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Welcome to this Lesson on how to do

“Standard” Multiplication.

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You need to check with your Teacher if they want

you to learn the “Standard” method of

multiplication or the “Lattice” method.

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You’re free to check out both methods, but in this

lesson you’ll learn the “Standard” method of

multiplication.

1 2 3 4 5 6 7 8 9 10 11 122 4 6 8 10 12 14 16 18 20 22 243 6 9 12 15 18 21 24 27 30 33 364 8 12 16 20 24 28 32 36 40 44 485 10 15 20 25 30 35 40 45 50 55 606 12 18 24 30 36 42 48 54 60 66 727 14 21 28 35 42 49 56 63 70 77 848 16 24 32 40 48 56 64 72 80 88 969 18 27 36 45 54 63 72 81 90 99 10810 20 30 40 50 60 70 80 90 100 110 12011 22 33 44 55 66 77 88 99 110 121 13212 24 36 48 60 72 84 96 108 120 132 144

By now you should know all of your Times Tables.

So you’ll know answers like 3 x 8 = 24

without counting.

x

=

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But you also need to know how to multiply numbers bigger than 12.

That’s because you need to be able to solve problems like this one …

Farmer Brown has 23 tomato gardens on his farm.

Each garden has 16 rows of 64 tomato plants.

How many tomato plants does Farmer Brown have?

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To answer this question you need to know how to multiply numbers that

are bigger than 12. Like 16 x 64.

But the biggest single number you’ll ever need to multiply by is 9, so you really only need to remember up to

your 10 times tables.

That’s already made your job of learning multiplication a lot easier!

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So here’s the problem that we’ll solve to show you how to do “Standard” multiplication.

Farmer Brown has 23 tomato gardens on his farm.

Each garden has 16 rows of 64 tomato plants.

How many tomato plants does Farmer Brown have?

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To solve problems like this, you have to decide on two things:

(1) What Answer are you looking for.&

(2) What Steps do you need to take to find the Answer.

The Answer you want is:“How many tomato plants does

Farmer Brown have?”

Or more simply, the

“Total number of tomato plants.”

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The 1st Step is to calculate how many Tomato plants there are in each

Garden. Each Garden has this many tomato

plants: 16 rows of 64 Tomato plants.

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9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8

xx

xx

xx

xx

xx

xx

xx

xx

xxxx

xx

xx

xx

xx

xx

xx

xxxxxxxx

xxxxxxxx

xxxxxxxxxxxxxxxx58605957

6264636158605957

626463

61

16 rows

64 per rowThis is what each Tomato garden looks like

The 2nd Step is to calculate …How many tomato plants Farmer

Brown has in his 23 tomato gardens.

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12345

678910

1112131415

1617181920

212223

This is what all of his 23 tomato gardens look like from high above.

You can draw a picture of the two Steps and the Answer like this:

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1st Step 2nd Step Answer

So here are the two Steps to get to the Answer.

1st Step: Number of tomato plants in each Garden.

2nd Step: Number of tomato plants in all 23 Gardens.

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1st Step:

16 x 64

2nd Step:Answer from Step 1 x 23

Answer: Total Plants

In the 1st step we multiply the16 rows by 64 Tomato plants in each

row.

You could write it down like this:16 x 64 =

But to multiply you must write it like this:

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64x

16

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Writing numbers in columns like this splits the “Singles” column to the right

from the “Tens” column to the left.When you have 10 “Singles” it

becomes a “Ten” and when you have 10 “Tens” it becomes a “Hundred”.This is just like using your 10 times

table.T S6 41 6

Singles Column.Tens Column.

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Rule # 1: Always put the smallest number at the bottom.

16 x 64 =

6416

16 is smaller than 64.

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Rule # 2: Make one calculation line for each of the digits in the bottom

line.Then add one more line for the

Answer.16 has 2 digits.

6416

12

1 2 One line for each of the 2

digits.

One line for the answer.

x

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Rule # 3: Multiply each digit on thetop line by each digit on the bottom

line starting from the right.

64 The 4 is the “ones” digit in the top line and 6 is the “ones” digit in the bottom

line.

x 16

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From your Times Tables you know that

6 x 4 = 24.

Multiply 6 x 4 = 24.

x 1664

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Write the 4 from the 24 below the 6 in the 16 like this:

6 x 4 = 24

64164

x

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The 2 in the answer 24 is 2 “Tens”.So you must “Carry” the 2 to the

“Tens” column below the 1 in the 16 like this: 6 x 4 = 24

641642

x

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641642

Multiply 6 x 6 = 36.

