multiplication and division of whole numbers let’s start by multiplying numbers that contain 2 or...

Multiplication and Division of Whole Numbers

Let’s start by multiplying numbers that contain 2 or more digits by a single digit…



For Example :



For Example : 1. Multiply 4 x 6



For Example : 1. Multiply 4 x 6 = 242. Put 4 in the ones place

of the answer, and carry your 2 on the tens place above the 5…

2





3. Multiply 4 x 5 and then add the 2 you carried…

2






4 x 5 = 20 20 + 2 = 22

2






4 x 5 = 20 20 + 2 = 224. Place the result next to the 4 in the answer

2


Now we will multiply a three digit number by a two digit number…

For Example :



For Example :

We will begin our multiplication by the number in the second row starting with the ones place… 5



For Example :


1. Multiply 5 x 8



For Example :

0


1. Multiply 5 x 8 = 402. Put the 0 in the ones place of the answer and carry the 4 above the tens place in the first row…

4



For Example :

0


1. Multiply 5 x 8 = 402. Put the 0 in the ones place of the

answer and carry the 4 above the tens place in the first row…

3. Now multiply 5 x 1 and then add 4

4



For Example :

9 0




3. Now multiply 5 x 1 and then add 44. 5 x 1 = 5, 5 + 4 = 9 : Place this

result in the tens place of the answer…

4



For Example :

9 0






5. Multiply 3 x 5

4



For Example :

1 5 9 0






5. Multiply 3 x 5 = 156. Place in the answer…

4



For Example :

1 5 9 0 0


7. Drop a zero into the ones place of the next line …

4



For Example :

1 5 9 0 4 0



8. 3 x 8 = 24

42



For Example :

1 5 9 0 5 4 0



8. 3 x 8 = 249. 3 x 1 = 3, 3 + 2 = 5

42



For Example :

1 5 9 09 5 4 0



8. 3 x 8 = 249. 3 x 1 = 3, 3 + 2 = 510. 3 x 3 = 9

42



For Example :

1 5 9 09 5 4 0



8. 3 x 8 = 249. 3 x 1 = 3, 3 + 2 = 510. 3 x 3 = 911. Now add the numbers…

42

+¿03

11

111


Now Long Division… we’ll start out easy…

2 ) 1 5 6



2 ) 1 5 6

- Since 2 can not divide 1, how many 2’s divide 15 without going over 15 ?



2 ) 1 5 6

- Since 2 can not divide 1, how many 2’s divide 15 without going over 15 ?

2 x 5 = 102 x 6 = 122 x 7 = 14 - place in answer above the 52 x 8 = 16

7



2 ) 1 5 6Now multiply and subtract…

7

1 41



2 ) 1 5 6

Drop the 6 for the next number to divide…

7

1 41 6



2 ) 1 5 67

1 41 6

- how many 2’s divide 16 ?



2 ) 1 5 67

1 41 6

8

1 60

- Multiply and subtract to find remainder…


1 1 ) 1 0 4 5

EXAMPLE # 2 (division ) :


1 1 ) 1 0 4 5


- 11 can not divide 10, how many 11’s divide 104 without going over 104 ?


1 1 ) 1 0 4 5


- 11 can not divide 10, how many 11’s divide 104 without going over 104 ?

11 x 9 = 99 - place in answer above the 411 x 10 = 110

9


1 1 ) 1 0 4 5


- Now multiply and subtract

9

995


1 1 ) 1 0 4 5


- Bring down the next digit

9

995 5


1 1 ) 1 0 4 5


9

995 5

- how many 11’s divide 55 without going over 55 ?


1 1 ) 1 0 4 5


9

995 5

- how many 11’s divide 55 without going over 55 ?

- 11 x 5 = 55 ( place in answer )

5


1 1 ) 1 0 4 5


9

995 5

5

550

- Now multiply and subtract

APPLICATION PROBLEMS

EXAMPLE :An offset press feeds at the rate of 140 impressions every hour. How many impressions are made in 4 hours ?


EXAMPLE :An offset press feeds at the rate of 140 impressions every hour.How many impressions are made in 4 hours ?

Multiply 140 x 4

We have a given rate of production given over a certain time frame. That rate multiplied by the number of time frames will give total production.


EXAMPLE :An offset press feeds at the rate of 140 impressions every hour.How many impressions are made in 4 hours ?

Multiply 140 x 4

14 0x 4

065

1560 impressions


EXAMPLE #2 ( applications ):A welder fabricates 35 steel water tanks for a price of $9,940.00.How much is each water tank cost to produce ?



Divide $9,940 by 35

When you are finding a per item cost, you will always divide the total dollars spent by the number of items produced.



Divide $9,940 by 35

When you are finding a per item cost, you will always divide the total dollars spent by the number of items produced.

284994035

−70294−280−140140

0

Each tank costs $284.00 to produce

EXAMPLE #3 ( applications ):Two sets of holes are drilled in an aluminum plate in the figure below.Find in inches dimensions A and B

A = _______ inchesB = _______ inches

7 holes equally spaced


20A

B30 40

150


A = _______ inchesB = _______ inches



20A

B30 40

150

Dimension A :

# of spaces between holes = # holes – 1


A = _______ inchesB = _______ inches



20A

B30 40

150

Dimension A :

# of spaces between holes = # holes – 1# of spaces between holes = 7 – 1 = 6


A = _______ inchesB = _______ inches



20A

B30 40

150

Dimension A :

# of spaces between holes = # holes – 1# of spaces between holes = 7 – 1 = 6

Distance A = 20” x 6 = 120“

120


A = _______ inchesB = _______ inches



20A

B30 40

150

To find dimension B… 120


A = _______ inchesB = _______ inches



20A

B30 40

150

To find dimension B, we will have to first find the distance between the first and last hole.

120


A = _______ inchesB = _______ inches



20A

B30 40

150


# of spaces = 5 – 1 = 4

120


A = _______ inchesB = _______ inches



20A

B30 40

150


# of spaces = 5 – 1 = 4 AND

12020

multiplication and division of whole numbers let’s start by multiplying numbers that contain 2 or...

Documents