Complete the Expression: Find the Missing Symbol in 5:5?5×1

Q: What does the colon symbol mean in math?

The colon (:) is another way to write division! So $ 5:5 $ means exactly the same as $ 5 \div 5 $ or $ \frac{5}{5} $.

Q: Why can't I just compare 5 and 5 directly?

You need to evaluate both expressions first! $ 5:5 $ equals 1, not 5. Always calculate the result of each side before comparing.

Q: How do I remember which inequality symbol to use?

Think of it like a mouth: The wide opening points to the larger number. Since 1

Q: What if both sides were equal?

If both expressions gave the same result, you'd use the equals sign (=). But here, 1 and 5 are different, so we need .

Q: Is there a shortcut for these problems?

Always follow order of operations: evaluate each expression completely first, then compare the final numbers. No shortcuts - accuracy is key!

Inequality Comparison with Division Notation

Choose the correct sign (?):

$5:5?5\times1$

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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

00:04 Any number divided by itself always equals 1

00:10 Any number multiplied by 1 always equals itself

00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$5:5?5\times1$

Step-by-step solution

To solve this problem, we need to evaluate the two expressions $5:5$ and $5 \times 1$ and then determine the correct relational sign between them.

Step 1: Evaluate $5:5$ . To find $5:5$ , we perform the division $5 \div 5$ , which is equal to $1$ .
Step 2: Evaluate $5 \times 1$ . To find $5 \times 1$ , we perform the multiplication, which is also equal to $5$ .
Step 3: Compare the results of the two evaluated expressions.
Evaluated result for $5:5$ is $1$ .
Evaluated result for $5 \times 1$ is $5$ .
Conclusion: Since $1$ is less than $5$ , the correct relational sign between the expressions is '<'.

Therefore, the correct inequality is $5:5 < 5 \times 1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division notation: The colon symbol : means division operation
Technique: Evaluate each side separately: 5:5 = 1, 5×1 = 5
Check: Compare final values to determine correct inequality symbol ✓

Common Mistakes

Avoid these frequent errors

Confusing the colon symbol with other operations
Don't treat 5:5 as multiplication or subtraction = completely wrong calculation! The colon : specifically means division in mathematical notation. Always remember that 5:5 means 5 ÷ 5.

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 $5:5$ means exactly the same as $5 \div 5$ or $\frac{5}{5}$ .

Why can't I just compare 5 and 5 directly?

You need to evaluate both expressions first! $5:5$ equals 1, not 5. Always calculate the result of each side before comparing.

How do I remember which inequality symbol to use?

Think of it like a mouth: The wide opening points to the larger number. Since 1 < 5, the mouth opens toward the 5.

What if both sides were equal?

If both expressions gave the same result, you'd use the equals sign (=). But here, 1 and 5 are different, so we need < or >.

Is there a shortcut for these problems?

Always follow order of operations: evaluate each expression completely first, then compare the final numbers. No shortcuts - accuracy is key!

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