Solve the Division Equation: Finding the Number That Equals 0 When Divided by 5

Q: Why can't any other number work besides 0?

Think about it: if you divide any positive number by 5, you get a positive result. If you divide any negative number by 5, you get a negative result. Only zero divided by 5 gives exactly zero!

Q: What's the difference between 0÷5 and 5÷0?

0÷5 = 0 (zero divided by any nonzero number equals zero). But 5÷0 is undefined - you cannot divide by zero in mathematics! Always keep the dividend and divisor straight.

Q: How do I solve division equations like this?

Use inverse operations! Since division and multiplication are opposites, multiply both sides by the divisor. So $ x ÷ 5 = 0 $ becomes $ x = 0 × 5 = 0 $.

Q: Can I use this method for any division equation?

Yes! For any equation like $ x ÷ a = b $, multiply both sides by a to get $ x = b × a $. This works because multiplication undoes division.

Q: What if the divisor was negative?

The same rule applies! Zero divided by any nonzero number equals zero, whether positive or negative. So $ 0 ÷ (-5) = 0 $ too.

Division Properties with Zero Quotients

$?:5=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Found the missing one

00:03 0 divided by any number is always equal to 0

00:08 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$?:5=0$

Step-by-step solution

To solve this problem, we follow the steps outlined below:

Step 1: Understand that we need a number $x$ such that dividing it by 5 gives us 0, i.e., $\frac{x}{5} = 0$ .
Step 2: Recognizing division, we apply its inverse operation by multiplying both sides of the equation by 5. This yields $x = 5 \times 0$ .
Step 3: Compute the right side of the equation: $5 \times 0 = 0$ .

Thus, the number we are looking for is 0. This number makes the equation true, since $\frac{0}{5} = 0$ .

Thus, we conclude that the solution to the equation $?:5=0$ is $0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division Rule: Only zero divided by any nonzero number equals zero
Technique: Use inverse operations: multiply both sides by the divisor
Check: Substitute back into original equation: $0 ÷ 5 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Confusing zero as divisor versus dividend
Don't think any number divided by zero equals zero = undefined result! Division by zero is impossible in mathematics. Always remember: only zero divided by a nonzero number equals zero.

Practice Quiz

Test your knowledge with interactive questions

$$ 2+0= $$

FAQ

Everything you need to know about this question

Why can't any other number work besides 0?

Think about it: if you divide any positive number by 5, you get a positive result. If you divide any negative number by 5, you get a negative result. Only zero divided by 5 gives exactly zero!

What's the difference between 0÷5 and 5÷0?

0÷5 = 0 (zero divided by any nonzero number equals zero). But 5÷0 is undefined - you cannot divide by zero in mathematics! Always keep the dividend and divisor straight.

How do I solve division equations like this?

Use inverse operations! Since division and multiplication are opposites, multiply both sides by the divisor. So $x ÷ 5 = 0$ becomes $x = 0 × 5 = 0$ .

Can I use this method for any division equation?

Yes! For any equation like $x ÷ a = b$ , multiply both sides by a to get $x = b × a$ . This works because multiplication undoes division.

What if the divisor was negative?

The same rule applies! Zero divided by any nonzero number equals zero, whether positive or negative. So $0 ÷ (-5) = 0$ too.

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