Step-by-StepStep-by-StepEveryday MathematicsEveryday Mathematics

ReviewReview

• Partial Sums AdditionPartial Sums Addition• Trade-First SubtractionTrade-First Subtraction• Partial Products MultiplicationPartial Products Multiplication• Partial Quotients DivisionPartial Quotients Division

Partial SumsPartial Sums

An Addition AlgorithmAn Addition Algorithm

268+ 483

600Add the hundreds (200 + 400)

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

Add the partial sums(600 + 140 + 11)

+ 11751

785+ 6411300Add the hundreds (700 + 600)

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

Add the partial sums(1300 + 120 + 6)

+ 6

1426

329+ 9891200 100

+ 18

1318

An alternative subtraction An alternative subtraction algorithm algorithm

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

Let’s try another one together

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 1515 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

Now, do this one on your own.

9 4 2

- 2 8 7

12

313 8

6 5 5

Last one! This one is tricky! 7 0 3

- 4 6 9

13

9 6

2 4 3

10

Partial Products Partial Products Algorithm for Algorithm for MultiplicationMultiplication

Calculate 50 X 60

67X 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

Calculate 10 X 20

14X 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.

Calculate 30 X 70

38X 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.

Partial QuotientsPartial QuotientsA Division AlgorithmA Division Algorithm

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 158There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240)

10 – 1st guess

- 12038

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 – 2nd 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 )

Let’s try another one

36 7,891100 – 1st guess

- 3,6004,291

Subtract

100 – 2nd guess

- 3,600

7 219 R7

Sum of guesses

Subtract

69110 – 3rd guess

- 360 331

9 – 4th guess

- 324

Now do this one on your own.

43 8,572100 – 1st guess

- 4,3004272

Subtract

90 – 2nd guess

-3870

15199 R 15

Sum of guesses

Subtract

4027 – 3rd guess- 301

1012 – 4th guess

- 86