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

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

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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