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Quizzes > Mathematics

Hard multiplication problems: tough practice quiz with answers

Quick quiz to tackle difficult multiplication questions. Instant answers.

Editorial: Review CompletedCreated By: Hariom SutharUpdated Aug 28, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for a challenging multiplication quiz on a dark blue background

Use this quiz to sharpen accuracy and speed on hard multiplication problems with multi-digit numbers; see instant answers for every question. If you want a fast refresher, try the multiplication fluency quiz, or build core facts with multiplication tables practice. You can also check fundamentals with a multiplication test 1-12 before coming back for harder sets.

What is 12 multiplied by 3?
36
42
30
32
To find 12 times 3, multiply the tens place: 10 × 3 = 30. Next, multiply the ones place: 2 × 3 = 6. Then add these results together to get 36. This uses the distributive property of multiplication.
What is the product of 15 and 4?
55
50
60
65
Multiply the tens: 10 × 4 = 40, then the ones: 5 × 4 = 20, and add them: 40 + 20 = 60. This breakdown helps you handle each place value. The distributive property ensures accuracy.
Calculate 9 times 14.
116
119
126
136
Use 9 × (10 + 4): first 9 × 10 = 90, then 9 × 4 = 36, and add: 90 + 36 = 126. This is a direct application of the distributive law. Breaking the problem into parts reduces errors.
Find the result of 11 multiplied by 7.
67
87
71
77
Eleven times seven can be thought of as (10 × 7) + (1 × 7) = 70 + 7 = 77. The distributive property simplifies the multiplication process. Always align place values for clarity.
What is 8 × 12?
88
86
108
96
Break 12 into 10 + 2: 8 × 10 = 80 and 8 × 2 = 16; sum is 80 + 16 = 96. This demonstrates how to use partial products. It's a key strategy in multiplication.
Compute 6 times 13.
72
78
68
84
Use (6 × 10) + (6 × 3) = 60 + 18 = 78. Partial products let you handle each digit separately. This is the foundation for larger problems.
What is the product of 14 and 6?
84
76
74
94
Split 14 into 10 + 4: 6 × 10 = 60; 6 × 4 = 24; add to get 84. The distributive property underpins this approach. It's efficient for mental math.
Calculate the product of 23 and 17.
413
391
407
383
Break 23 × 17 into (23 × 10) + (23 × 7) = 230 + 161 = 391. Using the distributive law streamlines two-digit multiplication. This method is scalable to larger numbers.
What is 125 multiplied by 4?
500
475
525
450
Since 125 × 4 = (100 × 4) + (25 × 4) = 400 + 100 = 500. Recognizing common base multiples speeds up calculation. Multiplying by 4 doubles twice.
Find 37 × 26.
982
942
952
962
Use (37 × 20) + (37 × 6) = 740 + 222 = 962. Partial products break down the task. This ensures accuracy for two-digit factors.
Compute 144 × 6.
824
904
864
854
Multiply hundreds, tens, and ones separately: 100×6=600, 40×6=240, 4×6=24; sum = 600 + 240 + 24 = 864. Place-value decomposition is key.
What is the result of 58 times 34?
1922
1982
1972
1962
Split into (58 × 30) + (58 × 4) = 1740 + 232 = 1972. The partial-product strategy handles multi-digit factors cleanly.
Calculate 89 × 12.
1008
1058
1068
1088
Use (89 × 10) + (89 × 2) = 890 + 178 = 1068. Breaking one factor into tens and units simplifies the work.
What is the product of 67 and 15?
1000
995
1020
1005
Compute (67 × 10) + (67 × 5) = 670 + 335 = 1005. Utilizing place-value breakdown ensures precision.
What is 256 multiplied by 78?
19888
19968
19978
20080
Split into (256 × 80) - (256 × 2) = 20480 - 512 = 19968. Using a small adjustment simplifies the multiplication. This is an efficient trick for near-round numbers.
Calculate 312 × 54.
16838
16858
16848
16748
Use (312 × 50) + (312 × 4) = 15600 + 1248 = 16848. This partial-sum method handles each chunk separately. It's vital for larger products.
Find the product of 483 and 297.
142451
143401
143451
143551
Compute (483 × 300) - (483 × 3) = 144900 - 1449 = 143451. Adjusting for the extra 3 reduces steps. This demonstrates smart decomposition.
What is 789 times 123?
98047
97057
96047
97047
Break into (789 × 100) + (789 × 23) = 78900 + (15780 + 2367) = 78900 + 18147 = 97047. Layering partial products keeps track of every term.
Compute the product of 654 and 321.
210934
208934
209934
209124
Use place-value expansion: (600×321) + (50×321) + (4×321) = 192600 + 16050 + 1284 = 209934. Each term is handled separately. This ensures no errors in carrying.
What is 1024 × 25?
25500
26000
24600
25600
Multiplying by 25 is the same as multiplying by 100 then dividing by 4: (1024 × 100) / 4 = 102400 / 4 = 25600. Recognizing factors of 100 simplifies the work.
Calculate 999 × 88.
87812
87912
88012
87902
Use (1000 × 88) - 88 = 88000 - 88 = 87912. This trick uses a near-round base to simplify. It's faster than standard long multiplication.
What is the product of 756 and 234?
177904
176894
176004
176904
Split into (756 × 200) + (756 × 34) = 151200 + (22680 + 3024) = 151200 + 25704 = 176904. Partial?product addition prevents mistakes.
Compute 1234 × 5678.
7016652
7006652
6996652
7006542
Multiply 1234 by 5000 = 6,170,000, then by 678 = 836,652; sum = 7,006,652. Breaking into large chunks reduces errors. This scales to any size.
What is the product of 9876 and 5432?
53656432
53646342
53546432
53646432
Use (9876 × 5000) + (9876 × 432) = 49,380,000 + 4,266,432 = 53,646,432. Partial sums even for five-digit factors keep you accurate.
Calculate the product of 12345 and 678.
8259910
8369900
8379910
8369910
Compute (12345 × 600) + (12345 × 78) = 7,407,000 + 962,910 = 8,369,910. Handling hundreds and tens separately keeps track of each component.
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Study Outcomes

