Solve the Division Problem: 72 ÷ 6

Q: Why split 72 into 60 + 12 instead of other combinations?

Because both 60 and 12 divide evenly by 6! We chose numbers that make the mental math easier: $ 60 ÷ 6 = 10 $ and $ 12 ÷ 6 = 2 $.

Q: Can I split 72 differently, like 36 + 36?

Absolutely! You could use $ 72 = 36 + 36 $, so $ (36 + 36) ÷ 6 = 6 + 6 = 12 $. The key is choosing numbers that divide easily by 6.

Q: How do I check if 12 is really the right answer?

Multiply your answer by the divisor: $ 12 × 6 = 72 $. If you get back to the original number (72), your division is correct!

Q: Is this method faster than long division?

For many problems, yes! When you can split numbers into friendly parts, mental math with the distributive property is often quicker and less error-prone than long division.

Division with Distributive Property Application

Solve the following division exercise:

$72:6=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this problem together.

00:10 We'll use the distributive law. Watch closely.

00:14 We'll split seventy-two into sixty, plus twelve.

00:18 Divide each part inside the parentheses by the outer number, then add them up.

00:24 Calculate each division carefully, then sum them.

00:29 And that's how we find the answer to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following division exercise:

$72:6=$

Step-by-step solution

Apply the distributive property of division and proceed to split the number 72 into the sum of 60 and 12. Simplifying the division operation allows us to solve the exercise without a calculator

Reminder - The distributive property of division 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

$(60+12):6=$

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

$(60:6)+(12:6)=$

Continue to solve according to the order of operations

$10+2=12$

Therefore the answer is option A - 12.

Shown below are the various steps of the solution:

$72:6=(60+12):6=60:6+12:6=10+2=12$

Final Answer

$12$

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Split larger numbers into smaller, easier parts
Technique: Break 72 into 60 + 12, then divide each part by 6
Check: Verify 12 × 6 = 72 to confirm the answer ✓

Common Mistakes

Avoid these frequent errors

Guessing without using the distributive property
Don't randomly try numbers like 16 or 11 without showing work = wrong answers and no learning! This wastes time and doesn't build math skills. Always break the dividend into friendly numbers that divide evenly.

Practice Quiz

Test your knowledge with interactive questions

$$ 140-70= $$

FAQ

Everything you need to know about this question

Why split 72 into 60 + 12 instead of other combinations?

Because both 60 and 12 divide evenly by 6! We chose numbers that make the mental math easier: $60 ÷ 6 = 10$ and $12 ÷ 6 = 2$ .

Can I split 72 differently, like 36 + 36?

Absolutely! You could use $72 = 36 + 36$ , so $(36 + 36) ÷ 6 = 6 + 6 = 12$ . The key is choosing numbers that divide easily by 6.

What if I don't know my multiplication tables well?

The distributive property helps with this! Break numbers into multiples of 10 when possible. For example, 60 ÷ 6 is easier because 6 × 10 = 60.

How do I check if 12 is really the right answer?

Multiply your answer by the divisor: $12 × 6 = 72$ . If you get back to the original number (72), your division is correct!

Is this method faster than long division?

For many problems, yes! When you can split numbers into friendly parts, mental math with the distributive property is often quicker and less error-prone than long division.

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