Question

Which sign makes the statement true?
12/15 ? 4/5
<
>
=

Answer 1

Which sign makes the statement true?
-3/12 ? -1/2
<
>
=

Answer 2

Which sign makes the statement true?
8 3/5 ? 8 5/8
<
>
=

Answer 3

Which sign makes the statement true?
-2/5 ? -6/15

Answer 4

Which sign makes the statement true?
2 ? 2/1

Answer 5

Which sign makes the statement true?
6 1/5 ? 6.35

Answer 6

To determine which sign makes the statement true, we need to compare the two fractions: \( \frac{12}{15} \) and \( \frac{4}{5} \).

First, we can simplify \( \frac{12}{15} \):
- The greatest common divisor (GCD) of 12 and 15 is 3.
- Dividing both the numerator and the denominator by 3, we get:
\[
\frac{12 \div 3}{15 \div 3} = \frac{4}{5}
\]

Now we can compare \( \frac{12}{15} \) and \( \frac{4}{5} \):
\[
\frac{12}{15} = \frac{4}{5}
\]

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

So, the statement is:
\[
\frac{12}{15} = \frac{4}{5}
\]

Answer 7

To determine which sign makes the statement true between \( -\frac{3}{12} \) and \( -\frac{1}{2} \), we first simplify \( -\frac{3}{12} \).

\[
-\frac{3}{12} = -\frac{1}{4} \quad (\text{by dividing the numerator and denominator by 3})
\]

Now we can compare \( -\frac{1}{4} \) and \( -\frac{1}{2} \).

To do so, it can help to express both fractions with the same denominator, which is 4:

\[
-\frac{1}{2} = -\frac{2}{4}
\]

Now we can compare:
- \( -\frac{1}{4} \)
- \( -\frac{2}{4} \)

Since \( -\frac{1}{4} \) is greater than \( -\frac{2}{4} \):

\[
-\frac{1}{4} > -\frac{1}{2}
\]

Therefore, the correct sign to make the statement true is \( > \).

So the final statement is:
\[
-\frac{3}{12} > -\frac{1}{2}
\]

Answer 8

To compare the mixed numbers \( 8 \frac{3}{5} \) and \( 8 \frac{5}{8} \), it's helpful to convert them into improper fractions first or decimal form.

### Step 1: Convert to improper fractions

1. **Convert \( 8 \frac{3}{5} \)**:
\[
8 \frac{3}{5} = 8 \times 5 + 3 = 40 + 3 = 43 \quad \text{so } 8 \frac{3}{5} = \frac{43}{5}
\]

2. **Convert \( 8 \frac{5}{8} \)**:
\[
8 \frac{5}{8} = 8 \times 8 + 5 = 64 + 5 = 69 \quad \text{so } 8 \frac{5}{8} = \frac{69}{8}
\]

### Step 2: Find a common denominator
The least common denominator of 5 and 8 is 40.

3. **Convert \( \frac{43}{5} \)**:
\[
\frac{43}{5} = \frac{43 \times 8}{5 \times 8} = \frac{344}{40}
\]

4. **Convert \( \frac{69}{8} \)**:
\[
\frac{69}{8} = \frac{69 \times 5}{8 \times 5} = \frac{345}{40}
\]

### Step 3: Compare the two fractions
Now we can compare \( \frac{344}{40} \) and \( \frac{345}{40} \).

Since:
\[
344 < 345
\]

### Conclusion
Therefore:
\[
8 \frac{3}{5} < 8 \frac{5}{8}
\]

The correct sign is \( < \). Thus, the statement reads:
\[
8 \frac{3}{5} < 8 \frac{5}{8}
\]

Answer 9

To compare \(-\frac{2}{5}\) and \(-\frac{6}{15}\), we can either convert both fractions to a common denominator or simplify them.

### Step 1: Simplifying \(-\frac{6}{15}\)

We can simplify \(-\frac{6}{15}\):
- Find the greatest common divisor (GCD) of 6 and 15, which is 3.
- Dividing the numerator and the denominator by 3 gives us:
\[
-\frac{6}{15} = -\frac{6 \div 3}{15 \div 3} = -\frac{2}{5}
\]

### Step 2: Compare the two fractions

Now we compare:
\[
-\frac{2}{5} \quad \text{and} \quad -\frac{2}{5}
\]

Since they are equal, we can conclude:
\[
-\frac{2}{5} = -\frac{6}{15}
\]

### Conclusion

The correct sign to make the statement true is \( = \). Thus, the final statement reads:
\[
-\frac{2}{5} = -\frac{6}{15}
\]

Answer 10

To compare the number \( 2 \) with the fraction \( \frac{2}{1} \), we can first recognize that:

\[
\frac{2}{1} = 2
\]

So both values are equal.

### Conclusion

The correct sign to make the statement true is \( = \). Thus, the statement reads:

\[
2 = \frac{2}{1}
\]

Answer 11

To compare \( 6 \frac{1}{5} \) and \( 6.35 \), we first convert the mixed number \( 6 \frac{1}{5} \) to decimal form.

### Step 1: Convert \( 6 \frac{1}{5} \) to decimal

1. The whole number part is \( 6 \).
2. The fraction \( \frac{1}{5} \) can be converted to decimal by dividing 1 by 5:
\[
\frac{1}{5} = 0.2
\]
3. Thus, we have:
\[
6 \frac{1}{5} = 6 + 0.2 = 6.2
\]

### Step 2: Compare \( 6.2 \) and \( 6.35 \)

Since \( 6.2 \) is less than \( 6.35 \), we can conclude:
\[
6 \frac{1}{5} < 6.35
\]

### Conclusion

The correct sign to make the statement true is \( < \). Thus, the statement reads:
\[
6 \frac{1}{5} < 6.35
\]