Solve Fraction Multiplication: 6/8 × 5/6 Step-by-Step

Q: Do I always need to simplify fraction multiplication results?

Yes, always simplify! Your final answer should be in lowest terms. Look for the GCD (Greatest Common Divisor) of the numerator and denominator, then divide both by that number.

Q: Can I simplify before multiplying instead?

Absolutely! You can cancel common factors first: $ \frac{6}{8} \times \frac{5}{6} $. Notice 6 appears in both numerator and denominator, so cross-cancel to get $ \frac{1}{8} \times \frac{5}{1} = \frac{5}{8} $.

Q: What if I can't find any common factors?

If the numerator and denominator share no common factors except 1, then your fraction is already in simplest form! For example, $ \frac{3}{7} $ cannot be simplified further.

Q: Why did we get different wrong answers in the choices?

Common errors include: adding instead of multiplying ($ \frac{11}{48} $), not multiplying correctly, or making calculation mistakes. Always multiply straight across and then simplify!

Fraction Multiplication with Simplification Steps

$\frac{6}{8}\times\frac{5}{6}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Make sure to multiply numerator by numerator and denominator by denominator

00:07 Reduce what we can

00:10 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

$\frac{6}{8}\times\frac{5}{6}=$

Step-by-step solution

To solve this problem, we'll multiply the fractions and simplify the result:

Step 1: Multiply the numerators together: $6 \times 5 = 30$ .
Step 2: Multiply the denominators together: $8 \times 6 = 48$ .
Step 3: Write the result as a single fraction: $\frac{30}{48}$ .
Step 4: Simplify the fraction by finding the GCD of 30 and 48, which is 6.
Step 5: Divide both the numerator and the denominator by their GCD:

$\frac{30 \div 6}{48 \div 6} = \frac{5}{8}$

Therefore, the solution to the problem is $\frac{5}{8}$ .

Final Answer

$\frac{5}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together, then multiply denominators together
Technique: Find GCD of 30 and 48 = 6, then divide both by 6
Check: Verify $\frac{5}{8}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the final fraction
Don't leave your answer as $\frac{30}{48}$ = wrong final form! The fraction isn't in simplest form and loses points. Always find the GCD and divide both numerator and denominator to get $\frac{5}{8}$ .

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{3}\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Do I always need to simplify fraction multiplication results?

Yes, always simplify! Your final answer should be in lowest terms. Look for the GCD (Greatest Common Divisor) of the numerator and denominator, then divide both by that number.

How do I find the GCD of 30 and 48?

List the factors: 30 = 1, 2, 3, 5, 6, 10, 15, 30 and 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The greatest common factor is 6!

Can I simplify before multiplying instead?

Absolutely! You can cancel common factors first: $\frac{6}{8} \times \frac{5}{6}$ . Notice 6 appears in both numerator and denominator, so cross-cancel to get $\frac{1}{8} \times \frac{5}{1} = \frac{5}{8}$ .

What if I can't find any common factors?

If the numerator and denominator share no common factors except 1, then your fraction is already in simplest form! For example, $\frac{3}{7}$ cannot be simplified further.

Why did we get different wrong answers in the choices?

Common errors include: adding instead of multiplying ( $\frac{11}{48}$ ), not multiplying correctly, or making calculation mistakes. Always multiply straight across and then simplify!

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