Calculate the Product: Solving 101 × 17 Step by Step

Q: Why break 101 into 100+1 instead of just multiplying directly?

Breaking 101 into 100+1 makes mental math much easier! Multiplying by 100 is simple (just add two zeros), and multiplying by 1 is even easier. This strategy works great for numbers close to round numbers like 100.

Q: Can I break down 17 instead of 101?

Absolutely! You could write 17 as (10+7) and calculate: $ 101×(10+7) = (101×10) + (101×7) = 1010 + 707 = 1717 $. Choose whichever breakdown feels easier!

Q: What if I get confused about which numbers to multiply?

Draw it out! Write $ (100+1)×17 $ and draw arrows from 17 to each term in parentheses. This helps you remember to multiply both 100×17 and 1×17.

Q: How do I know if 1,717 is reasonable?

Do a quick estimate: 101 is about 100, so 100×17 = 1,700. Since 101 is slightly bigger than 100, your answer should be slightly bigger than 1,700. The answer 1,717 makes perfect sense!

Q: Is there a faster way than the distributive property?

You can use standard multiplication (stacking the numbers), but the distributive property is often faster for mental math. Try both methods and see which one you prefer!

Q: What other numbers work well with this strategy?

This works great with numbers near round numbers! Try 99×25 as (100-1)×25, or 203×15 as (200+3)×15. Look for numbers close to 10, 100, 1000, etc.

Multiplication with Distributive Property

Solve the following problem:

$101\times17=$

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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 distribution law

00:07 Break down 101 into 100 plus 1

00:09 Make sure to multiply the outer term by each term in parentheses

00:16 Solve each multiplication separately and then sum up

00:20 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:

$101\times17=$

Step-by-step solution

In order to render the process easier for ourselves, we will use the distributive property over 101:

$(100+1)\times17=$

We will multiply 17 by each of the terms in parentheses:

$(100\times17)+(1\times17)=$

Let's solve the expressions in parentheses:

$1,700+17=1,717$

Final Answer

$1717$

Key Points to Remember

Essential concepts to master this topic

Rule: Break down numbers using distributive property for easier calculation
Technique: Split 101 as (100+1), then multiply: 100×17 = 1,700
Check: Verify final result: 1,700 + 17 = 1,717 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying when using distributive property
Don't calculate (100+1)×17 as 100+1+17 = 118! This completely ignores multiplication and gives a tiny wrong answer. Always multiply each term: (100×17) + (1×17) = 1,717.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why break 101 into 100+1 instead of just multiplying directly?

Breaking 101 into 100+1 makes mental math much easier! Multiplying by 100 is simple (just add two zeros), and multiplying by 1 is even easier. This strategy works great for numbers close to round numbers like 100.

Can I break down 17 instead of 101?

Absolutely! You could write 17 as (10+7) and calculate: $101×(10+7) = (101×10) + (101×7) = 1010 + 707 = 1717$ . Choose whichever breakdown feels easier!

What if I get confused about which numbers to multiply?

Draw it out! Write $(100+1)×17$ and draw arrows from 17 to each term in parentheses. This helps you remember to multiply both 100×17 and 1×17.

How do I know if 1,717 is reasonable?

Do a quick estimate: 101 is about 100, so 100×17 = 1,700. Since 101 is slightly bigger than 100, your answer should be slightly bigger than 1,700. The answer 1,717 makes perfect sense!

Is there a faster way than the distributive property?

You can use standard multiplication (stacking the numbers), but the distributive property is often faster for mental math. Try both methods and see which one you prefer!

What other numbers work well with this strategy?

This works great with numbers near round numbers! Try 99×25 as (100-1)×25, or 203×15 as (200+3)×15. Look for numbers close to 10, 100, 1000, etc.

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