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The Best Multiplication Table + 9 Tips for Easy Multiplication

Posted by Hannah Muniz | Apr 2, 2019 12:00:00 PM

General Education

 

feature_multiply_green_x

Whether you're planning to take the SAT soon or just want to brush up on your basic math skills, knowing your times tables and multiples is a vital part of understanding math. Here, we give you free printable multiplication table PDFs and go over the nine rules you should know about multiplication.

 

Multiplication Table 12 x 12

Below is a 12 x 12 multiplication chart showing all multiples of the numbers 0-12.

To use this chart, look for the two numbers you want to multiply together on the top row and in the leftmost column, and then find the box that connects these two numbers together.

For example, if you’re trying to find the product of 7 and 5, you'd look for 7 in the leftmost column and 5 in the top row, and then see where these two meet in the middle (35). (You can also look for 7 in the top row and 5 in the left column—as we’ll explain, the order in which you multiply doesn’t actually matter!)

 

0

1

2

3

4

5

6

7

8

9

10

11

12

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

2

3

4

5

6

7

8

9

10

11

12

2

0

2

4

6

8

10

12

14

16

18

20

22

24

3

0

3

6

9

12

15

18

21

24

27

30

33

36

4

0

4

8

12

16

20

24

28

32

36

40

44

48

5

0

5

10

15

20

25

30

35

40

45

50

55

60

6

0

6

12

18

24

30

36

42

48

54

60

66

72

7

0

7

14

21

28

35

42

49

56

63

70

77

84

8

0

8

16

24

32

40

48

56

64

72

80

88

96

9

0

9

18

27

36

45

54

63

72

81

90

99

108

10

0

10

20

30

40

50

60

70

80

90

100

110

120

11

0

11

22

33

44

55

66

77

88

99

110

121

132

12

0

12

24

36

48

60

72

84

96

108

120

132

144


We also offer two free printable PDFs of this 12 x 12 multiplication chart. The first table is in  portrait mode, and the second table is in landscape mode. Click the thumbnail for the version of the multiplication table you’d like to print out:

body_multiplication_table_portrait_pdfbody_multiplication_table_landscape_pdf

There are many ways you can use this multiplication table to your advantage.

If you’re in high school and planning to take the SAT or ACT soon, you can use this chart to help you remember basic multiplication pairs and multiples likely to come up on the SAT or ACT Math sections.

Being able to quickly do mental math on tricky problems involving multiplication can effectively reduce the time you spend attempting to solve the problem.

This chart will also teach you to avoid relying too much on your calculator on the SAT/ACT Math sections.

We recommend printing out a copy of this multiplication table and either hanging it up by your desk or study area or placing it in your binder for school so you can refer to it often to help you memorize the most common multiples.

 

body_remember_brainTime to turn on your brain!

 

9 Fundamental Rules for Remembering Multiples

As you use the multiplication table above, make sure you know all the basic rules for remembering multiples and how they work. Below, we go over the most common multiplication rules you should have memorized.

 

Rule 1: Order Doesn’t Matter in Multiplication

If all you’re doing is multiplying two or more numbers together—and aren’t doing any other math function such as adding, subtracting, or dividingthen the actual order of those numbers doesn’t matter.

In other words, 8 x 4 is the same exact problem as 4 x 8 (both equal 32).

This rule also works if you’re multiplying more than two numbers together. For example, 2 x 3 x 4 can be written as 2 x 4 x 3, 3 x 4 x 2, etc. Regardless of the order of the numbers being multiplied, this equation will always come out to 24.

This means that with the multiplication chart above, you may look for numbers in either the top row or the leftmost column. It doesn’t matter whether you’re connecting the 8 in the top row and the 4 in the left column, or the 8 in the left column and the 4 in the top row. Both ways will give you the same answer of 32.

Note, however, that the order does matter when you’re doing more than just multiplying numbers together. For example, if you’re multiplying and adding numbers in a problem, you’ll need to follow the order of operations to solve it correctly.

Many people use the acronym PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) to help them recall the correct order in which they must perform calculations to solve a math problem.

An easy way to remember this acronym is with the phrase, "Please excuse my dear Aunt Sally."

 

Rule 2: All Multiples of Even Numbers Are Even

No matter which even number you choosewhether it’s as low as 2 or as high as 33,809,236all multiples of even numbers will always be even as well.

Don’t believe me? Just look back at the multiplication table above. If you look at the column under 6, for example, you’ll see that all multiples of 6 are, in fact, even numbers! These multiples include 12, 18, 24, 30, 36, etc.

A number is even if the digit in the ones place is even (in other words, if it ends in 0, 2, 4, 6, or 8).

This rule works because whenever you multiply an even number by another even number or by an odd number, the product will always be even. Here are the formulas that illustrate this:

  • even x even = even
  • even x odd = even

 

Rule 3: All Multiples of Odd Numbers Follow an Even-Odd Pattern

Unlike Rule 2, all multiples of odd numbers aren’t, in fact, odd! Rather, multiples of odd numbers will always follow an even-odd pattern.

