Solve the Multiplication Problem: Calculate 12 × 33

Two-Digit Multiplication with Distributive Property

12×33= 12\times33=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's use the distributive law
00:06 Break down 12 into 10 plus 2
00:10 Break down 33 into 30 plus 3
00:16 Open the parentheses properly
00:20 Multiply each term in the first parentheses by each term in the second parentheses
00:41 Solve each multiplication separately and then add
01:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12×33= 12\times33=

2

Step-by-step solution

To make it easier for ourselves in the solving process, we'll break down 12 and 33 into exercises with smaller and more convenient numbers, preferably round numbers.

(10+2)×(30+3)= (10+2)\times(30+3)=

We'll solve the exercise using the distribution law:

We'll multiply the first term in the left parentheses by the first term in the right parentheses.

We'll multiply the first term in the left parentheses by the second term in the right parentheses.

We'll multiply the second term in the left parentheses by the first term in the right parentheses.

We'll multiply the second term in the left parentheses by the second term in the right parentheses.

And we get:

(10×30)+(10×3)+(2×30)+(2×3)= (10\times30)+(10\times3)+(2\times30)+(2\times3)=

We'll solve each of the expressions in parentheses and get:

300+30+60+6= 300+30+60+6=

We'll solve the exercise from left to right:

300+30=330 300+30=330

330+60=390 330+60=390

390+6=396 390+6=396

3

Final Answer

396

Key Points to Remember

Essential concepts to master this topic
  • Rule: Break down numbers into tens and ones for easier calculation
  • Technique: Use (10+2)×(30+3) = 10×30 + 10×3 + 2×30 + 2×3
  • Check: Verify 300+30+60+6 = 396 by standard multiplication ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to multiply all four terms in distributive property
    Don't just calculate (10×30)+(2×3) = 306! This skips the cross terms and gives wrong answers. Always multiply each term in the first parentheses by each term in the second parentheses: all four combinations.

Practice Quiz

Test your knowledge with interactive questions

\( 140-70= \)

FAQ

Everything you need to know about this question

Why break down 12 and 33 instead of just multiplying directly?

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Breaking numbers into tens and ones makes mental math much easier! Working with round numbers like 10 and 30 reduces calculation errors and helps you understand the multiplication process.

Do I have to use the distributive property for all multiplication?

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No, but it's especially helpful for two-digit numbers. For simple problems like 12×10, direct multiplication is faster. Use distributive property when it makes calculations clearer.

What if I get different partial products?

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Double-check each step: 10×30=300, 10×3=30, 2×30=60, 2×3=6. Make sure you're multiplying the right numbers and not mixing up the terms.

How can I remember to do all four multiplications?

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Think "FOIL" - First, Outer, Inner, Last terms. Or use a grid method: draw a 2×2 table with your broken-down numbers to ensure you don't miss any combinations.

Is there a faster way to check my answer?

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Yes! Use the standard algorithm (stacking numbers vertically) or estimate: 12×33 is close to 10×30=300, so 396 makes sense while 300 would be too low.

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