1.4 Multiply Whole Numbers

Use Multiplication Notation

Suppose you were asked to count all these pennies shown in Figure 1.16.

An image of 3 horizontal rows of pennies, each row containing 8 pennies. — **Figure 1.16**

Would you count the pennies individually? Or would you count the number of pennies in each row and add that number $3$ times.

$8 + 8 + 8$

Multiplication is a way to represent repeated addition. So instead of adding $8$ three times, we could write a multiplication expression.

$3 times 8$

We call each number being multiplied a factor and the result the product. We read $3 times 8$ as three times eight, and the result as the product of three and eight.

There are several symbols that represent multiplication. These include the symbol $\times$ as well as the dot, $\cdot$ , and parentheses $open parenthesis ).$

Note

Operation Symbols for Multiplication

To describe multiplication, we can use symbols and words.

Operation	Notation	Expression	Read as	Result
$Multiplication$	$\times$ $\cdot$ $()$	$3 times 8$ $3 times 8$ $3 open parenthesis 8 close parenthesis$	$three times eight$	$the product of 3 and 8$

Model Multiplication of Whole Numbers

There are many ways to model multiplication. Unlike in the previous sections where we used $base-10$ blocks, here we will use counters to help us understand the meaning of multiplication. A counter is any object that can be used for counting. We will use round blue counters.

Multiply Whole Numbers

In order to multiply without using models, you need to know all the one digit multiplication facts. Make sure you know them fluently before proceeding in this section.

Table 1.4 shows the multiplication facts. Each box shows the product of the number down the left column and the number across the top row. If you are unsure about a product, model it. It is important that you memorize any number facts you do not already know so you will be ready to multiply larger numbers.

**Table 1.4**
×	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0
1	1	2	3	4	5	6	7	8	9
2	2	4	6	8	10	12	14	16	18
3	3	6	9	12	15	18	21	24	27
4	4	8	12	16	20	24	28	32	36
5	5	10	15	20	25	30	35	40	45
6	6	12	18	24	30	36	42	48	54
7	7	14	21	28	35	42	49	56	63
8	8	16	24	32	40	48	56	64	72
9	9	18	27	36	45	54	63	72	81

What happens when you multiply a number by zero? You can see that the product of any number and zero is zero. This is called the Multiplication Property of Zero.

What happens when you multiply a number by one? Multiplying a number by one does not change its value. We call this fact the Identity Property of Multiplication, and $1$ is called the multiplicative identity.

Earlier in this chapter, we learned that the Commutative Property of Addition states that changing the order of addition does not change the sum. We saw that $8 + 9 = 17$ is the same as $9 + 8 = 17 .$

Is this also true for multiplication? Let’s look at a few pairs of factors.

$4 \cdot 7 = 28 7 \cdot 4 = 28$

$9 \cdot 7 = 63 7 \cdot 9 = 63$

$8 \cdot 9 = 72 9 \cdot 8 = 72$

When the order of the factors is reversed, the product does not change. This is called the Commutative Property of Multiplication.

To multiply numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition and subtraction.

$27; times 3 ___$

We start by multiplying $3$ by $7 .$

$3 \times 7 = 21$

We write the $1$ in the ones place of the product. We carry the $2$ tens by writing $2$ above the tens place.

The image shows a vertical multiplication problem of 27 times 3. An arrow indicates the 2 carried from 3 x 7 = 21 is in the tens place. Another arrow indicates the remaining 1 from 3 x 7 = 21 is written in the ones place below.

Then we multiply the $3$ by the $2,$ and add the $2$ above the tens place to the product. So $3 \times 2 = 6,$ and $6 + 2 = 8 .$ Write the $8$ in the tens place of the product.

A vertical multiplication problem showing 27 multiplied by 3, resulting in 81. An arrow indicates that the '8' in 81 is derived from (3 x 2) + the '2' carried from 3 x 7 = 21.

The product is $81 .$

When we multiply two numbers with a different number of digits, it’s usually easier to write the smaller number on the bottom. You could write it the other way, too, but this way is easier to work with.

