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Commutative Law of Multiplication (Math Quiz and Tutorial)

0
commutative law of multiplication
5 x 2 = 2 x 5 : The commutative law of multiplication allows one to swap numbers and still get the same result.

!! 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
commutative laws of addition and multiplication
The commutative laws of addition and multiplication allow one to swap the order of the terms and still get the same results.

!! 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!!

COMMUTATIVE LAW OF ADDITION

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

Elementary Arithmetic: Addition

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Elementary Arithmetics - Addition (quiz and brief tutorial)
A typical example of manual arithmetic is this pencil-and-paper addition. The five numbers are the summands (or addends or terms), and the result below the horizontal line is the sum. The handwritten digits on the top are the carries.

!! 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!!

Please go to Elementary Arithmetic: Addition to view this test

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

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The Multiplication Table (30x30 grid) - Elementary Math (Quiz and Tutorial)
The 30x30 grid is an advanced version of the multiplication table that everyone should be able to memorize by the end of the 3rd grade.

!! 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
The Multiplication Table (25x25 grid) - Elementary Math (Quiz and Tutorial)
The 25x25 grid is an advanced version of the multiplication table that everyone should be able to memorize by the end of the 3rd grade.

!! 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)

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The Multiplication Table (20x20 grid) - Elementary Math (Quiz and Tutorial)
The 20x20 grid is an advanced version of the multiplication table that everyone should be able to memorize by the end of the 2nd grade.

!! 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)

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The Multiplication Table (12x12 grid) - Elementary Math (Quiz and Tutorial)
The 12x12 grid is the simplest version of the multiplication table that everyone should be able to memorize.

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)

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Roman numerals
Clock face with Roman numerals

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
The Binary System (brief tutorial and quiz)
Binary database records consisting of strings of bits of ones and zeros

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)

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The configuration of this abacus can be used for both decimal and hexadecimal computation
One of the oldest calculating tools still in use today is the counting frame also known as abacus: Each bead above the crosspiece is worth five units, and each bead below is worth one. The rods from right to left indicate place value in powers of ten: ones, tens, hundreds, thousands, etc. This configuration can be used for both decimal and hexadecimal computation.

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