Question

-156/396 and -26/33 are equivalent fractions.

True
False

Answer 1

To determine if the fractions \(-156/396\) and \(-26/33\) are equivalent, we can simplify each fraction and compare them or find a common denominator.

Let's simplify \(-156/396\):

1. Find the greatest common divisor (GCD) of 156 and 396. The GCD is 78.
2. Divide both the numerator and the denominator by 78:

\[
\frac{-156}{396} = \frac{-156 \div 78}{396 \div 78} = \frac{-2}{5.08} \approx -0.3939
\]

Now let's simplify \(-26/33\):

The GCD of 26 and 33 is 1 (since they have no common factors other than 1), so:

\[
\frac{-26}{33} = \frac{-26}{33} \quad \text{(already in simplest form)}
\]

Now we check if -156/396 simplifies to -26/33:

1. Since \(-26/33\) remains as is, we switch to decimal format or cross-multiply:

- For -156/396:

-156 ÷ 396 is -0.3939

- For -26/33:

-26 ÷ 33 is approximately -0.7878

Since they yield very different results, the conclusion is:

\[
\text{False}
\]

Thus, \(-156/396\) and \(-26/33\) are not equivalent fractions.