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# Commutative Law of Multiplication (Math Quiz and Tutorial)

0

!! If you are familiar with the elementary concepts of the commutative law of multiplication, e.g. because you have taken the quiz before, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!

## INTRODUCTION

The Commutative Law of Multiplication allows one to change the order of numbers when multiplying them, or to say it in other words:
You can swap numbers and still get the same results when you multiply things!
In elementary arithmetics the commutative laws apply to multiplication and addition.

CAUTION: The commutative laws do not apply to subtraction and division!!

## COMMUTATIVE LAW OF MULTIPLICATION

### a • b = b • a

Example: 5 • 2 = 2 • 5
Explanation: 5 batches of 2 apples is the same as 2 batches of 5 apples (see picture above).
Benefit: At first you might think applying the commutative law of multiplication is of no use, but often when you have more than 2 terms and in combination with other arithmetic laws (e.g. the associative law), this can be a real time-saver.

Another example that demonstrates this last aspect more clearly:

= 1000 200
= 200000

In everyday-life situations we usually apply the commutative law of multiplication intuitively and in combination with two other laws: the associative and distributive laws of elementary arithmetics.
All three laws combined can speed up your mental arithmetics significantly. It is therefore recommended that you also read those related articles and take the quizzes to freshen up your knowledge and make it a routine behavior to look out for terms that can be regrouped, swapped or factored out (distributive law) to facilitate calculations.

## QUIZ

In the following a quiz with a variety of questions that test your knowledge and skill level in applying the commutative law of multiplication. Do not use a digital calculator, but try to solve the questions in your head.

#### IMPORTANT!!!

Once you push the button below the clock starts ticking!!

Click the button to take the test!

This quiz must be completed in 3 minutes.

# Commutative Law of Addition (Math Quiz and Tutorial)

0

!! If you are familiar with the elementary concepts of the commutative law of addition, e.g. because you have taken the quiz before, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!

## INTRODUCTION

The Commutative Law of Addition allows one to change the order of numbers when adding them, or to say it in other words:
You can swap numbers and still get the same results when you add things!
In elementary arithmetics the associative law applies to addition and subtraction.

CAUTION: The commutative law does not apply to subtraction and division!!

### a + b = b + a

Example: 2 + 8 = 8 + 2
Benefit: At first you might think applying the commutative law of addition is of no use, but often when you have more than 2 terms and in combination with other arithmetic laws (e.g. the associative law), this can be a real time-saver.

Another example of the commutative law in combination with the associative law that demonstrates this last aspect more clearly:

115 + 746 + 17 + 254 + 25 + 43          (now swap terms : commutative law)
= (115 + 25) + (746 + 254) + (17 + 43)          (now regroup terms : associative law)
= 140 + 1000 + 60          (now swap terms again : commutative law)
= (140 + 60) + 1000
= 200 + 1000
= 1200

In everyday-life situations we usually apply the commutative law of addition intuitively and in combination with two other laws: the associative and distributive laws of elementary arithmetics.
All three laws combined can speed up your mental arithmetics significantly. It is therefore recommended that you also read those related articles and take the quizzes to freshen up your knowledge and make it a routine behavior to look out for terms that can be regrouped, swapped or factored out (distributive law) to facilitate calculations.

## QUIZ

In the following a quiz with a variety of questions that test your knowledge and skill level in applying the commutative law of addition. Do not use a digital calculator, but try to solve the questions in your head.

#### IMPORTANT!!!

Once you push the button below the clock starts ticking!! Please go to Commutative Law of Addition (Math Quiz and Tutorial) to view this test

0

!! If you are familiar with the elementary concepts of addition, e.g. because you have taken the quiz before, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!

Addition is the (most) basic operation of arithmetic. It is very simple and straightforward, as you don’t have to worry in which order you add theterms, thus a+b = b+a, and a + (b+c) = (a+b) + c.

This is a result of the associative law of addition.

NOMENCLATURE

While “a+b” is called the sum of “a” and “b”, there are a variety of designations used for “a” and “b”:

• The most accurate appelations for “a” would be first addend, and for “b” second addend.
• Sometimes “a” is also called augment.
• “a” or “b” can also be called addend(s) or summand(s) or simply term(s).

In the following a quiz with a variety of questions that test your knowledge and skill level in elementary arithmetics.

