Find the Invariant Number in 2×0×20+5: Zero Property Investigation

Q: Why can both 2 and 20 be replaced but not 0?

The zero property of multiplication says that any number times zero equals zero. Since we have $ 2 \times 0 \times 20 $, the 0 makes the whole multiplication equal 0, no matter what 2 and 20 are!

Q: What happens if I change the 5 to a different number?

Changing 5 will change the final answer! Since $ 2 \times 0 \times 20 = 0 $, we get $ 0 + 5 = 5 $. If you change 5 to 8, the result becomes 8.

Q: Can I replace 2 with any number, even negative ones?

Yes! You can use any number - positive, negative, or even decimals. Examples: $ (-10) \times 0 \times 20 + 5 = 5 $ or $ 0.5 \times 0 \times 20 + 5 = 5 $

Q: How do I remember which numbers don't affect the result?

Look for the zero first! Any numbers being multiplied by zero become "invisible" to the final result. The zero is the key - it makes those other factors not matter.

Q: What if there were multiple zeros in the multiplication?

Even with multiple zeros like $ 2 \times 0 \times 0 \times 20 $, the result is still 0. Any zero in multiplication makes the whole product zero, so all non-zero factors can still be replaced.

Step-by-step video solution

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Step-by-step written solution

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1

Understand the problem

Which number can be replaced without changing the result of the exercise?

$2\times0\times20+5=$

2

Step-by-step solution

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

Step 1: Evaluate the multiplication of numbers.
Step 2: Apply the addition operation.
Step 3: Analyze each number's role and how it affects the result.

Now, let's work through each step:

Step 1: We begin with the expression $2 \times 0 \times 20 + 5$ . According to the order of operations (PEMDAS/BODMAS), we first focus on multiplication.

$2 \times 0 = 0$

Next, we multiply the result by 20:

$0 \times 20 = 0$

Step 2: Now, add 5 to the result:

$0 + 5 = 5$

The final result of the expression is 5.

Step 3: Analyzing the impact of each number on the result, we note:

The number 2 is part of a multiplication sequence, but since it's multiplied by 0, its initial value doesn't influence the result.
The zero $0$ is crucial as it nullifies the multiplication. Changing it would change the result of the entire expression significantly.
The number 20 is also nullified in the multiplication by zero. Its value will not affect the final result.
The number 5 is added after the multiplication and directly affects the result by finality addition. Changing it will alter the result.

Therefore, we conclude that the numbers 2 and 20 can be replaced without changing the result of the expression.

Thus, the correct answer is Answers (a) and (c).

3

Final Answer

Answers (a) and (c)

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero equals zero
Technique: Since $2 \times 0 = 0$ , then $0 \times 20 = 0$
Check: Replace 2 with any number: $99 \times 0 \times 20 + 5 = 5$ ✓

Common Mistakes

Avoid these frequent errors

Thinking zero can be replaced without changing the result
Don't replace the 0 with another number = completely different answer! If you change 0 to 3, you get $2 \times 3 \times 20 + 5 = 125$ instead of 5. Always remember that zero makes the entire multiplication equal zero, so only non-zero factors can be changed.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why can both 2 and 20 be replaced but not 0?

+

The zero property of multiplication says that any number times zero equals zero. Since we have $2 \times 0 \times 20$ , the 0 makes the whole multiplication equal 0, no matter what 2 and 20 are!

What happens if I change the 5 to a different number?

+

Changing 5 will change the final answer! Since $2 \times 0 \times 20 = 0$ , we get $0 + 5 = 5$ . If you change 5 to 8, the result becomes 8.

Can I replace 2 with any number, even negative ones?

+

Yes! You can use any number - positive, negative, or even decimals. Examples: $(-10) \times 0 \times 20 + 5 = 5$ or $0.5 \times 0 \times 20 + 5 = 5$

How do I remember which numbers don't affect the result?

+

Look for the zero first! Any numbers being multiplied by zero become "invisible" to the final result. The zero is the key - it makes those other factors not matter.

What if there were multiple zeros in the multiplication?

+

Even with multiple zeros like $2 \times 0 \times 0 \times 20$ , the result is still 0. Any zero in multiplication makes the whole product zero, so all non-zero factors can still be replaced.

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Find the Invariant Number in 2×0×20+5: Zero Property Investigation

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