Q. The value of \( -6 \times \frac{2}{3} \) is \( -4 \).

Q: What is -6 \times \frac{2}{3}?.

(-6)\times\frac{2}{3}=\frac{-6\times2}{3}=\frac{-12}{3}=-4. You can also cancel first: \frac{-6}{3}=-2, then -2\times2=-4.

Q: Why is the product negative?

Negative times a positive is negative by sign rules: (-)\times(+)=(-). Here -6 is negative and \frac{2}{3} is positive, so the result is negative.

Q: Can I simplify before multiplying?

Yes. Write -6 as \frac{-6}{1} and cancel common factors: \frac{-6}{1}\times\frac{2}{3}=\frac{-6\times2}{3}. Cancel 6 and 3 to get -2\times2=-4.

Q: How do I write -6 as a fraction to multiply?

Use -6=\frac{-6}{1}. Then \frac{-6}{1}\times\frac{2}{3}=\frac{-6\times2}{1\times3}=\frac{-12}{3}=-4.

Q: What is the decimal form of the answer?

The product -4 as a decimal is -4.0 (or just -4 ).

Q: What if both numbers were negative, e.g., -6\times -\frac{2}{3}?.

What if both numbers were negative, e.g., -6\times -\frac{2}{3}?.

Q: How can I show the multiplication as division first?

Think \times\frac{2}{3} as multiply by 2 then divide by 3: (-6)\times2=-12, then -12\div3=-4.

Answer

Simplify the product.

\(-6\cdot\frac{2}{3}\)

Multiply the numerator by \(-6\).

\(-6\cdot\frac{2}{3}=-\frac{12}{3}\)

Now divide.

\(-\frac{12}{3}=-4\)

Final result: \(-4\)

Detailed Explanation

Write the integer as a fraction.Every integer can be written as a fraction with denominator 1. So rewrite the problem as
\( -6 \times \frac{2}{3} = \frac{-6}{1} \times \frac{2}{3} \).
Multiply the fractions (numerators together, denominators together).Multiply numerators: \( -6 \times 2 = -12 \).
Multiply denominators: \( 1 \times 3 = 3 \).

So the product is \( \frac{-12}{3} \).
Simplify the fraction.Divide numerator and denominator by their greatest common divisor, which is 3:
\( \frac{-12}{3} = \frac{-12 \div 3}{3 \div 3} = \frac{-4}{1} = -4. \)
Check sign rule (explain the sign).A negative number times a positive number is negative, so the result is negative. That agrees with the simplified value \( -4 \).
Alternative method (cancel before multiplying).Start from \( \frac{-6}{1} \times \frac{2}{3} \). Cancel a common factor 3 between 6 and 3: \( \frac{-6}{1} \times \frac{2}{3} = \frac{-2}{1} \times \frac{2}{1} = \frac{-4}{1} = -4. \)

Final answer: \( -4 \)

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Arithmetic FAQs

What is \(-6 \times \frac{2}{3}\)?.

\((-6)\times\frac{2}{3}=\frac{-6\times2}{3}=\frac{-12}{3}=-4\). You can also cancel first: \(\frac{-6}{3}=-2\), then \(-2\times2=-4\).

Why is the product negative?

Negative times a positive is negative by sign rules: \((-)\times(+)=(-)\). Here \(-6\) is negative and \(\frac{2}{3}\) is positive, so the result is negative.

Can I simplify before multiplying?

Yes. Write \(-6\) as \(\frac{-6}{1}\) and cancel common factors: \(\frac{-6}{1}\times\frac{2}{3}=\frac{-6\times2}{3}\). Cancel 6 and 3 to get \(-2\times2=-4\).

How do I write \(-6\) as a fraction to multiply?

Use \(-6=\frac{-6}{1}\). Then \(\frac{-6}{1}\times\frac{2}{3}=\frac{-6\times2}{1\times3}=\frac{-12}{3}=-4\).

What is the decimal form of the answer?

The product \( -4 \) as a decimal is \( -4.0 \) (or just \( -4 \)).

What if both numbers were negative, e.g., \(-6\times -\frac{2}{3}\)?.

How can I show the multiplication as division first?

Think \( \times\frac{2}{3} \) as multiply by 2 then divide by 3: \((-6)\times2=-12\), then \(-12\div3=-4\).

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