Solve: Identifying the Redundant Term in 9:3+0:100

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

In this context, the colon represents multiplication. So 0:100 means $ 0 \times 100 = 0 $. Some textbooks use colons instead of × symbols for multiplication.

Q: Why can 100 be replaced without changing the answer?

Because any number multiplied by zero equals zero! Whether it's $ 0 \times 100 $, $ 0 \times 50 $, or $ 0 \times 999 $, the result is always 0, so the final answer stays 3.

Q: Can I replace the 0 instead of the 100?

No! If you replace 0 with another number, like 2:100 = 200, then the final answer becomes $ 3 + 200 = 203 $ instead of 3. The zero is essential for keeping the second term equal to zero.

Q: How do I solve problems like this step by step?

Follow order of operations:First: Calculate each multiplication/division from left to rightThen: Add the results togetherFinally: Test which number can change without affecting the final answer

Order of Operations with Zero Products

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

$9:3+0:100=$

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Understand the problem

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

$9:3+0:100=$

Step-by-step solution

To solve this problem, let's break down the expression step-by-step:

Step 1: Evaluate the division $9:3$ .
This represents the division $9 \div 3$ , which results in $3$ .
Step 2: Evaluate the expression $0:100$ .
Multiplication involving zero, $0 \times 100$ , results in $0$ .
Step 3: Combine the results from Steps 1 and 2 using addition.
We add the results from Step 1 and Step 2: $3 + 0 = 3$ .

Therefore, the expression $9:3 + 0:100$ simplifies to $3$ .

Next, we determine which number can be replaced without changing the result of the exercise:

The expression's result is unaffected by the term $0:100$ , because multiplying by zero always gives zero, contributing nothing to the sum.
Therefore, $100$ can be replaced without changing the overall result.

Comparing this analysis with the given choices, the correct answer is: $100$ .

Final Answer

100

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero equals zero
Technique: Calculate $9 \div 3 = 3$ and $0 \times 100 = 0$
Check: Replacing 100 with any number still gives $3 + 0 = 3$ ✓

Common Mistakes

Avoid these frequent errors

Confusing division and multiplication symbols
Don't read 0:100 as division = 0 ÷ 100 = 0! The colon symbol (:) can mean multiplication in some contexts. This expression means 0 × 100 = 0, but either way the result is zero. Always identify which operation the colon represents based on context.

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 this problem?

In this context, the colon represents multiplication. So 0:100 means $0 \times 100 = 0$ . Some textbooks use colons instead of × symbols for multiplication.

Why can 100 be replaced without changing the answer?

Because any number multiplied by zero equals zero! Whether it's $0 \times 100$ , $0 \times 50$ , or $0 \times 999$ , the result is always 0, so the final answer stays 3.

Can I replace the 0 instead of the 100?

No! If you replace 0 with another number, like 2:100 = 200, then the final answer becomes $3 + 200 = 203$ instead of 3. The zero is essential for keeping the second term equal to zero.

What if I replace the 9 or 3?

Replacing either would change the first part of the calculation. For example, if 9 becomes 6, then $6 \div 3 = 2$ , making the final answer $2 + 0 = 2$ instead of 3.

How do I solve problems like this step by step?

Follow order of operations:

First: Calculate each multiplication/division from left to right
Then: Add the results together
Finally: Test which number can change without affecting the final answer

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