Example 6

Multiply: $15 times 4.$

Write the numbers so the digits $5$ and $4$ line up vertically.	$15; times 4 _____$
Multiply $4$ by the digit in the ones place of $15.$ $4 \cdot 5 = 20.$
Write $0$ in the ones place of the product and carry the $2$ tens.	$1 2 5; times 4 _____; 0$
Multiply $4$ by the digit in the tens place of $15.$ $4 \cdot 1 = 4$ . Add the $2$ tens we carried. $4 + 2 = 6$ .
Write the $6$ in the tens place of the product.	$1 2 5; times 4 _____; 60$

Example 7

Multiply: $286 times 5.$

Write the numbers so the digits $5$ and $6$ line up vertically.	$286; times 5 _____$
Multiply $5$ by the digit in the ones place of $286.$ $5 \cdot 6 = 30.$
Write the $0$ in the ones place of the product and carry the $3$ to the tens place.Multiply $5$ by the digit in the tens place of $286.$ $5 \cdot 8 = 40$ .	$2 8 3 6; times 5 _____; 0$
Add the $3$ tens we carried to get $40 + 3 = 43$ . Write the $3$ in the tens place of the product and carry the 4 to the hundreds place.	$2 4 8 3 6; times 5 _____; 30$
Multiply $5$ by the digit in the hundreds place of $286.$ $5 \cdot 2 = 10.$ Add the $4$ hundreds we carried to get $10 + 4 = 14.$ Write the $4$ in the hundreds place of the product and the $1$ to the thousands place.	$2 4 8 3 6; times 5 _____; 1,430$

When we multiply by a number with two or more digits, we multiply by each of the digits separately, working from right to left. Each separate product of the digits is called a partial product. When we write partial products, we must make sure to line up the place values.

Example 8

Multiply: $62 open parenthesis 87 close parenthesis.$

Write the numbers so each place lines up vertically.
Start by multiplying 7 by 62. Multiply 7 by the digit in the ones place of 62. $7 \cdot 2 = 14.$ Write the 4 in the ones place of the product and carry the 1 to the tens place.
Multiply 7 by the digit in the tens place of 62. $7 \cdot 6 = 42.$ Add the 1 ten we carried. $42 + 1 = 43$ . Write the 3 in the tens place of the product and the 4 in the hundreds place.
The first partial product is 434.
Now, write a 0 under the 4 in the ones place of the next partial product as a placeholder since we now multiply the digit in the tens place of 87 by 62. Multiply 8 by the digit in the ones place of 62. $8 \cdot 2 = 16.$ Write the 6 in the next place of the product, which is the tens place. Carry the 1 to the tens place.
Multiply 8 by 6, the digit in the tens place of 62, then add the 1 ten we carried to get 49. Write the 9 in the hundreds place of the product and the 4 in the thousands place.
The second partial product is 4960. Add the partial products.

The product is $5,394.$

Example 9

Multiply:

ⓐ $47 times 10$
ⓑ $47 times 100.$

ⓐ $47 times 10$ .	$47; times 10 ___; 00; 470 ___; 470$
ⓑ $47 times 100$	$47; times 100 _____; 00; 000; 470 0 _____; 4,700$

When we multiplied $47$ times $10,$ the product was $470 .$ Notice that $10$ has one zero, and we put one zero after $47$ to get the product. When we multiplied $47$ times $100,$ the product was $4,700.$ Notice that $100$ has two zeros and we put two zeros after $47$ to get the product.

Do you see the pattern? If we multiplied $47$ times $10,000,$ which has four zeros, we would put four zeros after $47$ to get the product $470,000.$

When there are three or more factors, we multiply the first two and then multiply their product by the next factor. For example:

to multiply	$8 \cdot 3 \cdot 2$
first multiply $8 times 3$	$24 times 2$
then multiply $24 times 2$ .	$48$

Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation into words. Now we’ll reverse the process and translate word phrases into math notation. Some of the words that indicate multiplication are given in Table 1.5.

