10 11/16 ? 171/16

Question

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Answer 1

To compare the two fractions \( 10 \frac{11}{16} \) and \( \frac{171}{16} \), it is helpful to first convert \( 10 \frac{11}{16} \) into an improper fraction.

1. Convert \( 10 \frac{11}{16} \) to an improper fraction: \[ 10 \frac{11}{16} = \frac{10 \times 16 + 11}{16} = \frac{160 + 11}{16} = \frac{171}{16} \]

Now we can compare:

• \( 10 \frac{11}{16} = \frac{171}{16} \)
• \( 171/16 \) is the same as \( \frac{171}{16} \)

Thus, we have: \[ 10 \frac{11}{16} = \frac{171}{16} \]

The relation is: \[ 10 \frac{11}{16} , = , \frac{171}{16} \]

So, the answer is: \[ 10 \frac{11}{16} , = , \frac{171}{16} \]

Answer 2

1/2 ? 2

Answer 3

To compare \( \frac{1}{2} \) and \( 2 \), it's helpful to express both quantities in the same form.

1. We can rewrite \( 2 \) as a fraction: \[ 2 = \frac{2}{1} \]

2. Now, let's convert both fractions to have a common denominator. The least common denominator of \( 2 \) and \( 1 \) is \( 2 \):

   • Convert \( 2 \) to have a denominator of \( 2 \): \[ 2 = \frac{2 \times 2}{1 \times 2} = \frac{4}{2} \]

3. Now we can compare:

   • \( \frac{1}{2} \) is equivalent to \( \frac{1}{2} \)
   • \( 2 \) is equivalent to \( \frac{4}{2} \)

Now we can see that: \[ \frac{1}{2} < \frac{4}{2} \]

Therefore, the relationship is: \[ \frac{1}{2} < 2 \]

Answer 4

-5 18/25 ? 3/16

Answer 5

To compare \(-5 \frac{18}{25}\) and \(\frac{3}{16}\), we first convert \(-5 \frac{18}{25}\) into an improper fraction.

1. Convert \(-5 \frac{18}{25}\) to an improper fraction: \[ -5 \frac{18}{25} = -\left(5 \times 25 + 18\right)/25 = -\left(125 + 18\right)/25 = -\frac{143}{25} \]

Now we have:

• \(-5 \frac{18}{25} = -\frac{143}{25}\)
• \(\frac{3}{16}\)

Next, we need a common denominator to compare \(-\frac{143}{25}\) and \(\frac{3}{16}\). The least common multiple of \(25\) and \(16\) is \(400\).

2. Convert both fractions to have a denominator of \(400\): \[ -\frac{143}{25} = -\frac{143 \times 16}{25 \times 16} = -\frac{2288}{400} \] \[ \frac{3}{16} = \frac{3 \times 25}{16 \times 25} = \frac{75}{400} \]

Now we can compare:

• \(-\frac{2288}{400}\) and \(\frac{75}{400}\)

Since \(-2288\) is clearly less than \(75\), we have: \[ -\frac{2288}{400} < \frac{75}{400} \]

Thus, the relationship is: \[ -5 \frac{18}{25} < \frac{3}{16} \]

Answer 6

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–95/198 ? –11.540

Answer 7

To compare \(-\frac{95}{198}\) and \(-11.540\), we first need to express \(-\frac{95}{198}\) as a decimal.

1. Divide \(-95\) by \(198\) to find the decimal form: \[ -\frac{95}{198} \approx -0.4798 \]

Now we have:

• \(-\frac{95}{198} \approx -0.4798\)
• \(-11.540\)

Next, we can compare these two values.

Since \(-11.540\) is less than \(-0.4798\), we have: \[ -11.540 < -0.4798 \]

Thus, the relationship is: \[ -\frac{95}{198} > -11.540 \]

This means: \[ -\frac{95}{198} , > , -11.540 \]