Multiply Fractions: Solving 1/6 × 1/3 Step by Step

Q: Why do we multiply denominators and not add them?

When multiplying fractions, we're finding a fraction of a fraction. Think of $ \frac{1}{6} \times \frac{1}{3} $ as "one-third of one-sixth." This makes the result smaller, so we multiply to get $ \frac{1}{18} $.

Q: How is multiplying fractions different from adding fractions?

Adding fractions: Find common denominators first, then add numerators.Multiplying fractions: Multiply straight across - numerator × numerator, denominator × denominator. No common denominators needed!

Q: Do I always need to simplify my answer?

Yes! Always check if your answer can be simplified. Since $ \frac{1}{18} $ has 1 in the numerator, it's already in lowest terms. But other answers might need reducing.

Q: What if I get confused about which operation to use?

Look for key words: "of" usually means multiply (like "one-third of one-sixth"). Practice recognizing that multiplication makes fractions smaller, while addition combines parts.

Fraction Multiplication with Unit Numerators

$\frac{1}{6}\times\frac{1}{3}=$

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Step-by-step video solution

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00:00 Solve

00:03 We'll make sure to multiply numerator by numerator and denominator by denominator

00:06 Let's calculate the multiplications

00:09 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$\frac{1}{6}\times\frac{1}{3}=$

Step-by-step solution

To solve the problem of multiplying two fractions $\frac{1}{6}$ and $\frac{1}{3}$ , we'll follow these steps:

Step 1: Multiply the numerators of the fractions.
Step 2: Multiply the denominators of the fractions.
Step 3: Simplify the resulting fraction if necessary.

Let's apply these steps to our problem:

Step 1: Multiply the numerators: $1 \times 1 = 1$ .
Step 2: Multiply the denominators: $6 \times 3 = 18$ .

Therefore, the product of $\frac{1}{6}$ and $\frac{1}{3}$ is $\frac{1}{18}$ .

The solution to the problem is $\frac{1}{18}$ , which corresponds to choice 4.

Final Answer

$\frac{1}{18}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together, then multiply denominators together
Technique: For $\frac{1}{6} \times \frac{1}{3}$ , calculate 1 × 1 = 1 and 6 × 3 = 18
Check: Verify $\frac{1}{18}$ cannot be simplified further since GCD(1,18) = 1 ✓

Common Mistakes

Avoid these frequent errors

Adding denominators instead of multiplying
Don't calculate $\frac{1}{6} \times \frac{1}{3} = \frac{1}{6+3} = \frac{1}{9}$ ! This confuses fraction addition with multiplication rules. Always multiply denominators: 6 × 3 = 18 to get $\frac{1}{18}$ .

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 do we multiply denominators and not add them?

When multiplying fractions, we're finding a fraction of a fraction. Think of $\frac{1}{6} \times \frac{1}{3}$ as "one-third of one-sixth." This makes the result smaller, so we multiply to get $\frac{1}{18}$ .

How is multiplying fractions different from adding fractions?

Adding fractions: Find common denominators first, then add numerators.
Multiplying fractions: Multiply straight across - numerator × numerator, denominator × denominator. No common denominators needed!

Do I always need to simplify my answer?

Yes! Always check if your answer can be simplified. Since $\frac{1}{18}$ has 1 in the numerator, it's already in lowest terms. But other answers might need reducing.

What if I get confused about which operation to use?

Look for key words: "of" usually means multiply (like "one-third of one-sixth"). Practice recognizing that multiplication makes fractions smaller, while addition combines parts.

Can I use shortcuts when multiplying unit fractions?

With unit fractions (numerator = 1), just multiply the denominators! $\frac{1}{a} \times \frac{1}{b} = \frac{1}{a \times b}$ . For our problem: $\frac{1}{6} \times \frac{1}{3} = \frac{1}{6 \times 3} = \frac{1}{18}$ .

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