**Table 1.5**
Operation	Word Phrase	Example	Expression
Multiplication	times product twice	$3$ times $8$ the product of $3$ and $8$ twice $4$	$3 \times 8, 3 \cdot 8, (3) (8),$ $open parenthesis 3 close parenthesis 8, or 3 open parenthesis 8 close parenthesis$ $2 times 4$

Multiply Whole Numbers in Applications

We will use the same strategy we used previously to solve applications of multiplication. First, we need to determine what we are looking for. Then we write a phrase that gives the information to find it. We then translate the phrase into math notation and simplify to get the answer. Finally, we write a sentence to answer the question.

Example 14

Humberto bought $4$ sheets of stamps. Each sheet had $20$ stamps. How many stamps did Humberto buy?

We are asked to find the total number of stamps.

Write a phrase for the total.	the product of 4 and 20
Translate to math notation.	$4 times 20$
Multiply.
Write a sentence to answer the question.	Humberto bought 80 stamps.

Example 15

When Rena cooks rice, she uses twice as much water as rice. How much water does she need to cook $4$ cups of rice?

We are asked to find how much water Rena needs.

Write as a phrase.	twice as much as 4 cups
Translate to math notation.	$2 times 4$
Multiply to simplify.	8
Write a sentence to answer the question.	Rena needs 8 cups of water for 4 cups of rice.

Example 16

Van is planning to build a patio. He will have $8$ rows of tiles, with $14$ tiles in each row. How many tiles does he need for the patio?

We are asked to find the total number of tiles.

Write a phrase.	the product of 8 and 14
Translate to math notation.	$8 times 14$
Multiply to simplify.	$; 1 3 4; times 8 ___; 112$
Write a sentence to answer the question.	Van needs 112 tiles for his patio.

If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area. The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.

An image of two squares, one larger than the other. The smaller square is 1 centimeter by 1 centimeter and has the label “1 square centimeter”. The larger square is 1 inch by 1 inch and has the label “1 square inch”. — **Figure 1.17**

For a rectangular figure, the area is the product of the length and the width. Figure 1.18 shows a rectangular rug with a length of $2$ feet and a width of $3$ feet. Each square is $1$ foot wide by $1$ foot long, or $1$ square foot. The rug is made of $6$ squares. The area of the rug is $6$ square feet.

An image of a rectangle containing 6 blocks, 2 feet tall and 3 feet wide. This image has the label “2 times 3 = 6 feet squared”. — **Figure 1.18** The area of a rectangle is the product of its length and its width, or $6$ square feet.

Example 17

Jen’s kitchen ceiling is a rectangle that measures 9 feet long by 12 feet wide. What is the area of Jen’s kitchen ceiling?

We are asked to find the area of the kitchen ceiling.

Write a phrase for the area.	the product of 9 and 12
Translate to math notation.	$9 times 12$
Multiply.	$; 1 1 2; times 9 ___; 108$
Answer with a sentence.	The area of Jen's kitchen ceiling is 108 square feet.

Key Concepts

Operation	Notation	Expression	Read as	Result
$Multiplication$	$\times$ $\cdot$ $()$	$3 times 8$ $3 times 8$ $3 open parenthesis 8 close parenthesis$	$three times eight$	$the product of 3 and 8$

Multiplication Property of Zero
- The product of any number and 0 is 0.
  $a \cdot 0 = 0$
  $0 \cdot a = 0$
Identity Property of Multiplication
- The product of any number and 1 is the number.
  $1 \cdot a = a$
  $a \cdot 1 = a$
Commutative Property of Multiplication
- Changing the order of the factors does not change their product.
  $a \cdot b = b \cdot a$
Multiply two whole numbers to find the product.
1. Write the numbers so each place value lines up vertically.
2. Multiply the digits in each place value.
3. Work from right to left, starting with the ones place in the bottom number.
4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
5. If a product in a place value is more than 9, carry to the next place value.
6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
7. Insert a zero as a placeholder with each additional partial product.
8. Add the partial products.

Practice Makes Perfect

Use Multiplication Notation

In the following exercises, translate from math notation to words.

