Then multiply each part of one sum by each part of the other, and add the results

13. Calculate 10 X 20 14 X 23 Calculate 20 X 4 200 80 30 12 Calculate 3 X 10 Calculate 3 X 4 + Add the results 322 Let’s try another one.

14. Calculate 30 X 70 38 X 79 Calculate 70 X 8 2, 100 560 270 72 Calculate 9 X 30 Calculate 9 X 8 + Add the results Do this one on your own. 3002 Let’s see if you’re right.

15. Partial Quotients A Division Algorithm

16. The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. You might begin with multiples of 10 – they’re easiest. 12 158 There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 10 – 1st guess - 120 38 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 - 36 2 13 Sum of guesses Subtract Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )

17. Let’s try another one 36 7,891 100 – 1st guess - 3,600 4,291 Subtract 100 – 2 nd guess - 3,600 7 219 R7 Sum of guesses Subtract 691 10 – 3 rd guess - 360 331 9 – 4th guess - 324

18. Now do this one on your own. 43 8,572 100 – 1st guess - 4,300 4272 Subtract 90 – 2 nd guess -3870 15 199 R 15 Sum of guesses Subtract 402 7 – 3 rd guess - 301 101 2 – 4th guess - 86