Find the Missing Operator in 20?1=20: Basic Equation Solving

Q: Why does both multiplication and division by 1 work?

This is due to the identity properties! Any number multiplied by 1 stays the same, and any number divided by 1 also stays the same. So $ 20 \times 1 = 20 $ and $ 20 \div 1 = 20 $ are both true.

Q: What if none of the operations work?

That's rare, but if it happens, double-check your calculations. Make sure you're following the correct order of operations and doing the arithmetic correctly. Every well-written problem should have at least one correct answer.

Basic Operations with Identity Properties

Choose the correct sign (?):

$20\text{?}1=20$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the correct mathematical sign

00:05 Let’s calculate each possibility and select the correct one

00:20 20 plus 1 is not equal to 20

00:31 20 minus 1 is not equal to 20

00:37 Any number divided by 1 is always equal to itself

00:41 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$20\text{?}1=20$

Step-by-step solution

To solve this problem, we'll evaluate each mathematical operation:

Addition ( $+$ ): $20 + 1 = 21$ , which is not equal to 20.
Subtraction ( $-$ ): $20 - 1 = 19$ , which is not equal to 20.
Multiplication ( $\times$ ): $20 \times 1 = 20$ , which is equal to 20.
Division ( $\div$ ): $20 \div 1 = 20$ , which is equal to 20.

Both multiplication and division by 1 result in the number 20. Therefore, both operations maintain the equality.
However, based on the given choices, the operation that is likely represented by $\text{?}$ is division, i.e., $:$ .

Therefore, the correct sign that completes the equation $20 \text{?} 1 = 20$ is $:$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Multiplying or dividing by 1 keeps numbers unchanged
Testing Method: Try each operation: 20 + 1 = 21, 20 - 1 = 19
Verification: Check both $20 \times 1 = 20$ and $20 \div 1 = 20$ work ✓

Common Mistakes

Avoid these frequent errors

Choosing addition because it seems easiest
Don't assume addition is the answer without calculating = 20 + 1 = 21, not 20! This ignores the identity property of 1. Always test each operation systematically to find which ones actually make the equation true.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does both multiplication and division by 1 work?

This is due to the identity properties! Any number multiplied by 1 stays the same, and any number divided by 1 also stays the same. So $20 \times 1 = 20$ and $20 \div 1 = 20$ are both true.

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

The colon (:) is another way to write division, just like the ÷ symbol. So $20 : 1$ means the same thing as $20 \div 1$ , which equals 20.

How do I solve these missing operator problems?

Follow these steps: 1) Try each given operation one by one. 2) Calculate the result. 3) See which one makes the equation true. 4) Double-check your answer by substituting back.

Could there be more than one correct answer?

Yes! In this problem, both multiplication and division by 1 give the correct result. However, you need to choose from the given options. Look carefully at what symbols are provided in the multiple choice answers.

What if none of the operations work?

That's rare, but if it happens, double-check your calculations. Make sure you're following the correct order of operations and doing the arithmetic correctly. Every well-written problem should have at least one correct answer.

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