$4 times 7$

four times seven; the product of four and seven

$8 times 6$

$5 times 12$

five times twelve; the product of five and twelve

$3 times 9$

$open parenthesis 10 close parenthesis open parenthesis 25 close parenthesis$

ten times twenty-five; the product of ten and twenty-five

$open parenthesis 20 close parenthesis open parenthesis 15 close parenthesis$

$42 open parenthesis 33 close parenthesis$

forty-two times thirty-three; the product of forty-two and thirty-three

$39 open parenthesis 64 close parenthesis$

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

$3 times 6$

The image shows how gray circles can be set up to demonstrate the multiplication problem of 3 × 6.

$4 times 5$

$5 times 9$

A rectangular array of 45 grey circles, arranged in 5 rows and 9 columns. Below the array, the multiplication equation '5 x 9 = 45' is displayed, illustrating the product of the rows and columns.

$3 times 9$

Multiply Whole Numbers

In the following exercises, fill in the missing values in each chart.

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The first column has the values “x; 0; 1; 2; 3; 4; 5; 6; 7; 8; 9”. The second column has the values “0; 0; 0; null; 0; 0; 0; 0; null; 0; 0”. The third column has the values “1; 0; 1; 2; null; 4; 5; 6; null; 8; 9”. The fourth column has the values “2; 0; 2; 4; 6; null; 10; 12; 14; null; 18”. The fifth column has the values “3; null; 3; 6; null; null; 15; null; 21; 24; null”. The sixth column has the values “4; 0; null; 8; 12; 16; null; 24; null; null; 36”. The seventh column has the values “5; 0; null; null; 15; 20; null; null; 35; null; 45”. The eighth column has the values “6; 0; 6; 12; null; null; 30; null; null; 48; null”. The ninth column has the values “7; 0; 7; null; 21; 28; null; 42; null; null; null”. The tenth column has the values “8; null; 8; null; null; 32; 40; null; 56; 64; 72”. The eleventh column has the values “9; 0; null; 18; 27; null, null; 54; 63; null; null”.

An image of a table with 11 columns and 11 rows. The cells in the first row and first column are shaded darker than the other cells. The cells contain numbers and answers to the problem.

An image of a table with 8 columns and 7 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “x; 4; 5; 6; 7; 8; 9”. The first row has the values “x; 3; 4; 5; 6; 7; 8; 9”.

An image of a table with 8 columns and 7 rows. The cells in the first row and first column are shaded darker than the other cells. The cells contain numbers and answers to the problem.

PROD: An image of a table with 7 columns and 8 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “x; 3; 4; 5; 6; 7; 8; 9”. The first row has the values “x; 4; 5; 6; 7; 8; 9”.

An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first row has the values “x; 3; 4; 5; 6; 7; 8; 9”. The first column has the values “x; 6; 7; 8; 9”.

An image of a table with 8 columns and 5 rows. The cells in the first row and first column are shaded darker than the other cells. The cells contain numbers and answers to the problem.

An image of a table with 5 columns and 8 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “x; 3; 4; 5; 6; 7; 8; 9”. The first row has the values “x; 6; 7; 8; 9”.

PROD: An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “x; 5; 6; 7; 8; 9”. The first row has the values “x; 5; 6; 7; 8; 9”.

A dark teal and grey multiplication table showing the products of numbers 5 through 9. The rows and columns are labeled with these numbers, and the grid displays their respective multiplication results.

An image of a table with 6 columns and 6 rows. The cells in the first row and first column are shaded darker than the other cells. The cells not in the first row or column are all null. The first column has the values “x; 5; 6; 7; 8; 9”. The first row has the values “x; 5; 6; 7; 8; 9”.

In the following exercises, multiply.

