Solve the Division Problem: 186÷6 Step by Step

Q: Why split 186 into 180 + 6 specifically?

We choose numbers that are easily divisible by 6! Since $ 180 \div 6 = 30 $ and $ 6 \div 6 = 1 $, we can solve this mentally without long division.

Q: Can I split 186 into different numbers?

Yes! You could use $ 186 = 120 + 60 + 6 $ or other combinations. The key is choosing numbers that divide evenly by 6 to make calculation easier.

Q: What if the division doesn't work out evenly?

If there's a true remainder, you'll get a mixed number or decimal. But for $ 186 \div 6 $, it divides evenly to give exactly 31!

Q: Is this faster than long division?

For mental math, absolutely! The distributive property lets you use facts you already know (like $ 180 \div 6 = 30 $) instead of working through long division steps.

Q: How do I know my split is correct?

Check that your parts add back to the original: $ 180 + 6 = 186 $ ✓. Then verify each part divides evenly by your divisor.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem step by step.

00:09 First, we'll use the distributive law.

00:12 We'll break down 180 into a hundred-eighty and six.

00:17 Next, divide each number in parentheses by the outer number, then add them.

00:22 Calculate each division separately, and then sum the results.

00:27 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the following problem:

$186:6=$

2

Step-by-step solution

Apply the distributive property of division and proceed to split the number 186 into the sum of 180 and 6. This ultimately makes the division operation easier and allows us to solve the exercise without a calculator

Reminder - The distributive property of division actually allows us to split the larger number in a division problem into a sum or difference of smaller numbers, which makes the division operation easier and allows us to solve the exercise without a calculator

$(180+6):6=$

Apply the formula of the distributive property $(a+b):c=a:c+b:c$

$180:6+6:6=$

Continue to solve the problem according to the order of operations

$30+1=31$

Therefore the answer is option D - 31.

Below are the various steps of our solution:

$186:6= (180+6):6= 180:6+6:6= 30+1=31$

3

Final Answer

$31$

Key Points to Remember

Essential concepts to master this topic

Rule: Break dividend into sum of numbers divisible by divisor
Technique: $186 = 180 + 6$ since both divide evenly by 6
Check: Multiply answer back: $31 \times 6 = 186$ ✓

Common Mistakes

Avoid these frequent errors

Adding remainders incorrectly in long division
Don't just divide 186÷6 and write 30 remainder 6 as your final answer = gives wrong mixed number 30⅙! This ignores that 6÷6=1. Always complete the division of any remainder to get the whole number answer.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why split 186 into 180 + 6 specifically?

+

We choose numbers that are easily divisible by 6! Since $180 \div 6 = 30$ and $6 \div 6 = 1$ , we can solve this mentally without long division.

Can I split 186 into different numbers?

+

Yes! You could use $186 = 120 + 60 + 6$ or other combinations. The key is choosing numbers that divide evenly by 6 to make calculation easier.

What if the division doesn't work out evenly?

+

If there's a true remainder, you'll get a mixed number or decimal. But for $186 \div 6$ , it divides evenly to give exactly 31!

Is this faster than long division?

+

For mental math, absolutely! The distributive property lets you use facts you already know (like $180 \div 6 = 30$ ) instead of working through long division steps.

How do I know my split is correct?

+

Check that your parts add back to the original: $180 + 6 = 186$ ✓. Then verify each part divides evenly by your divisor.

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Solve the Division Problem: 186÷6 Step by Step

Division with Distributive Property

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