Calculate the Product: Solving 97 × 12 Step by Step

Q: Why split 12 into 10 + 2 instead of other combinations?

Multiples of 10 are easiest to work with! When you multiply by 10, you just add a zero. Other splits like 6 + 6 or 8 + 4 make the math harder.

Q: Can I split the 97 instead of the 12?

Absolutely! You could split 97 into 90 + 7 and calculate $ (90 + 7) × 12 $. The distributive property works both ways, so choose whichever feels easier.

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

That's why we check our work step by step! If $ 97 × 2 $ doesn't equal 194, go back and recalculate. Breaking problems into steps makes errors easier to find and fix.

Q: Is this method faster than regular multiplication?

It depends on your comfort level! This method helps you understand what multiplication really means and works great without a calculator. With practice, both methods become quick.

Q: Do I always have to show every single step like this?

For homework and tests, yes - showing steps proves you understand the concept! Once you master it, you can do some mental shortcuts, but the thinking process stays the same.

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 12 into 10 plus 2

00:11 Multiply the outer term by each term in parentheses

00:14 Calculate each product separately and then sum

00:17 Let's use long multiplication

00:25 Let's use long addition

00:28 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:

$97\times12=$

2

Step-by-step solution

Apply the distributive property of multiplication and proceed to split the number 12 that we obtained into a sum of 10 and 2. This allows us to work with smaller numbers and simplify the operation

Reminder - The distributive property of multiplication actually 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

$97×(10+2)=$

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

$97×10+97×2=$

Solve according to the order of operations

$970+97×2=$

Apply the distributive property of multiplication again and split the number 97 into a sum of 90 and 7. This allows us to work with smaller numbers and simplify the operation

$970+2×(90+7)=$

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

$970+90×2+7×2=$

Solve the problem according to the order of operations

$970+180+14=$

$1150+14=1164$

Therefore the answer is option C - 1164.

Shown below are the various steps of the solution:
$97×12= 97×(10+2)= 97×10+97×2= 970+(90+7)×2= 970+90×2+7×2= 970+180+14= 1150+14=1164$

3

Final Answer

$1164$

Key Points to Remember

Essential concepts to master this topic

Rule: Break larger numbers into sums using distributive property
Technique: Split 12 into 10 + 2, so 97 × 12 = 97 × (10 + 2)
Check: Verify 970 + 194 = 1164 by adding step by step ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply distributive property to all terms
Don't just multiply 97 × 10 and forget the second part = incomplete answer! This gives you only 970 instead of the full 1164. Always multiply by each term in the sum: 97 × 10 AND 97 × 2.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why split 12 into 10 + 2 instead of other combinations?

+

Multiples of 10 are easiest to work with! When you multiply by 10, you just add a zero. Other splits like 6 + 6 or 8 + 4 make the math harder.

Can I split the 97 instead of the 12?

+

Absolutely! You could split 97 into 90 + 7 and calculate $(90 + 7) × 12$ . The distributive property works both ways, so choose whichever feels easier.

What if I make an error in one of the smaller multiplications?

+

That's why we check our work step by step! If $97 × 2$ doesn't equal 194, go back and recalculate. Breaking problems into steps makes errors easier to find and fix.

Is this method faster than regular multiplication?

+

It depends on your comfort level! This method helps you understand what multiplication really means and works great without a calculator. With practice, both methods become quick.

Do I always have to show every single step like this?

+

For homework and tests, yes - showing steps proves you understand the concept! Once you master it, you can do some mental shortcuts, but the thinking process stays the same.

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Calculate the Product: Solving 97 × 12 Step by Step

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