Which sign makes the statement true?

Question

12/15 ? 4/5
<
>
=

Answer 1

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 2

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

Answer 3

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 4

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

Answer 5

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 6

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

Answer 7

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 8

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

Answer 9

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 10

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

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: \[ 6 \frac{1}{5} < 6.35 \]