Multiplying

Multiple Digit NumbersSixth Grade Remedial Math

Ms. Adams

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.

Instructional Goals

1. Identify place value in multiple digit numbers.

2. 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.

Table of Contents

1 Vocabulary

2Lesson 23

Lesson 1

4 Lesson 3

5 Lesson 4

VOCABULARY

Multiplication-Repeated addition of the same numberExample:

Multiple-The product of the number and any other whole numberExample: Multiples of 2 _ 2, 4, 6, 8, 10, 12, 14…Product

-the answer to a multiplication problemExample:

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:

PLACE

VALUE

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.

PlaceValue

Another way to visualize place value is by making a chart.

3 4 2

Hund

reds

Tens

One

s

In order to make the number 342, you need:•Three 100’s 100 + 100 + 100 = 300•Four 10’s 10 + 10 + 10 + 10 = 40•Two 1’s 1 + 1 = 2

Therefore…300 + 40 + 2 = 342

Remember: 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.

P L A C E U L AV

Check out the table below.

NumberThousands

Hundreds

Tens

Ones Representation

17 1 7

226 2 2 6

1,409 1 4 0 9

3,400 3 4 0 0

52 5 2

Let’s PracticeProblem 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

NOW IT’S YOUR TURN1. In 265, which digit is in the ones place?

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

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

24. 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

Single

Digit

Multiplication

Write an addition sentence for the picture.

___ groups, ____ scissors in each group

____ +____ + ____ = ____

3 x 2 = 6

3 2

2 2 2 6

Write an addition sentence for the picture.

___ groups, ____ gummy bears in each group

___ +___ + ___ + ___ + ___ =____

5 x 8 = 40

5 8

8 8 8 8 8 40

SINGLE

DIGITMULTIPLICATION

7 + 7 + 7 = 21

7 x 3 = 21 Draw 2 groups of six balls.

6 + 6 = 126 x 2 = 12

MULTIPLY ON YOUR OWN

7 x 4= ____28

8 x 4 = ____32

4 x 4 = ___165 x 5 = ___25

Multiplying By Two Digit NumbersYou 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 = 40Remember: 2 groups of 20

To solve this problem by multiplying first, write the problem vertically as such _ 20

x 2Be sure to

put the larger or

longer number on

top.

Multiplying By Two Digit NumbersFirst, multiply the digits in the ones place value.

2 0 x 2

0Second, multiply the single digit by the digit in the tens place value.

2 0 x 2

4 0

Last, the product is 40.

20 x 2

40

Multiplying By Two-Digit NumbersHere’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 0 00

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.

43 x 10

00 430

The last step is to add to get the product.43

x 1000

+ 430 430

Ten sets of 43 is 430. 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 = 430

Multiplying By Two-Digit Numbers

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.

2. 70 x 30 00 + 2100 2100

The product is2,100.

3. 90 x 2 180

The product is 180.

Multiplying Multiple Digit Numbers

Let’s multiply. 612 x 24

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+ 244814688

Multiplying Multiple Digit NumbersLet’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 4234230

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 NumbersLet’s work through this problem together.

8,346 x 52 16692+417300 433992

Multiply 8,346 and 2.

6 x 2 = 12Carry the digit

in the tens place value

above the four. Add 1 to the product of 4

and 5.

1

Multiply 8,346 and

50.

321

Add

Try this problem on your own.

168 x 95 840

+ 15120 15960

43 76

Click icon to add picture

NOW MULTIPLY ON YOUR OWN 320 x 123 960 6400 +32000 39360

1. 2. 38 x 24 152 + 380 532

3. 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.

Thousands Hundreds Tens Ones

Problem

Find the digit in the ones placevalue.

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