Solve the Ratio Equation: Finding the Missing Value in 10:? = 10

Q: What does the colon symbol mean in math?

The colon : symbol means division. So $ 10 : ? $ is the same as $ 10 ÷ ? $. It's just another way to write division!

Q: Why isn't the answer 10 since that's what we're dividing by?

That's a common mix-up! We're not dividing by 10. We're dividing 10 by some unknown number to get 10 as the result. Think: what number makes 10 ÷ ? = 10?

Q: How can I remember that dividing by 1 gives the same number?

Think of sharing! If you have 10 cookies and share them among 1 person (yourself), you still have all 10 cookies. That's why $ 10 ÷ 1 = 10 $.

Q: Are there other numbers that work besides 1?

No! Only 1 works. Try any other number: $ 10 ÷ 2 = 5 $, $ 10 ÷ 5 = 2 $. None of these equal 10, so 1 is the only solution.

Q: What if the equation was 10:? = 5 instead?

Then you'd solve $ 10 ÷ ? = 5 $. Since $ 10 ÷ 2 = 5 $, the answer would be 2. Always think: what do I divide the first number by to get the result?

Division Identity with Ratio Notation

$10:?=10$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Any number divided by 1 is always equal to itself

00:12 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

$10:?=10$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given equation as $10 : ? = 10$ .
Step 2: Understand that we need to determine what number the question mark represents.
Step 3: Apply the property of division: dividing any non-zero number by 1 returns the original number.
Step 4: Conclude that since $10 \div 1 = 10$ , replacing the question mark with 1 satisfies the equation.

Now, let's work through each step:

The equation is $10 : ? = 10$ . The expression $10 : 1 = 10$ helps us recognize that the number we divide 10 by to still get 10 is 1. Using the division identity property, dividing by 1 yields the numerator itself (>i.e.< 10).

Thus, the solution to the problem is that the question mark represents the number $1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Any number divided by 1 equals itself
Technique: Replace colon with division: 10 ÷ ? = 10
Check: Substitute back: 10 ÷ 1 = 10 ✓

Common Mistakes

Avoid these frequent errors

Assuming the missing value equals the result
Don't think 10 ÷ ? = 10 means ? = 10! This gives 10 ÷ 10 = 1, not 10. Always remember that dividing by 1 keeps the original number unchanged.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

What does the colon symbol mean in math?

The colon : symbol means division. So $10 : ?$ is the same as $10 ÷ ?$ . It's just another way to write division!

Why isn't the answer 10 since that's what we're dividing by?

That's a common mix-up! We're not dividing by 10. We're dividing 10 by some unknown number to get 10 as the result. Think: what number makes 10 ÷ ? = 10?

How can I remember that dividing by 1 gives the same number?

Think of sharing! If you have 10 cookies and share them among 1 person (yourself), you still have all 10 cookies. That's why $10 ÷ 1 = 10$ .

Are there other numbers that work besides 1?

No! Only 1 works. Try any other number: $10 ÷ 2 = 5$ , $10 ÷ 5 = 2$ . None of these equal 10, so 1 is the only solution.

What if the equation was 10:? = 5 instead?

Then you'd solve $10 ÷ ? = 5$ . Since $10 ÷ 2 = 5$ , the answer would be 2. Always think: what do I divide the first number by to get the result?

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