Do not use a digital calculator, but try to solve the questions in your head. You can also use paper and pencil or the note/memo app on your smartphone to carry out manual arithmetics (carry and borrow operations).

#### IMPORTANT!!!

Once you push the button below the clock starts ticking!!

# Multiplication Table – 30×30 Times Table (Timed Math Quiz)

0

!! If you are familiar with the 30×30 Multiplication Table, e.g. because you have taken the quiz already before, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!

## INTRODUCTION:

The multiplication table (aka times table) is a mathematical grid scheme that contains the results of the multiplication of 2 integer numbers up to a certain degree (usually 10×10 or 12×12, but sometimes also 20×20, 25×25 or even 30×30).

While some educators think it is sufficient to memorize the multiplication table up to a degree of 9×9, others believe one should be able to memorize the times table at least up to a degree of 12×12 or even 30×30. Personally I suggest memorizing the 30×30 grid by the end of the 4th grade, since you will also be able to quickly carry out decimal operations such as 2.8 • 1.7 etc.

The featured image of this article above depicts the 30×30 multiplication table as it is taught in 4th grade elementary school.

Please also note that there are other related articles (and quizzes) that test your knowledge on mastering the 12×12, the 20×20 and the 25×25 times tables.

### Multiplication Table (30×30 grid)

 x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 182 189 196 203 210 8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160 168 176 184 192 200 208 216 224 232 240 9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180 189 198 207 216 225 234 243 252 261 270 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 231 242 253 264 275 286 297 308 319 330 12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360 13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260 273 286 299 312 325 338 351 364 377 390 14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280 294 308 322 336 350 364 378 392 406 420 15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360 375 390 405 420 435 450 16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 336 352 368 384 400 416 432 448 464 480 17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340 357 374 391 408 425 442 459 476 493 510 18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 468 486 504 522 540 19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380 399 418 437 456 475 494 513 532 551 570 20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 21 21 42 63 84 105 126 147 168 189 210 231 252 273 294 315 336 357 378 399 420 441 462 483 504 525 546 567 588 609 630 22 22 44 66 88 110 132 154 176 198 220 242 264 286 308 330 352 374 396 418 440 462 484 506 528 550 572 594 616 638 660 23 23 46 69 92 115 138 161 184 207 230 253 276 299 322 345 368 391 414 437 460 483 506 529 552 575 598 621 644 667 690 24 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 624 648 672 696 720 25 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750 26 26 52 78 104 130 156 182 208 234 260 286 312 338 364 390 416 442 468 494 520 546 572 598 624 650 676 702 728 754 780 27 27 54 81 108 135 162 189 216 243 270 297 324 351 378 405 432 459 486 513 540 567 594 621 648 675 702 729 756 783 810 28 28 56 84 112 140 168 196 224 252 280 308 336 364 392 420 448 476 504 532 560 588 616 644 672 700 728 756 784 812 840 29 29 58 87 116 145 174 203 232 261 290 319 348 377 406 435 464 493 522 551 580 609 638 667 696 725 754 783 812 841 870 30 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780 810 840 870 900

The following quizz tests your ability to memorize the 30×30 grid. There is also a time limit, so that you can’t do too much mental arithmetic, since the goal of this chapter is to encourage you to really learn this table by heart.
Enjoy!

## QUIZ:

### Multiplication Table (30×30): Timed Test

#### Quiz Stats:

Number of questions: 50 (this is equivalent to 5.5% of all possible questions).
Testing mode: 5 randomized batches of 10 questions each
(i.e. each time you take this test you will be exposed to different batches of questions.)
Total testing time: 5 minutes (i.e. 6 seconds per question).
If you take the quiz on a desktop computer it is recommended that you finish about 2 minutes before the end of the testing time, since you are able to fill out the gaps faster with the help of the numerical keyboard.

#### Quiz Instructions:

Enter your answers in the gaps. Only use numeric figures; no blancs or other characters!

Since this is a timed test it is recommended that you fill out the gaps as quick as possible.

If you use a mobile device you should set it up such that you can input the numbers through a numerical key pad.
If you use a desktop computer you might also want to use the key pad to enter the figures with your right hand and move to the next gap by pressing the tab key with your left hand.

Don’t forget to push the “Next” button after each batch of 10 questions, and also do not forget to push the “Submit” button after completing the last batch of questions (page 5)!!

