Solve 38÷(-4)×12÷(-3): Sequential Operations with Negative Numbers

Q: Why do we get a positive answer when dividing by negative numbers?

Because we have two negative divisors: (-4) and (-3). When we multiply them together in the denominator, negative times negative equals positive, giving us $ \frac{38 \times 12}{+12} $.

Q: How do I remember the sign rules for multiplication and division?

Same signs = positive resultDifferent signs = negative resultSo: (+)(+) = +, (-)(−) = +, but (+)(−) = − and (−)(+) = −

Q: Why does the 12 break down into 4 × 3 in the solution?

This creates common factors with the denominator! Since we have 4 × 3 in both numerator and denominator, they cancel out, leaving just 38 as our answer.

Q: What if I get confused with the order of operations?

Remember: Division and multiplication have equal priority, so work from left to right. Or convert everything to fractions first - this often makes the signs clearer!

Sequential Division Operations with Negative Numbers

Solve the following equation:

$38:(-4)\cdot12:(-3)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Write every division as a fraction

00:18 Make sure to multiply numerator by numerator and denominator by denominator

00:29 Negative times negative always equals positive

00:42 Break down 12 into factors 4 and 3

00:49 Simplify what's possible

00:52 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

Solve the following equation:

$38:(-4)\cdot12:(-3)=$

Step-by-step solution

Let's begin by writing the two division exercises as a multiplication of two simple fractions:

$(38:(-4))\times(12:(-3))=$

$\frac{38}{-4}\times\frac{12}{-3}=$

Let's proceed to combine them into one exercise:

$\frac{38\times12}{-4\times-3}=$

Note that in the denominator of the fraction we are multiplying two negative numbers, therefore the result must be positive:

$\frac{38\times12}{4\times3}=$

Let's now break down the 12 in the fraction's numerator into a multiplication exercise:

$\frac{38\times4\times3}{4\times3}=$

Finally let's reduce the multiplication exercise 4X3 in the numerator and denominator and we should obtain the following:

$38$

Final Answer

$38$

Key Points to Remember

Essential concepts to master this topic

Rule: Perform divisions from left to right maintaining proper signs
Technique: Convert to fractions: $\frac{38}{-4} \times \frac{12}{-3} = \frac{38 \times 12}{-4 \times -3}$
Check: Negative times negative equals positive: (-4) × (-3) = +12 ✓

Common Mistakes

Avoid these frequent errors

Ignoring the rule that negative times negative equals positive
Don't treat (-4) × (-3) as negative = wrong denominator sign! This makes the final answer negative when it should be positive. Always remember that multiplying two negative numbers gives a positive result.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

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

FAQ

Everything you need to know about this question

Why do we get a positive answer when dividing by negative numbers?

Because we have two negative divisors: (-4) and (-3). When we multiply them together in the denominator, negative times negative equals positive, giving us $\frac{38 \times 12}{+12}$ .

Can I solve this without converting to fractions?

Yes! Work left to right: 38 ÷ (-4) = -9.5, then -9.5 × 12 = -114, finally -114 ÷ (-3) = 38. But the fraction method helps avoid sign errors!

How do I remember the sign rules for multiplication and division?

Same signs = positive result
Different signs = negative result
So: (+)(+) = +, (-)(−) = +, but (+)(−) = − and (−)(+) = −

Why does the 12 break down into 4 × 3 in the solution?

This creates common factors with the denominator! Since we have 4 × 3 in both numerator and denominator, they cancel out, leaving just 38 as our answer.

What if I get confused with the order of operations?

Remember: Division and multiplication have equal priority, so work from left to right. Or convert everything to fractions first - this often makes the signs clearer!

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