Solve the Multiplication Problem: Calculate 3×36

Q: Why break 36 into 30 + 6 instead of other combinations?

Breaking into multiples of 10 makes mental math easier! $ 3 \times 30 = 90 $ is simple to calculate, and $ 3 \times 6 = 18 $ is a basic multiplication fact.

Q: Can I use the distributive property for any multiplication?

Yes! The distributive property works for all multiplication problems. It's especially helpful when one number is large or ends in digits that are hard to multiply directly.

Q: What if I make an error in the smaller multiplications?

Double-check each step! Verify that $ 3 \times 30 = 90 $ and $ 3 \times 6 = 18 $ before adding them together.

Q: Is there a faster way to solve 3×36?

You could memorize the multiplication table, but the distributive property helps you understand why the answer is 108 and builds stronger number sense!

Q: How do I know I applied the distributive property correctly?

Make sure you multiply (not add) the outside number by each part inside the parentheses: $ 3 \times (30+6) = (3 \times 30) + (3 \times 6) $.

Distributive Property with Two-Digit Multiplication

Solve the following problem:

$3\times36=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together!

00:08 We will use the distributive law.

00:12 First, break down thirty-six into thirty plus six.

00:17 Next, multiply the outer factor by each term in parentheses.

00:22 Calculate each multiplication separately, then add them together.

00:26 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$3\times36=$

Step-by-step solution

Apply the distributive property of multiplication and proceed to split the number 36 into the sum of the numbers 30 and 6. This allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication essentially allows us to split the larger term in a multiplication problem into a sum or difference of smaller numbers, which makes multiplication easier and gives us the ability to solve the problem without a calculator

$3×(30+6)=$

Apply the distributive property formula $a(b+c)=ab+ac$

$3×30+3×6=$

Proceed to solve the problem according to the order of operations

$90+18= 108$

Therefore the answer is option D - 108.

Shown below are the various stages of our solution:

$3\times36=3\times(30+6)=(3\times30)+(3\times6)=90+18=108$

Final Answer

$108$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Break larger numbers into smaller, easier parts
Technique: Split 36 into 30 + 6, then calculate 3×30 + 3×6
Check: Verify 90 + 18 = 108 matches original calculation ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying when using distributive property
Don't write 3×36 = 3+30+3+6 = 42! This completely ignores multiplication and just adds all numbers together. Always multiply each part: 3×(30+6) = (3×30) + (3×6) = 90 + 18 = 108.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why break 36 into 30 + 6 instead of other combinations?

Breaking into multiples of 10 makes mental math easier! $3 \times 30 = 90$ is simple to calculate, and $3 \times 6 = 18$ is a basic multiplication fact.

Can I use the distributive property for any multiplication?

Yes! The distributive property works for all multiplication problems. It's especially helpful when one number is large or ends in digits that are hard to multiply directly.

What if I make an error in the smaller multiplications?

Double-check each step! Verify that $3 \times 30 = 90$ and $3 \times 6 = 18$ before adding them together.

Is there a faster way to solve 3×36?

You could memorize the multiplication table, but the distributive property helps you understand why the answer is 108 and builds stronger number sense!

How do I know I applied the distributive property correctly?

Make sure you multiply (not add) the outside number by each part inside the parentheses: $3 \times (30+6) = (3 \times 30) + (3 \times 6)$ .

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