Solve the Ratio Equation: Finding the Missing Number in 20:?=1

Q: What does the colon symbol (:) mean in math?

The colon (:) is another way to write division! So $ 20:a $ means exactly the same as $ 20 ÷ a $ or $ \frac{20}{a} $.

Q: Why can't the answer be 1 or 10?

Let's check: $ 20:1 = 20 $ (not 1), and $ 20:10 = 2 $ (not 1). Only when we divide 20 by 20 itself do we get 1!

Q: Is there a quick way to solve this type of problem?

Yes! When you see $ x:? = 1 $, the missing number is always x itself. This uses the property that any number divided by itself equals 1.

Q: What if the number was 0 instead of 20?

Great question! We can't divide by zero, so $ 0:0 $ is undefined in mathematics. This property only works for non-zero numbers.

Q: Can I write this as a regular division problem?

Absolutely! $ 20:a = 1 $ is the same as asking "What number divided into 20 gives 1?" The answer is still 20.

Division Operations with Self-Division Property

$20:?=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the unknown together.

00:07 Remember, any number divided by itself is always 1.

00:13 And that's how we solve the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$20:?=1$

Step-by-step solution

To solve this problem, we'll determine the number $a$ such that $20 : a = 1$ .

By definition of division, for the expression $20 : a = 1$ to hold true, $a$ must be equal to the dividend when the division results in 1.

In mathematical terms, this means that dividing a number by itself yields 1. Therefore, the only value that correctly satisfies $20 : a = 1$ is $a = 20$ .

This approach uses the fundamental property of division that dividing any non-zero number by itself results in 1, confirming that:

If $a = 20$ , the equation becomes $20 : 20 = 1$ , which is true.

Thus, the number that makes the equation true is $20$ .

The correct answer from the choices provided is option 3: $20$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Any non-zero number divided by itself always equals 1
Technique: For $20 : a = 1$ , we need $a = 20$
Check: Substitute back: $20 : 20 = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing ratio notation with subtraction or other operations
Don't interpret 20:a as 20-a or 20×a = wrong operations! The colon (:) means division, not subtraction or multiplication. Always read 20:a as "20 divided by a".

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 (:) is another way to write division! So $20:a$ means exactly the same as $20 ÷ a$ or $\frac{20}{a}$ .

Why can't the answer be 1 or 10?

Let's check: $20:1 = 20$ (not 1), and $20:10 = 2$ (not 1). Only when we divide 20 by 20 itself do we get 1!

Is there a quick way to solve this type of problem?

Yes! When you see $x:? = 1$ , the missing number is always x itself. This uses the property that any number divided by itself equals 1.

What if the number was 0 instead of 20?

Great question! We can't divide by zero, so $0:0$ is undefined in mathematics. This property only works for non-zero numbers.

Can I write this as a regular division problem?

Absolutely! $20:a = 1$ is the same as asking "What number divided into 20 gives 1?" The answer is still 20.

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