Find the Missing Symbol in Sequence: -0.9:-9:-4?0

Inequality Comparison with Division Sign Rules

Fill in the missing symbol (?):

0.9:9:4?0 -0.9:-9:-4\text{?}0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the appropriate sign
00:04 Let's take only the signs and check what will be the result sign
00:11 Negative divided by negative always equals positive
00:17 Positive divided by negative always equals negative
00:21 Negative is necessarily less than 0
00:24 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

Fill in the missing symbol (?):

0.9:9:4?0 -0.9:-9:-4\text{?}0

2

Step-by-step solution

Note that in the first step we are dividing a negative number by a negative number:

:=+ -:-=+

This means that the exercise can be written as follows:

+:?0 +:-?0

Now we are dividing a positive number by a negative number:

+:= +:-=-

Therefore, the final exercise will look like this:

?0 -?0

We are left with a negative number, meaning a number less than zero.

Therefore, the answer is:

<0 - < 0

3

Final Answer

>

Key Points to Remember

Essential concepts to master this topic
  • Sign Rules: Negative divided by negative equals positive result
  • Technique: Simplify 0.9÷(9)=+0.1 -0.9 ÷ (-9) = +0.1 then compare with 0
  • Check: Since 0.1 > 0, the symbol > makes the statement true ✓

Common Mistakes

Avoid these frequent errors
  • Confusing division and comparison symbols
    Don't treat the colon (:) as just division without considering the final comparison = wrong symbol choice! The expression asks you to compare the division result with zero. Always simplify the division first, then determine which comparison symbol (>, <, =) makes the statement true.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

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

FAQ

Everything you need to know about this question

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

+

The colon (:) represents division, just like the ÷ symbol. So 0.9:9 -0.9:-9 means 0.9÷(9) -0.9 ÷ (-9) .

How do I remember the sign rules for division?

+

Same signs = positive result and different signs = negative result. Since both numbers are negative, same signs give us a positive answer!

Why isn't the answer equals (=) since we get exactly 0.1?

+

We're comparing 0.1 with 0, not finding if they're equal. Since 0.1 is greater than 0, we need the > symbol to make the statement true.

What if I calculated the division wrong?

+

Double-check: 0.9÷(9)=0.9÷9=0.1 -0.9 ÷ (-9) = 0.9 ÷ 9 = 0.1 . The negatives cancel out! Then compare: is 0.1 greater than, less than, or equal to 0?

Could the answer ever be 'meaningless'?

+

No! This expression has a clear mathematical meaning. We can always divide numbers (except by zero) and compare the result with another number.

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