#### Note:

Depending on the version and settings of your browser, your screen-size and your device model, the correct answers that are displayed after you completed the test might not seem perfectly formatted.
Don’t worry about that. They will also immediately be emailed to you and should appear “nicer” in your email client.
Therefore you also don’t have to save the results page, since you can analyze your results in your email client. In fact that’s what most user do.
For this – and if you plan to take more quizzes – it is recommended that you register, so you won’t have to enter your email address each time you take a test.

#### IMPORTANT!!!

Once you push the button below the clock starts ticking!!

Please go to Multiplication Table – 30×30 Times Table (Timed Math Quiz) to view this test

# Multiplication Table – 25×25 Times Table (Timed Math Quiz)

0

!! If you are familiar with the 25×25 Multiplication Table, e.g. because you have previously taken the quiz already, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!

## INTRODUCTION:

The multiplication table (aka times table) is a mathematical grid scheme that contains the results of the multiplication of 2 integer numbers up to a certain degree (usually 10×10 or 12×12, but sometimes also 20×20, 25×25 or even 30×30).

While some educators think it is sufficient to memorize the multiplication table up to a degree of 9×9, others believe one should be able to memorize the times table at least up to a degree of 12×12 or even 25×25. Personally I suggest memorizing the 30×30 grid by the end of the 4th grade, since you will also be able to quickly carry out decimal operations such as 2.6 • 1.9 etc.

The featured image of this article above depicts the 25×25 multiplication table as it is taught in 3rd grade elementary school.

Please also note that there are other related articles (and quizzes) that test your knowledge on mastering the 12×12, the 20×20 and the 30×30 times tables.

### Multiplication Table (25×25 grid)

 • 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 154 161 168 175 8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160 168 176 184 192 200 9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180 189 198 207 216 225 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 231 242 253 264 275 12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260 273 286 299 312 325 14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280 294 308 322 336 350 15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360 375 16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 336 352 368 384 400 17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340 357 374 391 408 425 18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380 399 418 437 456 475 20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 21 21 42 63 84 105 126 147 168 189 210 231 252 273 294 315 336 357 378 399 420 441 462 483 504 525 22 22 44 66 88 110 132 154 176 198 220 242 264 286 308 330 352 374 396 418 440 462 484 506 528 550 23 23 46 69 92 115 138 161 184 207 230 253 276 299 322 345 368 391 414 437 460 483 506 529 552 575 24 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 504 528 552 576 600 25 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625

The following quizz tests your ability to memorize the 25×25 grid. There is also a time limit, so that you can’t do too much mental arithmetic, since the goal of this chapter is to encourage you to really learn this table by heart.
Enjoy!

## QUIZ:

### Multiplication Table (25×25): Timed Test

#### Quiz Stats:

Number of questions: 50 (this is equivalent to 8% of all possible questions).
Testing mode: 5 randomized batches of 10 questions each
(i.e. each time you take this test you will be exposed to different batches of questions.)
Total testing time:  5 minutes (i.e. 6 seconds per question).
If you take the quiz on a desktop computer it is recommended that you finish about 2 minutes before the end of the testing time, since you are able to fill out the gaps faster with the help of the numerical keyboard.

#### Quiz Instructions:

Enter your answers in the gaps. Only use numeric figures; no blancs or other characters!

Since this is a timed test it is recommended that you fill out the gaps as quick as possible.

If you use a mobile device you should set it up such that you can input the numbers through a numerical key pad.
If you use a desktop computer you might also want to use the key pad to enter the figures with your right hand and move to the next gap by pressing the tab key with your left hand.

Don’t forget to push the “Next” button after each batch of 10 questions, and also do not forget to push the “Submit” button after completing the last batch of questions (page 5)!!

#### Note:

Depending on the version and settings of your browser, your screen-size and your device model, the correct answers that are displayed after you completed the test might not seem perfectly formatted.
Don’t worry about that. They will also immediately be emailed to you and should appear “nicer” in your email client.
Therefore you also don’t have to save the results page, since you can analyze your results in your email client. In fact that’s what most user do.
For this – and if you plan to take more quizzes – it is recommended that you register, so you won’t have to enter your email address each time you take a test.

#### IMPORTANT!!!

Once you push the button below the clock starts ticking!!

Please go to Multiplication Table – 25×25 Times Table (Timed Math Quiz) to view this test

# Multiplication Table – 20×20 Times Table Grid (Timed Math Quiz)

0

!! If you are familiar with the 20×20 Multiplication Table, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!

