Solve the Division Problem: 200 ÷ 40

Q: Why can't I just divide 200 by 40 directly?

You absolutely can! $ 200 ÷ 40 = 5 $ directly. The method shown uses fraction simplification to teach the concept that $ \frac{200}{40} $ and division mean the same thing.

Q: How do I find the greatest common divisor quickly?

Look for the largest number that divides evenly into both numbers. Since 40 goes into 200 exactly 5 times with no remainder, 40 is the GCD here.

Q: What if the numbers don't divide evenly?

Then you'll get a remainder or decimal answer. For example: $ 200 ÷ 30 = 6.67 $ or $ 6\frac{2}{3} $. Both forms are correct!

Q: Is there a faster way to solve this?

Yes! Since both 200 and 40 end in zero, you can cancel the zeros first: $ \frac{200}{40} = \frac{20}{4} = 5 $. This makes the division easier.

Q: Why does the explanation use 40 as the common divisor?

Because 40 is the greatest common divisor of 200 and 40. Using the largest possible divisor gives us the simplest form in one step rather than multiple steps.

Division Operations with Simplification Methods

Solve the following expression:

$\frac{200}{40}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$\frac{200}{40}=$

Step-by-step solution

First we will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 40.

Then we will divide the fraction as follows:

$\frac{200:40}{40:40}=\frac{5}{1}=5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both numerator and denominator by their greatest common divisor
Technique: Find GCD of 200 and 40, which is 40: $\frac{200÷40}{40÷40} = \frac{5}{1}$
Check: Verify by multiplication: 5 × 40 = 200 ✓

Common Mistakes

Avoid these frequent errors

Dividing only the numerator or denominator
Don't divide just 200 by 40 to get 5/40 = wrong answer! This creates an unequal fraction that doesn't represent the original value. Always divide both the numerator AND denominator by the same number to maintain equality.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why can't I just divide 200 by 40 directly?

You absolutely can! $200 ÷ 40 = 5$ directly. The method shown uses fraction simplification to teach the concept that $\frac{200}{40}$ and division mean the same thing.

How do I find the greatest common divisor quickly?

Look for the largest number that divides evenly into both numbers. Since 40 goes into 200 exactly 5 times with no remainder, 40 is the GCD here.

What if the numbers don't divide evenly?

Then you'll get a remainder or decimal answer. For example: $200 ÷ 30 = 6.67$ or $6\frac{2}{3}$ . Both forms are correct!

Is there a faster way to solve this?

Yes! Since both 200 and 40 end in zero, you can cancel the zeros first: $\frac{200}{40} = \frac{20}{4} = 5$ . This makes the division easier.

Why does the explanation use 40 as the common divisor?

Because 40 is the greatest common divisor of 200 and 40. Using the largest possible divisor gives us the simplest form in one step rather than multiple steps.

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