$0 times 15$

$0 times 41$

$open parenthesis 99 close parenthesis 0$

$open parenthesis 77 close parenthesis 0$

$1 times 43$

$1 times 34$

$open parenthesis 28 close parenthesis 1$

$open parenthesis 65 close parenthesis 1$

$1 open parenthesis 240,055 close parenthesis$

240,055

$1 open parenthesis 189,206 close parenthesis$

ⓐ $7 times 6$
ⓑ $6 times 7$

ⓐ 42
ⓑ 42

ⓐ $8 times 9$
ⓑ $9 times 8$

$open parenthesis 79 close parenthesis open parenthesis 5 close parenthesis$

395

$open parenthesis 58 close parenthesis open parenthesis 4 close parenthesis$

$275 times 6$

1,650

$638 times 5$

$3,421 times 7$

23,947

$9,143 times 3$

$52 open parenthesis 38 close parenthesis$

1,976

$37 open parenthesis 45 close parenthesis$

$96 times 73$

7,008

$89 times 56$

$27 times 85$

2,295

$53 times 98$

$23 times 10$

230

$19 times 10$

$open parenthesis 100 close parenthesis open parenthesis 36 close parenthesis$

3,600

$open parenthesis 100 close parenthesis open parenthesis 25 close parenthesis$

$1,000 open parenthesis 88 close parenthesis$

88,000

$1,000 open parenthesis 46 close parenthesis$

$50 times 1,000,000$

50,000,000

$30 times 1,000,000$

$247 times 139$

34,333

$156 times 328$

$586 open parenthesis 721 close parenthesis$

422,506

$472 open parenthesis 855 close parenthesis$

$915 times 879$

804,285

$968 times 926$

$open parenthesis 104 close parenthesis open parenthesis 256 close parenthesis$

26,624

$open parenthesis 103 close parenthesis open parenthesis 497 close parenthesis$

$348 open parenthesis 705 close parenthesis$

245,340

$485 open parenthesis 602 close parenthesis$

$2,719 times 543$

1,476,417

$3,581 times 724$

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

the product of $18$ and $33$

18 · 33; 594

the product of $15$ and $22$

fifty-one times sixty-seven

51(67); 3,417

forty-eight times seventy-one

twice $249$

2(249); 498

twice $589$

ten times three hundred seventy-five

10(375); 3,750

ten times two hundred fifty-five

Mixed Practice

In the following exercises, simplify.

$38 times 37$

1,406

$86 times 29$

$415 minus 267$

148

$341 minus 285$

$6,251 plus 4,749$

11,000

$3,816 plus 8,184$

$open parenthesis 56 close parenthesis open parenthesis 204 close parenthesis$

11,424

$open parenthesis 77 close parenthesis open parenthesis 801 close parenthesis$

$947 times 0$

$947 plus 0$

$15,382 plus 1$

15,383

$15,382 times 1$

In the following exercises, translate and simplify.

the difference of 50 and 18

50 − 18; 32

the difference of 90 and 66

twice 35

2(35); 70

twice 140

20 more than 980

20 + 980; 1,000

65 more than 325

the product of 12 and 875

12(875); 10,500

the product of 15 and 905

subtract 74 from 89

89 − 74; 15

subtract 45 from 99

the sum of 3,075 and 95

3,075 + 95; 3,170

the sum of 6,308 and 724

366 less than 814

814 − 366; 448

388 less than 925

Multiply Whole Numbers in Applications

In the following exercises, solve.

Party supplies Tim brought 9 six-packs of soda to a club party. How many cans of soda did Tim bring?

Tim brought 54 cans of soda to the party.

Sewing Kanisha is making a quilt. She bought 6 cards of buttons. Each card had four buttons on it. How many buttons did Kanisha buy?

Field trip Seven school busses let off their students in front of a museum in Washington, DC. Each school bus had 44 students. How many students were there?

There were 308 students.

Gardening Kathryn bought 8 flats of impatiens for her flower bed. Each flat has 24 flowers. How many flowers did Kathryn buy?

Charity Rey donated 15 twelve-packs of t-shirts to a homeless shelter. How many t-shirts did he donate?

Rey donated 180 t-shirts.

School There are 28 classrooms at Anna C. Scott elementary school. Each classroom has 26 student desks. What is the total number of student desks?

Recipe Stephanie is making punch for a party. The recipe calls for twice as much fruit juice as club soda. If she uses 10 cups of club soda, how much fruit juice should she use?

