Which sign makes the statement true?

Question

3/6 ? 2/4

><=

Answer 1

To determine which sign makes the statement true, we need to compare the two fractions \( \frac{3}{6} \) and \( \frac{2}{4} \).

First, we can simplify these fractions:

• \( \frac{3}{6} = \frac{1}{2} \)
• \( \frac{2}{4} = \frac{1}{2} \)

Now, we have:

\( \frac{3}{6} = \frac{2}{4} \)

Since both fractions are equal, the correct sign to use is \( = \).

So the complete statement is:

\( \frac{3}{6} = \frac{2}{4} \)

Thus, none of the signs \( >, <, \) or \( \leq \) makes the statement true; the correct response is the equal sign \( = \).

Answer 2

-4/5 ? -3/10

Answer 3

To compare the fractions \(-\frac{4}{5}\) and \(-\frac{3}{10}\), we can either convert them to a common denominator or convert them to decimal form.

Let's convert both fractions into decimal form:

1. \(-\frac{4}{5} = -0.8\)
2. \(-\frac{3}{10} = -0.3\)

Now we compare the two values:

-0.8 is less than -0.3.

Thus, \(-\frac{4}{5} < -\frac{3}{10}\).

The correct sign is \( < \).

So, the complete statement is:

\(-\frac{4}{5} < -\frac{3}{10}\)

Answer 4

Which sign makes the statement true?

6 1/2 ? –8 11/16

Answer 5

To compare \(6 \frac{1}{2}\) and \(-8 \frac{11}{16}\), we first convert both mixed numbers to improper fractions.

1. Convert \(6 \frac{1}{2}\) to an improper fraction: \[ 6 \frac{1}{2} = 6 \times 2 + 1 = 12 + 1 = \frac{13}{2} \]

2. Convert \(-8 \frac{11}{16}\) to an improper fraction: \[ -8 \frac{11}{16} = -\left(8 \times 16 + 11\right) = -\left(128 + 11\right) = -139 \] This means we can express it as: \[ -8 \frac{11}{16} = -\frac{139}{16} \]

3. To compare the two fractions, it is useful to find a common denominator, which is 16 in this case. Convert \(\frac{13}{2}\) to have a denominator of 16: \[ \frac{13}{2} = \frac{13 \times 8}{2 \times 8} = \frac{104}{16} \]

Now we compare \(\frac{104}{16}\) with \(-\frac{139}{16}\):

• Since \(104\) is positive and \(-139\) is negative, it is clear that: \[ \frac{104}{16} > -\frac{139}{16} \]

Thus, the correct sign is \(>\).

So the complete statement is: \[ 6 \frac{1}{2} > -8 \frac{11}{16} \]

Answer 6

1 5/8 ? 1 1/5

Answer 7

To compare \( 1 \frac{5}{8} \) and \( 1 \frac{1}{5} \), we can convert both mixed numbers into improper fractions or decimals. Let's convert them into improper fractions.

1. Convert \( 1 \frac{5}{8} \) to an improper fraction: \[ 1 \frac{5}{8} = 1 \times 8 + 5 = 8 + 5 = \frac{13}{8} \]

2. Convert \( 1 \frac{1}{5} \) to an improper fraction: \[ 1 \frac{1}{5} = 1 \times 5 + 1 = 5 + 1 = \frac{6}{5} \]

Now we have:

• \( \frac{13}{8} \)
• \( \frac{6}{5} \)

Next, we can find a common denominator to compare these fractions. The least common multiple of 8 and 5 is 40.

3. Convert each fraction to have a denominator of 40:

• For \( \frac{13}{8} \): \[ \frac{13}{8} = \frac{13 \times 5}{8 \times 5} = \frac{65}{40} \]

• For \( \frac{6}{5} \): \[ \frac{6}{5} = \frac{6 \times 8}{5 \times 8} = \frac{48}{40} \]

Now we can compare:

• \( \frac{65}{40} \) and \( \frac{48}{40} \)

Since \( 65 > 48 \), we have: \[ \frac{13}{8} > \frac{6}{5} \]

Thus, the complete statement is: \[ 1 \frac{5}{8} > 1 \frac{1}{5} \]

Answer 8

7.3 ? 7.8

Answer 9

To compare the two decimal numbers \(7.3\) and \(7.8\):

• \(7.3\) is less than \(7.8\).

Thus, the correct sign to make the statement true is \( < \).

The complete statement is: \[ 7.3 < 7.8 \]

Answer 10

4 ? 4.0

Answer 11

To compare the two values \(4\) and \(4.0\):

• Both \(4\) and \(4.0\) represent the same quantity. Therefore, they are equal.

The correct sign to indicate their relationship is \( = \).

The complete statement is: \[ 4 = 4.0 \]