  1. Solve Challenging Multiplication Problems -

    Apply learned methods to tackle a variety of hard multiplication problems and verify your answers with confidence.

  2. Apply Advanced Multiplication Strategies -

    Use techniques such as partial products, breaking numbers apart, and mental math shortcuts to simplify difficult multiplication tasks.

  3. Enhance Calculation Speed and Accuracy -

    Improve your processing speed and reduce errors through repeated practice with time-tested tricky multiplication problems.

  4. Evaluate and Correct Your Solutions -

    Learn to analyze your answer process, spot miscalculations, and make corrections to strengthen your problem-solving skills.

  5. Build Confidence in Complex Multiplication -

    Develop the self-assurance needed to approach and master difficult multiplication problems under any testing scenario.

Cheat Sheet

  1. Distributive Property Splitting -

    Leverage the distributive property (a + b) × c = a×c + b×c to break down hard multiplication problems into manageable chunks. For example, 47 × 23 becomes (47×20) + (47×3) = 940 + 141 = 1081, a strategy endorsed by Khan Academy for tackling difficult multiplication problems. This method also helps when working through multiplication problems with answers to verify each partial result.

  2. Grid (Box) Method Mastery -

    According to the University of Nottingham's Centre for Mathematical Sciences, the grid method visually organizes numbers into place-value boxes for tricky multiplication problems. Splitting 156 × 34 into (100+50+6) and (30+4) yields a clear 5-box grid; sum each product to get 5,304. Practicing this on hard multiplication problems with answers builds confidence and reduces error rates.

  3. Pattern Tricks & Mnemonics -

    Memorize times-table patterns, such as the "finger trick" for 9×n (the sum of digits equals nine) or the 11× rule: 11×ab = a (a+b) b (e.g., 11×36 = 396). Research from the National Council of Teachers of Mathematics highlights how mnemonics accelerate recall for difficult multiplication problems under timed conditions. These memory aids cut down calculation time and enhance retention.

  4. Estimation and Compatibility Checks -

    Before finalizing any product, estimate by rounding factors (e.g., 198×52 ≈ 200×50 = 10,000) to ensure your precise answer lies in the expected range. NCTM guidelines recommend compatibility checks, comparing rounded values to your exact result to catch errors in multiplication problems with answers. This quick sanity check improves accuracy, especially on high-stakes quizzes.

  5. Progressive Difficulty & Timed Drills -

    Start with medium-level questions and gradually introduce hard multiplication problems to build both speed and accuracy, as suggested by educational research from Stanford University. Use timed quizzes of 5 - 10 problems, then review mistakes immediately by checking against answer keys. Regular practice with hard multiplication problems and answers trains your brain to solve complex calculations under pressure.

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