Solve the Multiplication Problem: Calculate 17 × 7

Q: Why split 17 into 10 + 7 instead of other combinations?

Splitting into 10 + 7 uses our base-10 number system! Multiplying by 10 is easy (just add a zero), making $ 10 \times 7 = 70 $ simple to calculate mentally.

Q: Can I use the distributive property with the 7 instead?

Yes! You could write $ 17 \times (5+2) = 17 \times 5 + 17 \times 2 = 85 + 34 = 119 $. Both methods work, but breaking down the larger number is usually easier.

Q: What if I forget the distributive property formula?

Think of it as sharing multiplication! When you have $ (a+b) \times c $, you're giving both parts inside the parentheses a turn to multiply by c.

Q: How do I know which number to break down?

Usually break down the larger number or the one that's harder to work with. In this case, 17 is more complex than 7, so we split 17 into simpler parts.

Q: What if I get different products when I distribute?

Double-check that you're multiplying correctly! $ 10 \times 7 = 70 $ and $ 7 \times 7 = 49 $. If your products are wrong, your final answer will be wrong too.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use the distributive law

00:07 Let's break down 17 into 10 plus 7

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

00:15 Solve each multiplication separately and then add

00:21 We'll use long addition

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following problem:

$17\times7=$

2

Step-by-step solution

Apply the distributive property of multiplication in order to split the number 17 into the sum of numbers 10 and 7. This ultimately 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 even without a calculator

$(10+7)\times7=$

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

$10\times7+7\times7=$

Proceed to solve according to the order of operations

$70+49=$

Therefore the answer is option C - 119.

Shown below are the various stages of the solution

$17\times7=(10+7)\times7=(10\times7)+(7\times7)=70+49=119$

3

Final Answer

$119$

Key Points to Remember

Essential concepts to master this topic

Rule: Break larger numbers into sums for easier multiplication
Technique: Use $17 \times 7 = (10+7) \times 7 = 70 + 49$
Check: Count by 17s seven times: 17, 34, 51, 68, 85, 102, 119 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying the distributed terms
Don't calculate 10 × 7 + 7 × 7 as 10 + 7 + 7 + 7 = 31! This confuses addition with multiplication and gives a drastically wrong answer. Always multiply each part: 10 × 7 = 70 and 7 × 7 = 49, then add the products.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why split 17 into 10 + 7 instead of other combinations?

+

Splitting into 10 + 7 uses our base-10 number system! Multiplying by 10 is easy (just add a zero), making $10 \times 7 = 70$ simple to calculate mentally.

Can I use the distributive property with the 7 instead?

+

Yes! You could write $17 \times (5+2) = 17 \times 5 + 17 \times 2 = 85 + 34 = 119$ . Both methods work, but breaking down the larger number is usually easier.

What if I forget the distributive property formula?

+

Think of it as sharing multiplication! When you have $(a+b) \times c$ , you're giving both parts inside the parentheses a turn to multiply by c.

How do I know which number to break down?

+

Usually break down the larger number or the one that's harder to work with. In this case, 17 is more complex than 7, so we split 17 into simpler parts.

Is there a faster way than using distributive property?

+

You could memorize multiplication tables or use a calculator, but the distributive property helps you understand multiplication and work with numbers you haven't memorized yet!

What if I get different products when I distribute?

+

Double-check that you're multiplying correctly! $10 \times 7 = 70$ and $7 \times 7 = 49$ . If your products are wrong, your final answer will be wrong too.

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