## INTRODUCTION:

The multiplication table (aka times table) is a mathematical grid scheme that contains the results of the multiplication of 2 integer numbers up to a certain degree (usually 10×10 or 12×12, but sometimes also 20×20, 25×25 or even 30×30).

While some educators think it is sufficient to memorize the multiplication table up to a degree of 9×9, others believe one should be able to memorize the times table at least up to a degree of 12×12 or even 20×20. Personally I suggest memorizing the 30×30 grid by the end of the 4th grade, since you will also be able to quickly carry out decimal operations such as 1.3 • 2.7 etc.

The featured image of this article above depicts the 20×20 multiplication table as it is taught in 1st grade elementary school.

Please also note that there are other related articles (and quizzes) that test your knowledge on mastering the 12×12, the 25×25 and the 30×30 times tables.

### Multiplication Table (20×20 grid)

 • 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160 9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260 14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280 15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340 18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380 20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

The following quizz tests your ability to memorize the 20×20 grid. There is also a time limit, so that you can’t do too much mental arithmetic, since the goal of this chapter is to encourage you to really learn this table by heart.
Enjoy!

## QUIZ:

### Multiplication Table (20×20): Timed Test

#### Quiz Stats:

Number of questions: 50 (this is equivalent to 12.5% of all possible questions).
Testing mode: 5 randomized batches of 10 questions each
(i.e. each time you take this test you will be exposed to different batches of questions.)
Total testing time:  5 minutes (i.e. 6 seconds per question).
If you take the quiz on a desktop computer it is recommended that you finish about 2 minutes before the end of the testing time, since you are able to fill out the gaps faster with the help of the numerical keyboard.

#### Quiz Instructions:

Enter your answers in the gaps. Only use numeric figures; no blancs or other characters!

Since this is a timed test it is recommended that you fill out the gaps as quick as possible.

If you use a mobile device you should set it up such that you can input the numbers through a numerical key pad.
If you use a desktop computer you might also want to use the key pad to enter the figures with your right hand and move to the next gap by pressing the tab key with your left hand.

Don’t forget to push the “Next” button after each batch of 10 questions, and also do not forget to push the “Submit” button after completing the last batch of questions (page 5)!!

#### Note:

Depending on the version and settings of your browser, your screen-size and your device model, the correct answers that are displayed after you completed the test might not seem perfectly formatted.
Don’t worry about that. They will also immediately be emailed to you and should appear “nicer” in your email client.
Therefore you also don’t have to save the results page, since you can analyze your results in your email client. In fact that’s what most user do.
For this – and if you plan to take more quizzes – it is recommended that you register, so you won’t have to enter your email address each time you take a test.

#### IMPORTANT!!!

Once you push the button below the clock starts ticking!!

Please go to Multiplication Table – 20×20 Times Table Grid (Timed Math Quiz) to view this test

# Multiplication Table – 12×12 Times Table (Timed Math Quiz)

0

If you are familiar with the 12×12 multiplication table, you may skip the theory part and head down to take the math quiz and test your knowledge.

## INTRODUCTION:

The multiplication table (also known as times table) is a mathematical grid scheme that contains the results of the multiplication of 2 integer numbers up to a certain degree (usually 10×10 or 12×12, but sometimes also 20×20, 25×25 or even 30×30).

While some educators think it is sufficient to memorize the multiplication table up to a degree of 9×9, others believe one should be able to memorize the times table at least up to a degree of 12×12 or even 20×20. Personally I suggest memorizing the 30×30 grid by the end of the 4th grade, since you will also be able to quickly carry out decimal operations such as 2.7 x 1.8 etc.

The featured image of this article above depicts the 12×12 multiplication table as it is taught in 1st grade elementary school.

Please also note that there are other related articles (and quizzes) that test your knowledge on mastering the 20×20, the 25×25 and the 30×30 times tables.

### Multiplication Table (12×12 grid)

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

The following quizz tests your ability to memorize the 12×12 grid. There is also a time limit, so that you can’t do too much mental arithmetic, since the goal of this chapter is to encourage you to really learn this table by heart.
Enjoy!

## QUIZ:

### Multiplication Table: Timed Test

#### Quiz Instructions:

Enter your answers in the gaps. Only use numeric figures; no blancs or other characters!
Since this is a timed test it is recommended that you use the key pad to enter the figures with your right hand and move to the next gap by pressing the tab key with your left hand.

