Q. \( 12 \times \frac{1}{6} \)

Q: What is the value of 12 \times \tfrac{1}{6}?

12 \times \tfrac{1}{6} = \tfrac{12}{6} = 2.

Q: How do you multiply a whole number by a fraction?

Convert the whole number to a fraction: 12 = \tfrac{12}{1}. Multiply numerators and denominators: \tfrac{12}{1}\times \tfrac{1}{6}=\tfrac{12}{6}=2.

Q: Can you simplify before multiplying?

Yes. Cancel common factors: 12\times\tfrac{1}{6}=(6\cdot2)\times\tfrac{1}{6}=2. Cancel 6 with 1/6 first to simplify.

Q: Why is multiplying by \tfrac{1}{6} the same as dividing by 6?

Multiplying by \tfrac{1}{6} equals multiplying by the reciprocal of 6, so 12\times\tfrac{1}{6}=12\div6=2.

Q: How can this be seen as repeated addition?

Adding \tfrac{1}{6} twelve times: \tfrac{1}{6}+\tfrac{1}{6}+\dots (12 terms) =\tfrac{12}{6}=2.

Q: What is the decimal form of the result?

The decimal is 2.0 (or simply 2).

Q: If you have 12 items and take one-sixth, how many items do you get?

One-sixth of 12 is 12\times\tfrac{1}{6}=2 items.

Q: How many \tfrac{1}{6} pieces make up 12? (Related but different)

That’s 12\div\tfrac{1}{6}=12\times6=72; there are 72 pieces of size \tfrac{1}{6} in 12.

Answer

\( 12 \times \frac{1}{6} = \frac{12}{6} = 2 \)

Multiply 12 by 1 and divide by 6, giving 2.

Detailed Explanation

Below is a step-by-step, detailed explanation of how to compute \( 12 \times \frac{1}{6} \).

Write the multiplication:

\( 12 \times \tfrac{1}{6} \)
Convert the whole number to a fraction:

Express 12 as a fraction with denominator 1: \( 12 = \tfrac{12}{1} \). So the product becomes \( \tfrac{12}{1} \times \tfrac{1}{6} \).
Multiply numerators and denominators:

Multiply the numerators together and the denominators together:

\[ \tfrac{12}{1} \times \tfrac{1}{6} = \tfrac{12 \times 1}{1 \times 6} = \tfrac{12}{6} \]
Simplify the fraction:

Both numerator and denominator are divisible by 6:

\[ \tfrac{12}{6} = \tfrac{12 \div 6}{6 \div 6} = \tfrac{2}{1} = 2 \]
Alternative (cancel before multiplying):

Cancel the 6 into 12 before multiplying:

\[ \tfrac{12}{1} \times \tfrac{1}{6} \rightarrow \tfrac{2}{1} \times \tfrac{1}{1} = 2 \]
\( 12 \times \tfrac{1}{6} = 2 \)

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FAQs

What is the value of \(12 \times \tfrac{1}{6}\)?

\(12 \times \tfrac{1}{6} = \tfrac{12}{6} = 2\).

How do you multiply a whole number by a fraction?

Convert the whole number to a fraction: \(12 = \tfrac{12}{1}\). Multiply numerators and denominators: \(\tfrac{12}{1}\times \tfrac{1}{6}=\tfrac{12}{6}=2\).

Can you simplify before multiplying?

Yes. Cancel common factors: \(12\times\tfrac{1}{6}=(6\cdot2)\times\tfrac{1}{6}=2\). Cancel \(6\) with \(1/6\) first to simplify.

Why is multiplying by \(\tfrac{1}{6}\) the same as dividing by 6?

Multiplying by \(\tfrac{1}{6}\) equals multiplying by the reciprocal of 6, so \(12\times\tfrac{1}{6}=12\div6=2\).

How can this be seen as repeated addition?

Adding \(\tfrac{1}{6}\) twelve times: \(\tfrac{1}{6}+\tfrac{1}{6}+\dots\) (12 terms) \(=\tfrac{12}{6}=2\).

What is the decimal form of the result?

The decimal is \(2.0\) (or simply \(2\)).

If you have 12 items and take one-sixth, how many items do you get?

One-sixth of 12 is \(12\times\tfrac{1}{6}=2\) items.

How many \(\tfrac{1}{6}\) pieces make up 12? (Related but different)

That’s \(12\div\tfrac{1}{6}=12\times6=72\); there are 72 pieces of size \(\tfrac{1}{6}\) in 12.

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