Solve -12:-6·(-8+4): Order of Operations with Negative Numbers

Q: Why do I solve the division before the multiplication?

Division and multiplication have equal priority in PEMDAS, so you solve them from left to right. Since division ($ -12 ÷ (-6) $) appears first, you do it before the multiplication.

Q: How do I know if dividing two negatives gives a positive?

Remember the sign rules: negative ÷ negative = positive. Think of it as $ \frac{-12}{-6} = \frac{12}{6} = 2 $. The two negative signs cancel each other out!

Q: What if I forget to solve the parentheses first?

You'll get the wrong answer! Parentheses have the highest priority in PEMDAS. Always solve $ (-8 + 4) = -4 $ before doing any other operations.

Q: Can I rewrite the division as a fraction?

Absolutely! Writing $ -12 ÷ (-6) $ as $ \frac{-12}{-6} $ often makes it easier to see that you're dividing two negatives, which gives a positive result.

Q: How do I check if my final answer is correct?

Substitute your answer back into the original expression: $ -12 ÷ (-6) × (-8 + 4) $. Following order of operations should give you $ -8 $ again!

Order of Operations with Division and Multiplication

$-12:-6\cdot(-8+4)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's solve according to the correct order of operations

00:07 Always calculate parentheses first

00:19 Convert division to fraction

00:26 Negative divided by negative always equals positive

00:41 Calculate the quotient

00:45 Substitute in our exercise and continue solving

00:50 Positive times negative always equals negative

00:54 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-12:-6\cdot(-8+4)=$

Step-by-step solution

Let's first solve the expression in parentheses:

$-8+4=-4$

Now the expression is:

$-12:-6\times-4=$

Let's solve the expression from left to right.

We'll write the division as a simple fraction like this:

$\frac{-12}{-6}=$

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

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

Therefore:

$\frac{12}{6}=2$

Now the expression we got is:

$2\times-4=$

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

$+\times-=-$

Therefore the result is:

$2\times-4=-8$

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Solve parentheses first, then division and multiplication left to right
Division Technique: $-12 ÷ (-6) = +2$ because negative divided by negative equals positive
Verification: Work backwards: $2 × (-4) = -8$ , then $-8 ÷ (-6) = \frac{4}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Solving division and multiplication in wrong order
Don't solve $-6 × (-4)$ first to get 24, then divide $-12 ÷ 24 = -0.5$ ! This ignores left-to-right order and gives the wrong answer. Always solve division and multiplication from left to right after handling parentheses.

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 division before the multiplication?

Division and multiplication have equal priority in PEMDAS, so you solve them from left to right. Since division ( $-12 ÷ (-6)$ ) appears first, you do it before the multiplication.

How do I know if dividing two negatives gives a positive?

Remember the sign rules: negative ÷ negative = positive. Think of it as $\frac{-12}{-6} = \frac{12}{6} = 2$ . The two negative signs cancel each other out!

What if I forget to solve the parentheses first?

You'll get the wrong answer! Parentheses have the highest priority in PEMDAS. Always solve $(-8 + 4) = -4$ before doing any other operations.

Can I rewrite the division as a fraction?

Absolutely! Writing $-12 ÷ (-6)$ as $\frac{-12}{-6}$ often makes it easier to see that you're dividing two negatives, which gives a positive result.

How do I check if my final answer is correct?

Substitute your answer back into the original expression: $-12 ÷ (-6) × (-8 + 4)$ . Following order of operations should give you $-8$ again!

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Solve -12:-6·(-8+4): Order of Operations with Negative Numbers

Order of Operations with Division and Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I solve the division before the multiplication?

How do I know if dividing two negatives gives a positive?

What if I forget to solve the parentheses first?

Can I rewrite the division as a fraction?

How do I check if my final answer is correct?

🌟 Unlock Your Math Potential

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