Solve -49÷(-7)×3×(-1/4): Multiple Operations with Negative Numbers

Q: Why does negative divided by negative equal positive?

Think of division as "how many groups". When you divide -49 by -7, you're asking "how many groups of -7 fit into -49?" The answer is 7 positive groups!

Q: Should I work left to right or follow PEMDAS?

For multiplication and division only, work left to right since they have equal priority. So solve $ -49÷(-7) $ first, then multiply by 3, then by $ -\frac{1}{4} $.

Q: How do I multiply by a negative fraction?

Multiply the numbers normally: $ 21 \times \frac{1}{4} = \frac{21}{4} $. Then apply the negative sign to get $ -\frac{21}{4} $.

Q: Why do I need to convert to a mixed number?

Mixed numbers like $ -5\frac{1}{4} $ are easier to understand than improper fractions. Divide 21÷4 = 5 remainder 1, so $ \frac{21}{4} = 5\frac{1}{4} $.

Division and Multiplication with Signed Numbers

Solve the following equation:

$-49:-7\cdot3\cdot-\frac{1}{4}=$

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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 write division as a fraction

00:10 Negative divided by negative always equals positive

00:21 Let's calculate the quotient

00:27 Let's continue solving one operation at a time

00:32 Positive times negative always equals negative

00:38 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:

$-49:-7\cdot3\cdot-\frac{1}{4}=$

Step-by-step solution

Let's begin by writing the division exercise as a simple fraction:

$\frac{-49}{-7}\times3\times(-\frac{1}{4})=$

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

$\frac{49}{7}\times3\times(-\frac{1}{4})=$

Let's proceed to solve the division exercise:

$7\times3\times-\frac{1}{4}=$

Let's now solve the exercise from left to right:

$7\times3=21$

We should obtain the following exercise:

$21\times-\frac{1}{4}=$

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

$-\frac{21}{4}$

Let's write the result as a mixed fraction:

$-\frac{21}{4}=-5\frac{1}{4}$

Final Answer

$-5\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Sign Rules: Negative divided by negative equals positive
Order: Work left to right: $\frac{-49}{-7} = 7$ , then multiply by 3
Check: Count negative signs: odd number = negative result ✓

Common Mistakes

Avoid these frequent errors

Forgetting sign rules when dividing negative numbers
Don't keep the negative sign when dividing -49÷(-7) = still negative! This ignores the rule that negative÷negative=positive, giving -7 instead of +7. Always remember: same signs give positive results, different signs give negative results.

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 does negative divided by negative equal positive?

Think of division as "how many groups". When you divide -49 by -7, you're asking "how many groups of -7 fit into -49?" The answer is 7 positive groups!

How do I keep track of all the negative signs?

Count the negative signs in the entire problem. If you have an odd number of negatives, your final answer is negative. Even number of negatives = positive answer.

Should I work left to right or follow PEMDAS?

For multiplication and division only, work left to right since they have equal priority. So solve $-49÷(-7)$ first, then multiply by 3, then by $-\frac{1}{4}$ .

How do I multiply by a negative fraction?

Multiply the numbers normally: $21 \times \frac{1}{4} = \frac{21}{4}$ . Then apply the negative sign to get $-\frac{21}{4}$ .

Why do I need to convert to a mixed number?

Mixed numbers like $-5\frac{1}{4}$ are easier to understand than improper fractions. Divide 21÷4 = 5 remainder 1, so $\frac{21}{4} = 5\frac{1}{4}$ .

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