Move left to the next digit on the top line, but stay with the 6 on the

bottom line until you’ve finished with the top line.

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6416843

In the answer 6 x 6 = 36, the 6 is a “Ten”. So 6 plus the 2 that you

“Carried” to the “Tens” column earlier gives you 6 + 2 = 8.

Carry the 3 to the “Hundreds” column from

6 x 6 = 36 and fill in the 6 + 2 = 8 “Tens”. x

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6416

384

There are no more digits to the left of the 6 on the top line.

The 3 that you carried earlier is the only “Hundred” so you just need to

fill it in.No more digits.

x

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6416

384

Next move one digit to the left on the bottom line.

The 1 in 16 is a “Ten”.

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6416

384

Because the 1 in the 16 that you are about to multiply is a “Ten”, the “Singles” digit to the right in the

bottom line becomes a 0.

0

x

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6416

384

Multiply 1 x 4 = 4 and write the 4 in the next place to the left of the 0.There are no “Hundreds” to carry.

40

x

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6416

384

Stay with the 1 on the bottom line and move one digit left on the top line, multiply 1 x 6 = 6 and write it to the left of the 4.

640

Multiply 1 x 6 =

6.

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6416

384

You’ve multiplied the two numbers making

these two lines below them.Next, add the two lines to get the

answer.

640v

+=

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6416

384

1,024 is the answer to Step 1.

+ 640 24= 1 0

v

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When you write 23 x 1,024 in a sentence you add a comma “,” after 3 digits to the

right.This makes it easier to read in a sentence.But when you multiply you want to keep your digits in their columns so you leave

out the “,” 102423

The number of tomato plants in each Garden = 1,024. Now you can do the 2nd Step: Number of tomato plants in

all 23 Gardens.

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1st Step:

16 x 64 =

1,024

2nd Step:1,024 x 23

Answer: Total Plants

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Remember Rule # 1: Always put the smallest number at the

bottom.

23 x 1,024 =23 is smaller than 1,024. 1024

23

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Remember Rule # 2.Make one calculation line

for each digit in the bottom line.Starting with the digit to the right on the bottom line, multiply each digit in the top

line.You write the 2 in 3 x 4 = 12 in the “Singles”

column and carry the 1 “Ten”.x

1,02423

2

3 x 4 = 12

1

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1,024 2372

6 + 1 = 7.

Multiply 3 x 2 = 6 and add 6 to the 1 that you carried and write 7 in the

“Tens” column.

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This one is easy because any number multiplied by 0 always equals 0.

It doesn’t matter how big the number is. Even 1,000,000,000 x 0 = 0. So just write

3 x 0 = 0 in the “Hundreds” column.

x

1,02423

072

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Next write 3 x 1 = 3 in the “Thousands”

column.

x 1024

233072

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There are no more digits to the left of the 1 on the top line.

Move to the next digit to the left on the bottom line and go back to the

first digit to the right in the top line.

No more digits.x

102423

3072

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Because the 2 in the 23 that you are about to multiply is a “Ten”, the “Singles” digit to the right in the

bottom line becomes a 0.

x 1024

233072

0

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Multiply 2 x 4 = 8 and write the 8 in the next place to the left of the 0.There are no “Hundreds” to carry.

x 1024

233072

80

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Stay with the 2 on the bottom line and move one digit left on the top line, multiply 2 x 2 = 4 and write it to the left of the 8.

102423

3072480

Multiply 2 x 2 = 4

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Stay with the 2 on the bottom line and move one digit left on the top line, 2 x 0 = 0. Write 0 to the left of the 4.

102423

30720480

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Stay with the 2 on the bottom line and move one digit left on the top line, 2 x 1 = 2. Write 2 to the left of the 0.

102423

30722048

0

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You’ve multiplied the last digit to the left on both lines. So all that’s left is to add the two lines together to get your answer.

102423

3072+ 20480=

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The answer to Step 2 is 23,552.

102423

30722048023552

The number of tomato plants in each Garden = 1,024 and the number of tomato

plants in all 23 Gardens = 23,552. That’s the answer to the problem!

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1st Step:

16 x 64 =

1,024

2nd Step:1,024 x 23= 23,552

Answer: Total Plants

=23,552

You can get a Wall Hanging at

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to follow and practice your

multiplication.

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