Q. \[ 2 \times \frac{2}{3} \] as a fraction.

Q: What is 2 \times \frac{2}{3} as a fraction?

Multiply: write 2 as \frac{2}{1}. \frac{2}{1} \times \frac{2}{3} = \frac{4}{3}.

Q: Can I use repeated addition to find the product?

Yes. 2 \times \frac{2}{3} = \frac{2}{3} + \frac{2}{3} = \frac{4}{3}.

Q: Is \frac{4}{3} in simplest form?

Yes; \gcd(4,3)=1, so \frac{4}{3} is fully simplified.

Q: How do I express \frac{4}{3} as a mixed number?

Divide: 4 \div 3 = 1 remainder 1. Mixed form is 1\frac{1}{3}.

Q: What is \frac{4}{3} as a decimal and percent?

What is \frac{4}{3} as a decimal and percent?

Q: Can I simplify before multiplying (cross-cancellation)?

Yes, but here \frac{2}{1} \times \frac{2}{3} has no common factors to cancel, so multiply directly to get \frac{4}{3}.

Q: Why is the product greater than \frac{2}{3}?

Because multiplying by 2 doubles the fraction: 2 \times \frac{2}{3} = twice \frac{2}{3}, giving \frac{4}{3}, which is larger than \frac{2}{3}.

Answer

Multiply the whole number by the numerator: \(2\times\frac{2}{3}=\frac{4}{3}=1\frac{1}{3}\)

Detailed Explanation

Step-by-step solution

Write the whole number 2 as a fraction with denominator 1: \(2=\frac{2}{1}\). This allows using the fraction multiplication rule.
Multiply the two fractions by multiplying numerators and multiplying denominators:

\(\displaystyle \frac{2}{1}\times\frac{2}{3}=\frac{2\times 2}{1\times 3}\).

This follows because (a/b)×(c/d) = (a×c)/(b×d).
Compute the products: \(\displaystyle \frac{2\times 2}{1\times 3}=\frac{4}{3}\).
Simplify if possible. The greatest common divisor of 4 and 3 is 1, so \(\displaystyle \frac{4}{3}\) is already in simplest form.
Optional: as a mixed number, \(\displaystyle \frac{4}{3}=1\frac{1}{3}\) because 4 divided by 3 is 1 remainder 1.

Final answer (as a fraction): \(\displaystyle \frac{4}{3}\)

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FAQs

What is \(2 \times \frac{2}{3}\) as a fraction?

Multiply: write 2 as \(\frac{2}{1}\). \(\frac{2}{1} \times \frac{2}{3} = \frac{4}{3}\).

How do you multiply a whole number by a fraction?

Convert the whole number to a fraction over 1, then multiply numerators and denominators: \(\frac{a}{1} \times \frac{b}{c} = \frac{ab}{c}\).

Can I use repeated addition to find the product?

Yes. \(2 \times \frac{2}{3} = \frac{2}{3} + \frac{2}{3} = \frac{4}{3}\).

Is \(\frac{4}{3}\) in simplest form?

Yes; \(\gcd(4,3)=1\), so \(\frac{4}{3}\) is fully simplified.

How do I express \(\frac{4}{3}\) as a mixed number?

Divide: \(4 \div 3 = 1\) remainder 1. Mixed form is \(1\frac{1}{3}\).

What is \(\frac{4}{3}\) as a decimal and percent?

Can I simplify before multiplying (cross-cancellation)?

Yes, but here \(\frac{2}{1} \times \frac{2}{3}\) has no common factors to cancel, so multiply directly to get \(\frac{4}{3}\).

Why is the product greater than \(\frac{2}{3}\)?

Because multiplying by 2 doubles the fraction: \(2 \times \frac{2}{3} =\) twice \(\frac{2}{3}\), giving \(\frac{4}{3}\), which is larger than \(\frac{2}{3}\).

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