Step-by-Step Everyday Mathematics Review

1. Step-by-StepEveryday MathematicsReview Partial Sums Addition Trade-First Subtraction Partial Products Multiplication Partial Quotients Division

2. Partial Sums An Addition Algorithm

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

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

5. 329 + 989 + 18 Do this one on your own Let's see if you're right. 1200 100 1318 Well Done!

6. Trade-First Subtraction An alternative subtraction algorithm

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

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

9. 13 8 12 3 9 4 2 - 2 8 7 Now, do this one on your own. 6 5 5 Let's see if you're right. Congratulations!

10. 9 Last one! This one is tricky! 6 13 10 7 0 3 - 4 6 9 2 3 4 Oh, no! What do we do now? Let's trade from the hundreds column Let's see if you're right. Congratulations!

11. Partial Products Algorithm for Multiplication

12. + 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 6 7 X 5 3 3,000 Calculate 50 X 60 350 Calculate 50 X 7 180 Calculate 3 X 60 21 Calculate 3 X 7 3,551 Add the results

13. + Let’s try another one. 1 4 X 2 3 200 Calculate 10 X 20 80 Calculate 20 X 4 30 Calculate 3 X 10 12 Calculate 3 X 4 322 Add the results

14. + Do this one on your own. 3 8 Let’s see if you’re right. X 7 9 2, 100 Calculate 30 X 70 560 Calculate 70 X 8 270 Calculate 9 X 30 72 Calculate 9 X 8 3002 Add the results

15. Partial Quotients A Division Algorithm

16. 12 158 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. 13 R2 There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) - 120 10 – 1st guess Subtract 38 There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 3 – 2nd guess - 36 Subtract 2 13 Sum of guesses 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. 36 7,891 Let’s try another one 219 R7 - 3,600 100 – 1st guess Subtract 4,291 - 3,600 100 – 2nd guess Subtract 691 - 360 10 – 3rd guess 331 - 324 9 – 4th guess 7 219 R7 Sum of guesses

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

19. Congratulations on a job well done!