What do I mean by this? Let’s look at an example. Take the odd number 7. Below are the multiples of 7. Each multiple has been highlighted in either yellow (even) or blue (odd):

 

0

1

2

3

4

5

6

7

8

9

10

11

12

7

0

7

14

21

28

35

42

49

56

63

70

77

84

 

As you can see, the multiples of 7, an odd number, follow a clear pattern of even, odd, even, odd, and so on.

This pattern works because of a fundamental rule in math: an odd number multiplied by an even number will always be even, but an odd number multiplied by an odd number will always be odd.

Here are the formulas to help you remember this concept:

  • odd x even = even
  • odd x odd = odd

 

body_nature_leaves_patternNature has patterns just like math does.

 

Rule 4: The Only Multiple of 0 Is 0

As you likely noticed in the multiplication chart above, any time you multiply 0 by a numberwhether that number is 5, 0.0004758, or 6,783,390,391the product will always equal 0.

Basically, since any number times 0 is equal to 0, all multiples of 0 are therefore 0 as well.

 

Rule 5: A Multiple of 1 Always Equals the Number Being Multiplied

Whenever a numberno matter how small or big it might beis multiplied by 1, the answer will be equal to the original number you started with. For example, 9 x 1 = 9. And 12,351 x 1 = 12,351.

Here are some multiples of 1 taken from the chart above:

 

1

2

3

4

5

6

7

8

9

10

11

12

1

1

2

3

4

5

6

7

8

9

10

11

12

 

 

Rule 6: All Multiples of 5 End in 0 or 5

If you look at the multiplication chart above, you’ll notice that all multiples of 5 end in either a 0 or 5. Knowing this makes it easy to remember what numbers are multiples of 5, even if they’re super high. In short, anything that ends in a 5 or 0 is for sure a multiple of 5.

Here is a small chart showing some of the multiples of 5:

 

0

1

2

3

4

5

6

7

8

9

10

11

12

5

0

5

10

15

20

25

30

35

40

45

50

55

60

 

 

Rule 7: For Multiples of 10, Just Add a 0

To find a multiple of 10, all you need to do is add a 0 to the end of the number being multiplied by 10. So if you have the problem 10 x 27, you should know right away that the answer is 270 (27 with a 0 added to the end of it).

This rule also means that all multiples of 10 end in 0 (this is similar to Rule 6, which states that all multiples of 5 end in either a 5 or 0). In other words, any number you see that ends in a 0, whether it’s 640 or 4,328,120, will be a multiple of 10.

Here’s a chart showing some common multiples of 10:

 

0

1

2

3

4

5

6

7

8

9

10

11

12

10

0

10

20

30

40

50

60

70

80

90

100

110

120

 

 

body_0_calculatorZero can be a very useful number in multiplication.

 

Rule 8: Up to 11 x 9, All Multiples of 11 Are Repeated Digits

As the multiplication table above shows, all multiples of 11 up to 11 x 9 are equal to the digit being multiplied repeated once. So if you multiply 11 by 6, for example, the answer will be 66 (you just repeat 6the number being multiplied by 11).

Note that this trick only works up to factor 9. Once you hit 10, the product will not equal two repeated digits.

Here are the multiples of 11 using the factors 1-9:

 

1

2

3

4

5

6

7

8

9

11

11

22

33

44

55

66

77

88

99

 

 

Rule 9: For 12, Multiply by 10 and 2 Then Add Together

Multiples of 12 can be difficult to memorize and a little overwhelming, but there’s an easy trick you can use to quickly find any multiple of 12. All you have to do is multiply the factor (the number being multiplied by 12) by 10, multiply that same factor by 2, and then add these together.

This might sound complicated, but it’s really not!

Written out as an equation (in which a is any factor of 12), this trick would look like this:

12a = 10a + 2a

Let’s walk through an example. Say you want to find the product of 12 x 9. The quickest way to do this would be to first multiply 9 by 10; this gives us 90. Next, multiply 9 by 2 to get 18.

Finally, add together 90 and 18. This gives us 108, which is the answer to our original problem: 12 x 9.

Try this trick with other factors and then double-check your answer with the multiplication chart or a calculator.

 

What’s Next?

Want to brush up on other basic math skills? Then check out our expert guides on how to find the mean of a data set (coming soon) and how to use the acceleration formula (coming soon). 

Need help preparing for the SAT/ACT Math section? Learn everything you need to know about what kinds of topics are tested on SAT Math and ACT Math.

Have friends who also need help with test prep? Share this article!
Hannah Muniz
About the Author

Hannah graduated summa cum laude from the University of Southern California with a bachelor’s degree in English and East Asian languages and cultures. After graduation, she taught English in Japan for two years via the JET Program. She is passionate about education, writing, and travel.



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