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Multiplying Multiple Digit Numbers

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Multiplying Multiple Digit Numbers. Sixth Grade Remedial Math Ms. Adams. Welcome.

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Welcome to sixth grade math. Today you will learn how to multiply multiple digit numbers. I am your tutorial guide Miss Adams. I currently teach sixth grade math at Jane Macon Middle School. I hope that you will learn a lot today so that you can successfully master the objectives presented in this lesson.

Please take note of the guide tabs on each page. This will help you navigate through the tutorial. Please feel free to go back and review any of the pages. Good luck with successfully completing this tutorial.

- Identify place value in multiple digit numbers.
- Represent multiplication with single digit numbers by modeling repeated
- addition.
- 3. Multiply a two digit number by a multiple of 10.
- 4. Multiply a multiple digit number by a multiple digit number.

-Repeated addition

of the same number

Example:

V

O

C

A

B

U

L

A

R

Y

Multiple

-The product of the number and any other whole number

Example:

Multiples of 2 _ 2, 4, 6, 8, 10, 12, 14…

Product

-the answer to a

multiplication problem

Example:

Factor

-a number that will divide

into another number without

a remainder

Example:

Factors of 20 _ 1, 2, 4, 5, 10, 20

Place Value

-the value of a digit as determined by its position in a number; the name of the place or location of a digit in a number

Example:

L

A

C

E

V

A

L

UE

Place value is the position of a digit within a

number.

How do we represent the number 342?

By using 3 hundred blocks, 4 rows of ten

blocks, and 2 single blocks.

Use the fewest number of blocks to

represent the number.

Another way to visualize place value is by making a

chart.

PlaceValueRemember: The value of whole numbers

increase from right to left. For example,

the ten place value is greater than the

ones place value. The hundreds place

value is greater than the tens and ones

place value.

Tens

Hundreds

Ones

- In order to make the number 342, you need:
- Three100’s 100 + 100 + 100 = 300
- Four10’s 10 + 10 + 10 + 10 = 40
- Two1’s 1 + 1 = 2
- Therefore…
- 300 + 40 + 2 = 342

Problem 1: Identify the digit in the tens place value.

941

*Think about how many sets of ten are needed to display this number.

The answer is ….4

Problem 2: Identify the digit in the hundreds place value.

1,043

*How many hundreds are needed to make the number?

Answer : 0

In 265, which digit is in the ones place?

5

2. In 397, which digit is in the tens place?

9

3. In 627, which digit is in the tens place?

2

4. In 901, which digit is in the hundreds place?

9

5. In 270, which digit is in the hundreds place?

2

Multiplication is repeated addition that is symbolized by the operation symbol “x”.

Multiplication means to have groups of the same size.

3 x 4

3 4 4 3

3 x 4 = 3 + 3 + 3 + 3 = 12

Number of

groups

Number in

each group

Number of

groups

Number in

each group

Digit

Multiplication

Write an addition sentence

for the picture.

___ groups, ____ scissors

in each group

____ +____ + ____ = ____

3 x 2 = 6

Write an addition sentence

for the picture.

___ groups, ____ gummy bears

in each group

___ +___ + ___ + ___ + ___ =____

5 x 8 = 40

5

8

2

3

8

8

8

8

40

8

6

2

2

2

I

N

G

LE

D

I

G

I

T

Multiplication

Draw 3 groups of seven sticks.

7 + 7 + 7 = 21

Draw 2 groups of six balls.

7 x 3 = 21

6 + 6 = 12

6 x 2 = 12

Multiplying By Two Digit Numbers

You will learn how to multiply a single digit

number by a number that ends in zero.

Let’s take a look at the problem below.

20 x 2

Using repeated addition: 20 + 20 = 40

Remember: 2 groups of 20

To solve this problem by multiplying first, write the

problem vertically as such _ 20

x 2

Be sure to put the larger or longer number on top.

Multiplying By Two Digit Numbers

First, multiply the digits in the ones place value.

2 0

x 2

0

Last, the product is 40.

20

x 2

40

Second, multiply the single digit

by the digit in the tens place value.

2 0

x 2

4 0

Multiplying By Two-Digit Numbers

Here’s another example.

43 x 10

First, set the problem up vertically.

43

x 10

Second, multiply 43 by 0.

43 43

x 0 x 0

000

Next, multiply 43 by the one in the tens place value.

43

x 10

00

430

Put a zero to hold the ones place value before multiplying the number in the tens place value.

Multiplying By Two-Digit Numbers

43

x 10

00

430

The last step is to add to get the product.

43

x 10

00

+ 430

430

Ten sets of 43 is 430.

43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 = 430

Be sure to line up the place values after multiplying.

Practice

Try these on your own. Multiply.

1. 59

x 10

00

+ 590

590

The product is 590.

70

x 30

00

+ 2100

2100

The product is

2,100.

90

x 2

180

The product is 180.

When multiplying multiple digit numbers by each other,

set the problem up vertically.

612

x 24

Multiply 612 and four.

612

x 4

2448

Multiply 612 and 20.

612

x 20

000

+12240

12240 612 x 24 = 14,688

Add the products together.

12240

+ 2448

14688

Multiplying Multiple Digit Numbers

Multiplying Multiple Digit Numbers

Let’s’ try this problem together. 423

x 211

First, multiply 423 by the one in the ones place value.

423

x 211

423

Next, multiply 423 by the one in the tens place value.

(We’re basically multiplying 423 and 10). 423

x 211

423

4230

Then, multiply 423 by the two in the hundreds place value.

423

x 211

423

4230 Add 423 x 211 = 84,600

84600

423

4230

+ 84600

89253

Multiplying Multiple Digit Numbers

Let’s work through this problem together.

8,346

x 52

16692

+417300

433992

Try this problem on your own.

168

x 95

840

+ 15120

15960

3

6

7

1

2

1

4

3

Multiply 8,346 and 2.

6 x 2 = 12

Carry the digit in the tens place value above the four. Add 1 to the product of 4 and 5.

Multiply 8,346 and 50.

Add

NOW MULTIPLY ON YOUR OWN

1.

320

x 123

960

6400

+32000

39360

3.

2.

38

x 24

152

+ 380

532

226

x 115

1130

2260

+ 22600

25990

Place value is the position of a digit within a

number.

Think about how many ones, tens, hundreds,

or thousands are needed to create a number.

ThousandsHundredsTensOnes

Problem

Find the digit in the ones place

value.

688

Answer: 8

Multiplication is repeated addition where

there are groups of the same size.

9 x 9

There are 9 groups with 9 in each group.

Solve by adding.

9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 81

9 x 9 = 81

When multiplying by more

than one digit, place value is

important.

Start by multiplying by the digit in the ones place. Carry the digits,

if needed, and continue multiplying by the digit in the tens place value.

Don’t forget to put a zero to hold the ones place value before multiplying by the

tens place value. Add the numbers together. Be sure to line up the

numbers in columns.

13

x 13

39

+130

169

In conclusion…

- Take your time.
- Ask yourself questions to help you along the way.
- Multiplication is repeated addition.
- Remember to carry over, if necessary, when multiplying.
- Thank you for your time. Happy Multiplying!

Resources

- http://www.aaamath.com/B/g6_31ax1.htm#section2
- http://www.mathsisfun.com/numbers/multiplication-long.html
- http://www.homeschoolmath.net/teaching/md/multiplication-repeated-addition.php
- http://mathatube.com/tables-charts-placevalue-chartshtml.html
- http://www.helpingwithmath.com/by_subject/multiplication/mul_by_10_3nbt3.htm

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