Determine the Sign: -9/4 × 1/2 × 10/3 Fraction Multiplication

Multiplication Sign Rules with Negative Fractions

What will be the sign of the result of the exercise?

9412103 -\frac{9}{4}\cdot\frac{1}{2}\cdot\frac{10}{3}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the result sign
00:03 Let's find what sign each number has
00:11 Negative times positive always equals negative
00:16 And again, negative times positive always equals negative
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What will be the sign of the result of the exercise?

9412103 -\frac{9}{4}\cdot\frac{1}{2}\cdot\frac{10}{3}

2

Step-by-step solution

We will look only at whether the fraction is negative or positive.

In other words, the multiplication exercise looks like this:

×+×+= -\times+\times+=

If we solve the exercise from left to right, we'll first multiply minus by plus:

×+= -\times+=-

Now the remaining exercise is:

×+= -\times+=-

Therefore, the sign of the exercise result will be negative.

3

Final Answer

-

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Odd number of negatives gives negative result
  • Technique: Count negatives: (-9/4) × (+1/2) × (+10/3) = 1 negative
  • Check: Verify pattern: - × + × + = - (negative result) ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to count negative signs properly
    Don't ignore the negative sign or count it wrong = positive result instead of negative! The negative in -9/4 makes the entire product negative. Always count each negative sign carefully before determining the final sign.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why don't I need to multiply the actual numbers?

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For sign determination, you only need to count negative signs! The actual numbers don't affect whether the result is positive or negative - just the signs do.

What if there were two negative fractions?

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Two negatives would give a positive result! Remember: even number of negatives = positive, odd number of negatives = negative.

How do I remember the sign rules?

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Think of it like this: negative × positive = negative (like debt × growth = more debt). Then negative × positive = negative again!

Does the order of multiplication matter for signs?

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No! You can multiply in any order. The sign rules work the same way: ×+×+ -\times+\times+ always equals negative.

What if one of the fractions was zero?

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If any fraction is zero, the entire product is zero - regardless of the signs! Zero has no positive or negative sign.

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