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-17/336 ? -82 1/2

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11 answers

To compare \(-\frac{17}{336}\) with \(-82 \frac{1}{2}\), we first need to convert \(-82 \frac{1}{2}\) into an improper fraction:

\[ -82 \frac{1}{2} = -\frac{165}{2} \]

Next, we need a common denominator to compare \(-\frac{17}{336}\) and \(-\frac{165}{2}\). The least common multiple of 336 and 2 is 336.

Now, we convert \(-\frac{165}{2}\) to a fraction with a denominator of 336:

\[ -\frac{165}{2} = -\frac{165 \times 168}{2 \times 168} = -\frac{27720}{336} \]

Now we can compare:

\(-\frac{17}{336}\) and \(-\frac{27720}{336}\)

Since both fractions have the same denominator, we compare their numerators.

\( -17 \) is greater than \( -27720 \) (because -17 is closer to zero). Therefore:

\(-\frac{17}{336} > -\frac{165}{2}\)

In inequality notation:

\(-\frac{17}{336} > -82 \frac{1}{2}\)

So, the final comparison is:

\(-\frac{17}{336} > -82 \frac{1}{2}\)

9 158/631 ? 9
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To compare \(9 \frac{158}{631}\) with \(9\), we need to convert the mixed number \(9 \frac{158}{631}\) into an improper fraction.

  1. Convert \(9 \frac{158}{631}\) into an improper fraction:

\[ 9 \frac{158}{631} = 9 + \frac{158}{631} = \frac{9 \times 631 + 158}{631} = \frac{5679 + 158}{631} = \frac{5837}{631} \]

  1. Now, we compare \(\frac{5837}{631}\) with \(9\). We can express \(9\) as a fraction with the same denominator of \(631\):

\[ 9 = \frac{9 \times 631}{631} = \frac{5679}{631} \]

  1. Now we can compare the two fractions:

\[ \frac{5837}{631} \quad \text{and} \quad \frac{5679}{631} \]

Since \(5837 > 5679\), we have:

\[ \frac{5837}{631} > \frac{5679}{631} \]

Therefore:

\[ 9 \frac{158}{631} > 9 \]

In inequality notation:

\[ 9 \frac{158}{631} > 9 \]

370/534 ? -44/59

To compare \(\frac{370}{534}\) with \(-\frac{44}{59}\), we need to first express both fractions with a common denominator, or convert them to decimal values for easier comparison.

Step 1: Simplify \(\frac{370}{534}\)

We'll simplify \(\frac{370}{534}\) first.

The greatest common divisor (GCD) of 370 and 534 can be found as follows:

  • The prime factorization of 370 is \(2 \times 5 \times 37\).
  • The prime factorization of 534 is \(2 \times 3 \times 89\).

The GCD is \(2\).

Now we simplify:

\[ \frac{370 \div 2}{534 \div 2} = \frac{185}{267} \]

Step 2: Express both fractions in decimal form

We can convert both fractions to decimal to compare them directly.

  1. For \(\frac{185}{267}\):

    \[ \frac{185}{267} \approx 0.6925 \]

  2. For \(-\frac{44}{59}\):

    \[ -\frac{44}{59} \approx -0.7458 \]

Step 3: Compare the decimal values

Now we can easily compare the two decimal values:

\[ 0.6925 > -0.7458 \]

Conclusion

Therefore, we find:

\[ \frac{370}{534} > -\frac{44}{59} \]

In inequality notation:

\[ \frac{370}{534} > -\frac{44}{59} \]

-1/2 ? -47

To compare \(-\frac{1}{2}\) with \(-47\), we can convert both numbers into a format that makes comparison simple.

  1. Understand the values:

    • \(-\frac{1}{2}\) is a small negative number (just below zero).
    • \(-47\) is a much larger negative number.

  2. Comparing the two: Since \(-\frac{1}{2}\) is closer to zero than \(-47\), we can conclude that:

\[ -\frac{1}{2} > -47 \]

Conclusion

In inequality notation:

\[ -\frac{1}{2} > -47 \]

This afternoon, Alec saw 5/6 of his friends. Marvin saw 11/12 of his friends. Who saw a greater fraction of his friends?

A. Alec

B. Marvin

To determine who saw a greater fraction of their friends, we need to compare \(\frac{5}{6}\) (Alec) and \(\frac{11}{12}\) (Marvin).

Step 1: Find a common denominator

The least common denominator (LCD) of 6 and 12 is 12.

Step 2: Convert both fractions to have a common denominator of 12

  • For Alec's fraction \(\frac{5}{6}\):

\[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]

  • For Marvin's fraction \(\frac{11}{12}\):

\[ \frac{11}{12} \text{ remains the same.} \]

Step 3: Compare the fractions

Now we can compare:

  • Alec's fraction: \(\frac{10}{12}\)
  • Marvin's fraction: \(\frac{11}{12}\)

Since \(11/12\) is greater than \(10/12\):

\[ \frac{10}{12} < \frac{11}{12} \]

Conclusion

Thus, Marvin saw a greater fraction of his friends.

The answer is: B. Marvin

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35.6 ? 35.75

To compare \(35.6\) and \(35.75\), we can convert both numbers to a consistent decimal format.

  1. Convert \(35.6\) to the same decimal places: \[ 35.6 = 35.60 \]

  2. Now, compare the two values:

    • \(35.60\)
    • \(35.75\)

Since \(35.75\) is greater than \(35.60\), we have:

\[ 35.6 < 35.75 \]

Conclusion

Thus, in inequality notation:

\[ 35.6 < 35.75 \]