Solve -(-7+4)÷(-9): Negative Numbers and Division Practice

Order of Operations with Negative Signs

Solve the following equation:

(7+4):(9)= -(-7+4):(-9)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's begin solving the problem.
00:10 Remember, we follow the order of operations carefully.
00:14 First, solve inside the parentheses.
00:21 A negative times a negative gives us a positive. Great job!
00:33 Express division using a fraction for clarity.
00:38 Remember, a positive divided by a negative results in a negative.
00:44 Factor nine into three times three for easier calculations.
00:49 Now let's simplify everything we can.
00:52 And that's how we arrive at the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

(7+4):(9)= -(-7+4):(-9)=

2

Step-by-step solution

In order to solve the equation we must follow the order of operations beginning with the parentheses:

7+4=3 -7+4=-3

We should obtain the following expression:

(3):(9)= -(-3):(-9)=

Let's apply the rule:

(x)=+x -(-x)=+x

Therefore:

(3)=3 -(-3)=3

Resulting in the following expression:

3:(9)= 3:(-9)=

Let's proceed to write the expression as a simple fraction:

+39= \frac{+3}{-9}=

Note that we are dividing a positive number by a negative number, so the result must be a negative number:

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

Next let's expand the 9 in the denominator of the fraction:

33×3= -\frac{3}{3\times3}=

Finally let's reduce the 3 in both the numerator and denominator of the fraction:

13 -\frac{1}{3}

3

Final Answer

13 -\frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Order: Parentheses first, then negation, finally division
  • Technique: (3)=+3 -(-3) = +3 using double negative rule
  • Check: 3÷(9)=13 3 ÷ (-9) = -\frac{1}{3} positive÷negative=negative ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring parentheses and applying negation incorrectly
    Don't solve (7+4)÷(9) -(-7+4)÷(-9) as 7+4÷(9) -7+4÷(-9) = wrong order! This skips parentheses and mixes up the negation, giving completely wrong results. Always solve parentheses first, then apply the outer negation.

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 do I solve the parentheses first before applying the negative sign?

+

Order of operations (PEMDAS) requires parentheses first! The expression (7+4) -(-7+4) means "negative of the result" from the parentheses, not negative applied to individual terms.

How does the double negative rule work here?

+

When you have (3) -(-3) , the rule "negative times negative equals positive" applies. So (3)=+3 -(-3) = +3 . Think of it as (1)×(3)=+3 (-1) × (-3) = +3 .

Why is the final answer negative?

+

Because we're dividing a positive number by a negative number: +39 \frac{+3}{-9} . The rule is: positive ÷ negative = negative, so our answer is 13 -\frac{1}{3} .

Can I simplify the fraction differently?

+

Yes! You can factor out the common factor: 39=3÷39÷3=13 \frac{3}{9} = \frac{3÷3}{9÷3} = \frac{1}{3} . Since we determined the sign is negative, the final answer is 13 -\frac{1}{3} .

What if I forget to change the sign when dividing?

+

Always remember the sign rules for division! Use this memory trick: "same signs give positive, different signs give negative." Here we have different signs (+ and -), so the result is negative.

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