Determine the Sign: -0.9 ÷ 1.1 ÷ (-4) Step-by-Step Solution

Sign Rules with Multiple Division Operations

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

0.91.1:(4) \frac{-0.9}{1.1}:(-4)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 First, let's determine the sign of the result.
00:15 Think about what sign each number has. Are they positive or negative?
00:24 Remember, a negative number divided by a positive number is always negative.
00:30 And a negative number divided by another negative number is always positive.
00:36 Great job! That's how we find the sign of the answer to this problem.

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?

0.91.1:(4) \frac{-0.9}{1.1}:(-4)

2

Step-by-step solution

Let's see if the number is negative or positive.

As you can see, in the expression the numerator is negative and the denominator is positive.

That is, the division exercise will look like this:

+:= \frac{-}{+}:-=

The result of the expression will be a negative number, since we are dividing a negative number by a positive number.

Therefore, the exercise that will be obtained will look like this:

:=+ -:-=+

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

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Rule: Count negative signs to determine final sign
  • Technique: Two negatives make positive: (-) ÷ (+) ÷ (-) = (+)
  • Check: Even number of negatives gives positive result ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to apply sign rules to each operation separately
    Don't just look at the first division and ignore the second = wrong sign! Students often see -0.9 ÷ 1.1 and think the answer is negative, forgetting about ÷ (-4). Always work through each division step by step, applying sign rules at each stage.

Practice Quiz

Test your knowledge with interactive questions

Convert \( \frac{7}{2} \)into its reciprocal form:

FAQ

Everything you need to know about this question

Why does dividing by a negative number change the sign?

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Think of division as repeated subtraction. When you divide by a negative number, you're essentially asking 'how many times does this negative number fit?' This reverses the direction, changing the sign.

How do I keep track of signs in multiple operations?

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Write out each step: 0.91.1=negative \frac{-0.9}{1.1} = \text{negative} , then negative÷(4)=positive \text{negative} ÷ (-4) = \text{positive} . Count the negative signs - even number means positive result!

Does the order of operations matter for signs?

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Yes! Always follow left to right for division. First do 0.9÷1.1 -0.9 ÷ 1.1 , then divide that result by 4 -4 . Don't rearrange the operations.

What if I get confused with all the negative signs?

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Use the counting method: Count how many negative signs you have total. If it's an even number, your final answer is positive. If it's odd, your final answer is negative.

Can I just ignore the decimal values and focus on signs?

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Absolutely! For sign determination, you only need to track positive and negative signs. The actual decimal values don't affect whether your final answer is positive or negative.

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