Solve Fraction Multiplication: Calculate 7/8 × 4/6

Q: Can I simplify before multiplying to make it easier?

Yes! You can cross-cancel first. Notice $ \frac{4}{6} $ simplifies to $ \frac{2}{3} $, so $ \frac{7}{8} \times \frac{2}{3} = \frac{14}{24} = \frac{7}{12} $.

Q: Why can't I just add the fractions instead?

The multiplication symbol (×) means you multiply, not add! Adding fractions requires common denominators and gives a completely different answer.

Q: Do I always need to simplify my answer?

Yes, always! Math answers should be in simplest form unless specifically told otherwise. Unsimplified fractions are often marked as incorrect.

Fraction Multiplication with Simplification

$\frac{7}{8}\times\frac{4}{6}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Make sure to multiply numerator by numerator and denominator by denominator

00:09 Calculate the multiplications

00:23 Factorize 28 into factors 7 and 4

00:26 Factorize 48 into factors 12 and 4

00:30 Simplify what's possible

00:35 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

$\frac{7}{8}\times\frac{4}{6}=$

Step-by-step solution

The multiplication of fractions $\frac{7}{8}$ and $\frac{4}{6}$ requires the direct operation of multiplying numerators with numerators and denominators with denominators.

Multiply the numerators: $7 \times 4 = 28$
Multiply the denominators: $8 \times 6 = 48$
Form the resulting fraction: $\frac{28}{48}$

Now, we need to simplify $\frac{28}{48}$ . Find the greatest common divisor (GCD) of 28 and 48, which is 4.

Divide both numerator and denominator by their GCD: $\frac{28 \div 4}{48 \div 4} = \frac{7}{12}$

Therefore, the solution to the problem is $\frac{7}{12}$ .

Thus, the correct answer is $\frac{7}{12}$ , which corresponds to choice 3.

Final Answer

$\frac{7}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together and denominators together separately
Technique: Calculate $7 \times 4 = 28$ and $8 \times 6 = 48$
Check: Simplify by dividing both parts by GCD: $\frac{28}{48} = \frac{7}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the final fraction
Don't leave $\frac{28}{48}$ as your final answer! This equals $\frac{7}{12}$ but looks wrong and gets marked incorrect. Always find the GCD and reduce fractions to lowest terms.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{3}+\frac{1}{4}=$

FAQ

Everything you need to know about this question

Can I simplify before multiplying to make it easier?

Yes! You can cross-cancel first. Notice $\frac{4}{6}$ simplifies to $\frac{2}{3}$ , so $\frac{7}{8} \times \frac{2}{3} = \frac{14}{24} = \frac{7}{12}$ .

How do I find the GCD of 28 and 48?

List factors of each number: 28 = 1, 2, 4, 7, 14, 28 and 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The greatest common factor they share is 4.

Why can't I just add the fractions instead?

The multiplication symbol (×) means you multiply, not add! Adding fractions requires common denominators and gives a completely different answer.

What if one of the fractions is a whole number?

Treat whole numbers as fractions with denominator 1. For example, $3 \times \frac{2}{5} = \frac{3}{1} \times \frac{2}{5} = \frac{6}{5}$ .

Do I always need to simplify my answer?

Yes, always! Math answers should be in simplest form unless specifically told otherwise. Unsimplified fractions are often marked as incorrect.

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Solve Fraction Multiplication: Calculate 7/8 × 4/6

Fraction Multiplication with Simplification

❤️ 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

Can I simplify before multiplying to make it easier?

How do I find the GCD of 28 and 48?

Why can't I just add the fractions instead?

What if one of the fractions is a whole number?

Do I always need to simplify my answer?

🌟 Unlock Your Math Potential

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