Stephanie should use 20 cups of fruit juice.

Gardening Hiroko is putting in a vegetable garden. He wants to have twice as many lettuce plants as tomato plants. If he buys 12 tomato plants, how many lettuce plants should he get?

Government The United States Senate has twice as many senators as there are states in the United States. There are 50 states. How many senators are there in the United States Senate?

There are 100 senators in the U.S. senate.

Recipe Andrea is making potato salad for a buffet luncheon. The recipe says the number of servings of potato salad will be twice the number of pounds of potatoes. If she buys 30 pounds of potatoes, how many servings of potato salad will there be?

Painting Jane is painting one wall of her living room. The wall is rectangular, 13 feet wide by 9 feet high. What is the area of the wall?

The area of the wall is 117 square feet.

Home décor Shawnte bought a rug for the hall of her apartment. The rug is 3 feet wide by 18 feet long. What is the area of the rug?

Room size The meeting room in a senior center is rectangular, with length 42 feet and width 34 feet. What is the area of the meeting room?

The area of the room is 1,428 square feet.

Gardening June has a vegetable garden in her yard. The garden is rectangular, with length 23 feet and width 28 feet. What is the area of the garden?

NCAA basketball According to NCAA regulations, the dimensions of a rectangular basketball court must be 94 feet by 50 feet. What is the area of the basketball court?

The area of the court is 4,700 square feet.

NCAA football According to NCAA regulations, the dimensions of a rectangular football field must be 360 feet by 160 feet. What is the area of the football field?

Everyday Math

Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price rose $$ 12$ per share. How much money did Javier’s portfolio gain?

Javier’s portfolio gained $3,600.

Salary Carlton got a $$ 200$ raise in each paycheck. He gets paid 24 times a year. How much higher is his new annual salary?

Writing Exercises

How confident do you feel about your knowledge of the multiplication facts? If you are not fully confident, what will you do to improve your skills?

Answers will vary.

How have you used models to help you learn the multiplication facts?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

A self-assessment chart for multiplication skills, including using notation, modeling, multiplying whole numbers, translating word phrases, and applying multiplication. — **Figure 1.19**

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

ⓐ	$open parenthesis 11 close parenthesis 1$
The product of any number and one is the number.	$11$
ⓑ	$1 times 42$
Multiplying by one does not change the value.	$42$

	the product of 12 and 27
Translate.	$12 times 27$
Multiply.	$324$

	twice two hundred eleven
Translate.	2(211)
Multiply.	422

×	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0
1	1	2	3	4	5	6	7	8	9
2	2	4	6	8	10	12	14	16	18
3	3	6	9	12	15	18	21	24	27
4	4	8	12	16	20	24	28	32	36
5	5	10	15	20	25	30	35	40	45
6	6	12	18	24	30	36	42	48	54
7	7	14	21	28	35	42	49	56	63
8	8	16	24	32	40	48	56	64	72
9	9	18	27	36	45	54	63	72	81

ⓐ	$0 times 11$
The product of any number and zero is zero.	$0$
ⓑ	$open parenthesis 42 close parenthesis 0$
Multiplying by zero results in zero.	$0$

×	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0
1	1	2	3	4	5	6	7	8	9
2	2	4	6	8	10	12	14	16	18
3	3	6	9	12	15	18	21	24	27
4	4	8	12	16	20	24	28	32	36
5	5	10	15	20	25	30	35	40	45
6	6	12	18	24	30	36	42	48	54
7	7	14	21	28	35	42	49	56	63
8	8	16	24	32	40	48	56	64	72
9	9	18	27	36	45	54	63	72	81

×	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0
1	1	2	3	4	5	6	7	8	9
2	2	4	6	8	10	12	14	16	18
3	3	6	9	12	15	18	21	24	27
4	4	8	12	16	20	24	28	32	36
5	5	10	15	20	25	30	35	40	45
6	6	12	18	24	30	36	42	48	54
7	7	14	21	28	35	42	49	56	63
8	8	16	24	32	40	48	56	64	72
9	9	18	27	36	45	54	63	72	81