To compare \( \frac{1}{4} \) and \( -\frac{6}{25} \), we can convert them both to a common denominator or convert them to decimal form. ### Method 1: Convert to decimal 1. Convert \( \frac{1}{4} \) to a decimal: \[ \frac{1}{4} = 0.25 \] 2. Convert \( -\frac{6}{25} \) to a decimal: \[ -\frac{6}{25} = -0.24 \] ### Comparison: Now we can compare the two decimal values: - \( 0.25 \) (which is \( \frac{1}{4} \)) - \( -0.24 \) (which is \( -\frac{6}{25} \)) Since \( 0.25 \) is greater than \( -0.24 \), we can conclude that: \[ \frac{1}{4} > -\frac{6}{25} \] ### Method 2: Common denominator 1. The least common multiple of 4 and 25 is 100. 2. Convert \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{25}{100} \] 3. Convert \( -\frac{6}{25} \): \[ -\frac{6}{25} = -\frac{24}{100} \] ### Comparison: Now we have: - \( \frac{25}{100} \) - \( -\frac{24}{100} \) Since \( 25 > -24 \), it confirms that: \[ \frac{1}{4} > -\frac{6}{25} \] In summary, the final comparison is: \(\frac{1}{4} > -\frac{6}{25}\)

To compare \(-3.8\) and \(-3.80\), we can observe the values directly. - \(-3.8\) is equivalent to \(-3.80\) because the trailing zero does not change the value of the number. Thus, we can conclude that: \[ -3.8 = -3.80 \] So, in terms of the comparison: \(-3.8 = -3.80\)

-2 9/20 ? -2 >

To compare -2 9/20 and -2, we first need to convert -2 9/20 into an improper fraction or a decimal.

-2 9/20 can be written as:

\[ -2 9/20 = -\left(2 + \frac{9}{20}\right) = - \frac{40}{20} - \frac{9}{20} = -\frac{49}{20} \]

Next, we simplify -2 into a fraction with a denominator of 20:

\[ -2 = -\frac{40}{20} \]

Now we can compare -49/20 with -40/20.

Since -49 is less than -40, we have:

\[ -\frac{49}{20} < -\frac{40}{20} \]

Therefore, we can conclude that:

\[ -2 \frac{9}{20} < -2 \]

So the comparison is:

\(-2 \frac{9}{20} < -2\) (or in terms of your original symbols, -2 9/20 < -2)

1/4 ? -6/25

To compare \( \frac{1}{4} \) and \( -\frac{6}{25} \), we can convert them both to a common denominator or convert them to decimal form.

Method 1: Convert to decimal

Convert \( \frac{1}{4} \) to a decimal: \[ \frac{1}{4} = 0.25 \]
Convert \( -\frac{6}{25} \) to a decimal: \[ -\frac{6}{25} = -0.24 \]

Comparison:

Now we can compare the two decimal values:

\( 0.25 \) (which is \( \frac{1}{4} \))
\( -0.24 \) (which is \( -\frac{6}{25} \))

Since \( 0.25 \) is greater than \( -0.24 \), we can conclude that:

\[ \frac{1}{4} > -\frac{6}{25} \]

Method 2: Common denominator

The least common multiple of 4 and 25 is 100.
Convert \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{25}{100} \]
Convert \( -\frac{6}{25} \): \[ -\frac{6}{25} = -\frac{24}{100} \]

Comparison:

Now we have:

\( \frac{25}{100} \)
\( -\frac{24}{100} \)

Since \( 25 > -24 \), it confirms that:

\[ \frac{1}{4} > -\frac{6}{25} \]

In summary, the final comparison is:

\(\frac{1}{4} > -\frac{6}{25}\)

-3.8 ? -3.80

To compare \(-3.8\) and \(-3.80\), we can observe the values directly.

\(-3.8\) is equivalent to \(-3.80\) because the trailing zero does not change the value of the number.

Thus, we can conclude that:

\[ -3.8 = -3.80 \]

So, in terms of the comparison:

\(-3.8 = -3.80\)