#### Quiz Stats:

Number of questions: 72
Testing time for mobile device holders: 5 minutes (~4s/question).
If you take the quiz on a desktop computer it is recommended that you reduce the testing time to 3 minutes.

#### IMPORTANT!!

Once you push the button below the clock starts ticking!!

Please go to Multiplication Table – 12×12 Times Table (Timed Math Quiz) to view this test

# Roman Numerals (Math Quiz)

0

If you are familiar with the rules and theory of the Roman numeral system you may skip the theory part and head down to take the math quiz and test your knowledge.

INTRODUCTION:

As the name says, Roman numerals were used by the Romans, and they continued to be use till the 14th century, when they were gradually replaced by the more convenient decimal system.
The Roman numeral system is based on seven symbols:

 Symbol I V X L C D M Wert 1 5 10 50 100 500 1000

Numbers are formed by combining symbols together. The following rules apply:

RULES:

1. Symbols are placed from left to right in sequence of value, i.e. the largest symbol is placed to the very left, and the smallest to the very right. Their combined value is obtained by adding up the values of the individual symbols.
This is the general underlying rule, however (and this makes it tricky!!) one must avoid repeating four symbols in succession (e.g. writing “IIII” to express “4” ist not permitted). Therefore these additional rules apply:

2. If a symbol with a lower value is placed before (i.e. to the left of) a certain symbol, then the value of the symbol with the lower value shall be subtracted from the value of the symbol with the higher value. In doing so only one symbol with a lower value may preceed a symbol with a higher value.

Example 1:
CX = 100 + 10 = 110
XC = 100 – 10 = 90

Example 2:
CXX = 100 + 10 +10 = 120
(XXC to express 80 is not permitted!!)
Instead: 80 = LXXX = 50 + 10 + 10 + 10

Example 3:
998 = CMXCVIII (und not IIM)

3. The symbols I, X, C, and M may only be repeated up to three times in succession.

4. V, L, and D must not preceed a symbol with a higher value, and they also may not be repeated two (or more) times in succession.

Example 4:
(LD to express 450 is not permitted!!)
Instead: 450 = CDL = -100 + 500 + 50

USAGE:
Roman numerals are still used today in several niche contexts, like in the names of Popes and monarchs, the hour marks on clocks and timepieces (see the featured image of this article), some sport events (e.g. the Summer and Winter Olympics, and the Super Bowl), etc. More examples of modern usage can be found here.

QUIZ:

Please go to Roman Numerals (Math Quiz) to view this test

# The Binary Numeral System (Math Quiz)

0

If you are familiar with the rules and theory of the Roman numeral system you may skip the theory part and head down to take the math quiz and test your knowledge.

INTRODUCTION:

The cardinal number (or base) of the binary numeral system is the figure “2”. Thus only 2 figures are necessary to express numbers by this binary system: typically 0 and 1. Such numbers represented in this system are therefore commonly called binary numbers. The locic gates in the digital electronic circuits of modern-day computers and mobile phones and their software are based on the binary numeral system, which explains the importance of this numeral systems.

EXAMPLE for the conversion of the binary number 100101 to the decimal numeral system:

1010012 = [ ( 1 ) × 25 ] + [ ( 0 ) × 24 ] + [ ( 1 ) × 23 ] + [ ( 0) × 22 ] + [ ( 0 ) × 21 ] + [ ( 1 ) × 20 ]
= [ 1 × 32 ] + [ 0 × 16 ] + [ 1 × 8 ] + [ 0 × 4 ] + [ 0 × 2 ] + [ 1 × 1 ]
= 4110

QUIZ:

Please go to The Binary Numeral System (Math Quiz) to view this test

# The Decimal System (Math Quiz)

0

If you are familiar with the rules and theory of the decimal numeral system you may skip the theory part and head down to take the math quiz and test your knowledge.

INTRODUCTION:

Our numeral system, also known as the decimal system, uses the figures 0, 1, 2, …, 9. The position (place) in a sequence of figures where a certain figure (digit) is listed determines its weight or value: Ones (O), Tens (D), Hundreds (H), Thousands (T), … Therefore our numeral system is also called place-value system or Decimal Numeral System. 1, 10, 100, 1000, … are the number of stages of the decimal system. They are obtained by successive multiplation with the cardinal number 10.

QUIZ:

Please go to The Decimal System (Math Quiz) to view this test