Find Equivalent Forms of 13×29: Multiplication Expression Analysis

Q: Why does (10+3)×(30-1) equal 13×29?

Because 10+3 = 13 and 30-1 = 29! The parentheses show us to add or subtract first, then multiply. It's like saying 'thirteen times twenty-nine' but written in a different form.

Q: Can I remove the parentheses and just multiply everything?

No! Without parentheses, 10×3×30×1 means multiply all four numbers together, giving 900. With parentheses, you must add/subtract first, then multiply the results.

Q: What's the point of writing numbers this way?

Breaking numbers into friendly parts can make mental math easier! For instance, (10+3)×(30-1) might help you see patterns or use the distributive property for faster calculation.

Q: Do I need to calculate the final answer?

Not necessarily! The question asks which equation is the same as 13×29. You just need to verify that both expressions are equivalent - they represent the same multiplication.

Multiplication Decomposition with Parenthetical Forms

Which equation is the same as the following?

$13\times29$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the way to break down this problem.

00:09 We'll use the distributive law. It's really helpful!

00:13 First, let's split thirteen into ten plus three.

00:18 Next, we'll split twenty-nine into thirty minus one.

00:22 And there you have it! That's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which equation is the same as the following?

$13\times29$

Step-by-step solution

We solve each of the options and keep in mind the order of arithmetic operations: calculation of the operation within parentheses, multiplication and division (from left to right), addition and subtraction (from left to right).

$(10+3)\times(30-1)=13\times29$

$10\times3\times30\times1=30\times30\times1=900$

$(10\times3)\times30=13\times30$

$10\times3+29=30+29=59$

Therefore, the answer is option A.

Final Answer

$(10+3)\times(30-1)$

Key Points to Remember

Essential concepts to master this topic

Rule: Break numbers into sum/difference forms while maintaining original value
Technique: Convert 13 to (10+3) and 29 to (30-1)
Check: Evaluate both expressions: (10+3)×(30-1) = 13×29 = 377 ✓

Common Mistakes

Avoid these frequent errors

Multiplying individual components separately
Don't calculate 10×3×30×1 = 900! This treats the decomposition as four separate factors instead of two grouped expressions. Always keep parentheses intact and multiply (10+3) as one unit times (30-1) as another unit.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why does (10+3)×(30-1) equal 13×29?

Because 10+3 = 13 and 30-1 = 29! The parentheses show us to add or subtract first, then multiply. It's like saying 'thirteen times twenty-nine' but written in a different form.

Can I remove the parentheses and just multiply everything?

No! Without parentheses, 10×3×30×1 means multiply all four numbers together, giving 900. With parentheses, you must add/subtract first, then multiply the results.

How do I know which decomposition is correct?

Check if the parts inside parentheses add up to the original numbers! For example: 10+3 = 13 and 30-1 = 29. If they don't match, it's wrong.

What's the point of writing numbers this way?

Breaking numbers into friendly parts can make mental math easier! For instance, (10+3)×(30-1) might help you see patterns or use the distributive property for faster calculation.

Do I need to calculate the final answer?

Not necessarily! The question asks which equation is the same as 13×29. You just need to verify that both expressions are equivalent - they represent the same multiplication.

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