Solve 13 × 8: Step-by-Step Multiplication Problem

Q: Why use the distributive property instead of regular multiplication?

The distributive property breaks hard multiplications into easier ones! Instead of memorizing $ 13 \times 8 $, you can use facts you already know like $ 13 \times 10 = 130 $.

Q: How do I know whether to use addition or subtraction?

Look at how you break down the number! If you write $ 8 = 10 - 2 $, then use subtraction. If you write $ 8 = 5 + 3 $, then use addition.

Q: Can I break down 13 instead of 8?

Absolutely! You could write $ 13 \times 8 = (10 + 3) \times 8 = 80 + 24 = 104 $. Choose whichever breakdown feels easier to you!

Q: What if I get confused with the signs?

Remember: whatever operation is inside the parentheses stays the same when you distribute. $ a \times (b - c) = a \times b - a \times c $, not plus!

Q: Is there a faster way to check my answer?

Yes! Use the standard algorithm or try a different breakdown. For example: $ 13 \times 8 = 13 \times (4 + 4) = 52 + 52 = 104 $ ✓

Distributive Property with Two-Digit Multiplication

Solve the following problem:

$13\times8=$

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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

00:07 Let's break down 8 to 10 minus 2

00:10 Make sure to multiply the outer term by each term in parentheses

00:19 Solve each multiplication separately and then subtract

00:27 Let's use long subtraction

00:38 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

Solve the following problem:

$13\times8=$

Step-by-step solution

Apply the distributive property of multiplication in order to break down the number 13 into a subtraction exercise with smaller numbers. This allows us to work with smaller numbers and ultimately simplify the operation

Reminder - The distributive property of multiplication actually allows us to break down the larger term in the multiplication exercise into a sum or difference of smaller numbers, which makes the multiplication operation easier and gives us the ability to solve the exercise even without a calculator

$13\times(10-2)=$

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

$13\times10-13\times2=$

Proceed to solve the problem according to the order of operations

$130-26=$

Therefore the answer is option D - 104.

Shown below are the various stages of the solution:

$13\times8=13\times(10-2)=13\times10-13\times2=130-26=104$

Final Answer

$104$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Break larger numbers into sums or differences for easier calculation
Technique: Rewrite $13 \times 8 = 13 \times (10-2)$ to simplify multiplication
Check: Verify $130 - 26 = 104$ by standard multiplication method ✓

Common Mistakes

Avoid these frequent errors

Incorrectly applying the distributive property
Don't write $13 \times (10-2) = 13 \times 10 + 13 \times 2 = 130 + 26 = 156$ ! This changes subtraction to addition and gives the wrong answer. Always keep the same operation: $13 \times (10-2) = 13 \times 10 - 13 \times 2$ .

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why use the distributive property instead of regular multiplication?

The distributive property breaks hard multiplications into easier ones! Instead of memorizing $13 \times 8$ , you can use facts you already know like $13 \times 10 = 130$ .

How do I know whether to use addition or subtraction?

Look at how you break down the number! If you write $8 = 10 - 2$ , then use subtraction. If you write $8 = 5 + 3$ , then use addition.

Can I break down 13 instead of 8?

Absolutely! You could write $13 \times 8 = (10 + 3) \times 8 = 80 + 24 = 104$ . Choose whichever breakdown feels easier to you!

What if I get confused with the signs?

Remember: whatever operation is inside the parentheses stays the same when you distribute. $a \times (b - c) = a \times b - a \times c$ , not plus!

Is there a faster way to check my answer?

Yes! Use the standard algorithm or try a different breakdown. For example: $13 \times 8 = 13 \times (4 + 4) = 52 + 52 = 104$ ✓

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