Multiply Fractions: Calculate 6/7 × 3/5 Step-by-Step

Q: Why don't I need a common denominator like when adding fractions?

Great question! Multiplication is different from addition. When multiplying fractions, you work with the fractions as they are - just multiply straight across. Common denominators are only needed for adding or subtracting fractions.

Q: Do I always multiply the top numbers together and bottom numbers together?

Yes, always! For $ \frac{a}{b} \times \frac{c}{d} $, the answer is $ \frac{a \times c}{b \times d} $. This rule works for any fraction multiplication problem.

Q: Should I simplify before or after multiplying?

You can do either! Some students find it easier to simplify first by canceling common factors, while others prefer to multiply first then simplify. Both methods give the same answer.

Q: How do I know if my final answer can be simplified?

Check if the numerator and denominator share any common factors. For $ \frac{18}{35} $, since 18 = 2×3×3 and 35 = 5×7, they share no common factors, so it's already in lowest terms.

Fraction Multiplication with Cross Numerators

$\frac{6}{7}\times\frac{3}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 Remember, multiply the numerators with each other, and the denominators with each other.

00:13 Now, let's calculate those products step by step.

00:16 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{6}{7}\times\frac{3}{5}=$

Step-by-step solution

To solve the problem of multiplying the fractions $\frac{6}{7}$ and $\frac{3}{5}$ , we follow these steps:

Step 1: Multiply the numerators together. The numerators are 6 and 3. So, $6 \times 3 = 18$ .
Step 2: Multiply the denominators together. The denominators are 7 and 5. So, $7 \times 5 = 35$ .
Step 3: Write the resulting fraction. This gives us $\frac{18}{35}$ .

Therefore, the solution to the problem is $\frac{18}{35}$ .

Final Answer

$\frac{18}{35}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together, then denominators together separately
Technique: Calculate 6 × 3 = 18 and 7 × 5 = 35
Check: Verify $\frac{18}{35}$ cannot simplify further (no common factors) ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting instead of multiplying
Don't add across like $\frac{6+3}{7+5} = \frac{9}{12}$ ! This completely changes the operation and gives wrong results. Always multiply numerators together AND denominators together when multiplying fractions.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why don't I need a common denominator like when adding fractions?

Great question! Multiplication is different from addition. When multiplying fractions, you work with the fractions as they are - just multiply straight across. Common denominators are only needed for adding or subtracting fractions.

Do I always multiply the top numbers together and bottom numbers together?

Yes, always! For $\frac{a}{b} \times \frac{c}{d}$ , the answer is $\frac{a \times c}{b \times d}$ . This rule works for any fraction multiplication problem.

Should I simplify before or after multiplying?

You can do either! Some students find it easier to simplify first by canceling common factors, while others prefer to multiply first then simplify. Both methods give the same answer.

How do I know if my final answer can be simplified?

Check if the numerator and denominator share any common factors. For $\frac{18}{35}$ , since 18 = 2×3×3 and 35 = 5×7, they share no common factors, so it's already in lowest terms.

What if one of the fractions is actually a whole number?

Treat the whole number as a fraction with denominator 1! For example, $4 \times \frac{3}{5} = \frac{4}{1} \times \frac{3}{5} = \frac{12}{5}$ . This keeps the same multiplication rule.

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