Solve the Fraction Division and Polynomial Subtraction: 49m/35n : 2n/7m - (2m²/n² - 4)

Q: Why do I multiply by the reciprocal when dividing fractions?

Division by a fraction is the same as multiplication by its reciprocal. So $ a \div \frac{b}{c} = a \times \frac{c}{b} $. This makes the calculation much easier!

Q: How do I handle the negative sign in front of parentheses?

When you see -(expression), you must distribute the negative to every term inside. So $ -(\frac{2m^2}{n^2} - 4) = -\frac{2m^2}{n^2} + 4 $.

Q: Do I need a common denominator for this problem?

Yes! To subtract $ \frac{49m^2}{10n^2} - \frac{2m^2}{n^2} $, convert to common denominator: $ \frac{49m^2}{10n^2} - \frac{20m^2}{10n^2} $.

Q: Why is the final answer written as 2.9 instead of a fraction?

The fraction $ \frac{29}{10} $ equals 2.9 as a decimal. Both forms are correct, but the decimal form matches the given answer choices.

Fraction Division with Polynomial Subtraction

$\frac{49m}{35n}:\frac{2n}{7m}-(\frac{2m^2}{n^2}-4)=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:12 Negative times positive is always negative

00:17 Negative times negative is always positive

00:23 Let's factor 35 into 7 and 5

00:27 Let's reduce what we can

00:44 Divide 49 by 10

00:51 Let's use the commutative law and arrange the exercise

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

$\frac{49m}{35n}:\frac{2n}{7m}-(\frac{2m^2}{n^2}-4)=\text{?}$

Step-by-step solution

To solve this problem, let's go through it step-by-step:

Step 1: Simplify the division of fractions: $\frac{49m}{35n}:\frac{2n}{7m}$
Step 2: This is equivalent to multiplying: $\frac{49m}{35n} \times \frac{7m}{2n}$
Step 3: Simplify: Multiply numerators and denominators: $\frac{49 \cdot 7 \cdot m^2}{35 \cdot 2 \cdot n^2}$
Step 4: Compute simplification: $\frac{343m^2}{70n^2} \rightarrow \frac{49m^2}{10n^2}$
Step 5: Substitute back to expression: $\frac{49m^2}{10n^2} - (\frac{2m^2}{n^2} - 4)$
Step 6: Express $\frac{2m^2}{n^2}$ in terms of 10 denominator: $\frac{20m^2}{10n^2}$
Step 7: Calculate complete subtraction: $\frac{49m^2}{10n^2} - \frac{20m^2}{10n^2} + 4$
Step 8: Simplify result: $\frac{29m^2}{10n^2} + 4$

Therefore, the solution to the problem is $2.9\frac{m^2}{n^2} + 4$ .

Final Answer

$2.9\frac{m^2}{n^2}+4$

Key Points to Remember

Essential concepts to master this topic

Division Rule: To divide fractions, multiply by the reciprocal
Technique: Convert $\frac{49m}{35n}:\frac{2n}{7m}$ to $\frac{49m}{35n} \times \frac{7m}{2n} = \frac{49m^2}{10n^2}$
Check: Verify by substituting test values and ensuring operations follow order ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute the negative sign correctly
Don't just subtract the first term and ignore the sign = wrong final answer! When you have -(a - b), this becomes -a + b, not -a - b. Always distribute the negative sign to every term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I multiply by the reciprocal when dividing fractions?

Division by a fraction is the same as multiplication by its reciprocal. So $a \div \frac{b}{c} = a \times \frac{c}{b}$ . This makes the calculation much easier!

How do I handle the negative sign in front of parentheses?

When you see -(expression), you must distribute the negative to every term inside. So $-(\frac{2m^2}{n^2} - 4) = -\frac{2m^2}{n^2} + 4$ .

Do I need a common denominator for this problem?

Yes! To subtract $\frac{49m^2}{10n^2} - \frac{2m^2}{n^2}$ , convert to common denominator: $\frac{49m^2}{10n^2} - \frac{20m^2}{10n^2}$ .

Why is the final answer written as 2.9 instead of a fraction?

The fraction $\frac{29}{10}$ equals 2.9 as a decimal. Both forms are correct, but the decimal form matches the given answer choices.

How can I check if my answer is right?

Substitute simple values for m and n (like m=1, n=1) into both your answer and the original expression. If they give the same result, you're correct! ✓

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime