Solve the Ratio Equation: Finding the Missing Value in 50:? = 50

Q: Why isn't the answer 50 since both sides equal 50?

The 50 on the right is the result of the division, not the missing divisor! Think of it as: "50 divided by what number gives me 50?" Only dividing by 1 keeps the number unchanged.

Q: How do I convert ratio notation to division?

The colon (:) means "divided by". So $ 50:? $ becomes $ \frac{50}{?} $. The first number is the dividend, the second is the divisor.

Q: What's the identity property of division?

The identity property states that any number divided by 1 equals itself. For example: $ \frac{7}{1} = 7 $, $ \frac{100}{1} = 100 $, and $ \frac{50}{1} = 50 $.

Q: Can I solve this by cross-multiplying?

Yes! Rewrite as $ \frac{50}{?} = \frac{50}{1} $, then cross-multiply: $ 50 \times 1 = 50 \times ? $. This gives $ 50 = 50? $, so $ ? = 1 $.

Q: How can I check if 1 is really correct?

Substitute back into the original: $ 50:1 = \frac{50}{1} = 50 $ ✓. Since both sides equal 50, our answer is correct!

Division Properties with Identity Operations

$50:?=50$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve the mystery of the unknown number.

00:07 Remember, any number divided by one is just the number itself.

00:13 And that's how we find the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$50:?=50$

Step-by-step solution

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

Step 1: Identify that this is a division problem, with the result already given as 50.
Step 2: Apply the identity property of division, which states that dividing any number by 1 results in the number itself.
Step 3: Recognize that since $\frac{50}{x} = 50$ , the only value for $x$ that makes this true is 1.

Now, let's work through each step:
Step 1: We are given $50 : ? = 50$ , which is equivalent to finding a number $x$ such that $\frac{50}{x} = 50$ .
Step 2: According to division properties, the only number we can divide 50 by to still get 50 is 1.
Step 3: Therefore, the unknown divisor must be 1.

Hence, the solution to the problem is that the missing number is $x = 1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Property: Any number divided by 1 equals itself
Technique: Rewrite $50:? = 50$ as $\frac{50}{?} = 50$
Check: Substitute answer back: $\frac{50}{1} = 50$ ✓

Common Mistakes

Avoid these frequent errors

Thinking the missing value equals the dividend
Don't assume the answer is 50 because both sides equal 50 = wrong logic! This ignores how division works. Always think: what number makes $\frac{50}{?} = 50$ true?

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why isn't the answer 50 since both sides equal 50?

The 50 on the right is the result of the division, not the missing divisor! Think of it as: "50 divided by what number gives me 50?" Only dividing by 1 keeps the number unchanged.

How do I convert ratio notation to division?

The colon (:) means "divided by". So $50:?$ becomes $\frac{50}{?}$ . The first number is the dividend, the second is the divisor.

What's the identity property of division?

The identity property states that any number divided by 1 equals itself. For example: $\frac{7}{1} = 7$ , $\frac{100}{1} = 100$ , and $\frac{50}{1} = 50$ .

Can I solve this by cross-multiplying?

Yes! Rewrite as $\frac{50}{?} = \frac{50}{1}$ , then cross-multiply: $50 \times 1 = 50 \times ?$ . This gives $50 = 50?$ , so $? = 1$ .

How can I check if 1 is really correct?

Substitute back into the original: $50:1 = \frac{50}{1} = 50$ ✓. Since both sides equal 50, our answer is correct!

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