Find Equivalent Expressions for 39×19: Multiplication Practice

Q: Why doesn't (30×9)+(10×9) equal 39×19?

Because addition and multiplication follow different rules! $ (30×9)+(10×9) = 270+90 = 360 $, but $ 39×19 = 741 $. They're completely different values.

Q: How do I know (40-1)×(20-1) is correct?

Substitute the values: $ (40-1) = 39 $ and $ (20-1) = 19 $, so we get $ 39×19 $ - exactly what we started with!

Q: Do I need to follow order of operations for all options?

Absolutely! Always do operations inside parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right.

Q: Can I use the distributive property to check my work?

Yes! For option C: $ (40-1)×(20-1) = 40×20 - 40×1 - 1×20 + 1×1 = 800-40-20+1 = 741 $. This confirms our answer!

Expression Equivalence with Factored Forms

Which equation is the same as the following?

$39\times19$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the expression representing the correct factorization of the exercise

00:03 Let's use the distributive law

00:06 Let's factor 39 into 40 minus 1

00:09 Let's factor 19 into 20 minus 1

00:12 And this is the solution to the question

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?

$39\times19$

Step-by-step solution

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

$(30×9)+(10×9)= 270+90$

$(30+9)×(10×9)= 39×90$

$(40-1)×(20-1)= 39×19$

$(40-1)+(20×1)= 39+20$

Therefore, the answer is option C.

Final Answer

$(40-1)\times(20-1)$

Key Points to Remember

Essential concepts to master this topic

Equivalence Rule: Two expressions are equal if they produce the same value
Technique: Use (40-1)×(19-1) = 39×19 by substitution
Check: Calculate each option to verify: 39×19 = 741 ✓

Common Mistakes

Avoid these frequent errors

Assuming expressions look equivalent without calculating
Don't think (30×9)+(10×9) equals 39×19 just because it uses the same digits = 360, not 741! Visual similarity doesn't guarantee mathematical equality. Always calculate the actual value of each expression to verify equivalence.

Practice Quiz

Test your knowledge with interactive questions

$12:(2\times2)=$

FAQ

Everything you need to know about this question

Why doesn't (30×9)+(10×9) equal 39×19?

Because addition and multiplication follow different rules! $(30×9)+(10×9) = 270+90 = 360$ , but $39×19 = 741$ . They're completely different values.

How do I know (40-1)×(20-1) is correct?

Substitute the values: $(40-1) = 39$ and $(20-1) = 19$ , so we get $39×19$ - exactly what we started with!

Do I need to follow order of operations for all options?

Absolutely! Always do operations inside parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right.

What if two options give the same answer?

That would mean both are equivalent to the original expression! But in this problem, only option C gives $39×19 = 741$ .

Can I use the distributive property to check my work?

Yes! For option C: $(40-1)×(20-1) = 40×20 - 40×1 - 1×20 + 1×1 = 800-40-20+1 = 741$ . This confirms our answer!

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