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

Solve the following exercise:

\( (+6)\cdot(+9)= \)

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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