Comparing Fractions: Equivalent Fractions

To solve this problem, we'll follow these steps:

• Step 1: Simplify both fractions to their lowest terms.
• Step 2: Compare the simplified fractions.

Now, let's work through each step:

Step 1: Simplification
Simplify $\frac{5}{25}$:
- The greatest common divisor of 5 and 25 is 5.
- Divide the numerator and the denominator by 5: $\frac{5}{25} = \frac{5 \div 5}{25 \div 5} = \frac{1}{5}$.
The fraction $\frac{5}{25}$ simplifies to $\frac{1}{5}$.
The fraction $\frac{1}{5}$ stays the same as it is already in its simplest form.

Step 2: Comparison
Since both fractions simplify to $\frac{1}{5}$, they are indeed equal.

Therefore, the solution to the problem is that the missing sign is $=$.

To solve the problem, we begin by comparing the fractions $\frac{1}{2}$ and $\frac{2}{4}$. We will simplify $\frac{2}{4}$ to see if it is equivalent to $\frac{1}{2}$.

Let's simplify $\frac{2}{4}$. We do this by finding the greatest common divisor (GCD) of 2 and 4, which is 2. We then divide both the numerator and the denominator by 2:

Now, we see that $\frac{2}{4}$ simplifies to $\frac{1}{2}$.

Since $\frac{2}{4}$ simplifies to $\frac{1}{2}$, the two fractions are equivalent.

Therefore, we fill in the missing sign with an equals sign:

$=$

To determine the missing sign between $\frac{1}{9}$ and $\frac{3}{27}$, we will first simplify the fraction $\frac{3}{27}$.

Step 1: Simplify $\frac{3}{27}$.
The greatest common divisor (GCD) of 3 and 27 is 3. So, we divide both the numerator and the denominator by 3:

$\frac{3 \div 3}{27 \div 3} = \frac{1}{9}$

Step 2: Compare $\frac{1}{9}$ and the simplified version of $\frac{3}{27}$, which is $\frac{1}{9}$.

Since both fractions are equal, we fill in the missing sign with an equals sign.

Therefore, the correct answer is $=$.

We will compare the fractions $\frac{2}{8}$ and $\frac{4}{16}$ by simplifying them to their lowest terms.

Step 1: Simplify $\frac{2}{8}$:
The greatest common divisor (GCD) of 2 and 8 is 2.
Dividing the numerator and the denominator by 2 gives us:
$\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$

Step 2: Simplify $\frac{4}{16}$:
The greatest common divisor (GCD) of 4 and 16 is 4.
Dividing the numerator and the denominator by 4 gives us:
$\frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4}$

Step 3: Compare the simplified fractions:
Both $\frac{1}{4}$ and $\frac{1}{4}$ are equal.

Therefore, the correct comparison sign to fill in the blank is $=$.

To solve this problem, let's follow these steps:

• Step 1: Simplify the fraction $\frac{6}{21}$.
• Step 2: Compare the fractions $\frac{2}{7}$ and the simplified form of $\frac{6}{21}$.

Now, let's carry out these steps:

Step 1: Simplify $\frac{6}{21}$.
To simplify $\frac{6}{21}$, we find the greatest common divisor (GCD) of 6 and 21, which is 3. Dividing the numerator and the denominator by their GCD, we get:

$\frac{6 \div 3}{21 \div 3} = \frac{2}{7}$.

Step 2: Now, compare $\frac{2}{7}$ with the simplified form of $\frac{6}{21}$, which is also $\frac{2}{7}$. Thus, we have:

$\frac{2}{7} = \frac{2}{7}$.

Therefore, the missing sign between the fractions $\frac{2}{7}$ and $\frac{6}{21}$ is $=$.

To solve this problem, we'll compare the two fractions $\frac{2}{3}$ and $\frac{8}{12}$ to determine the suitable mathematical sign between them.

Step 1: Simplify the fraction $\frac{8}{12}$.

• The greatest common divisor of 8 and 12 is 4.
• Divide the numerator and the denominator of $\frac{8}{12}$ by 4:
  $\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$.

Step 2: Now we compare the fractions $\frac{2}{3}$ and the simplified $\frac{8}{12} = \frac{2}{3}$.

• Since both fractions $\frac{2}{3}$ and $\frac{2}{3}$ are identical, they are equal.

Therefore, the missing sign to make the statement true is $=$, since both fractions are equivalent.

This corresponds to choice id="3".

Therefore, the solution to the problem is $=$.

To compare the fractions $\frac{3}{4}$ and $\frac{6}{8}$, we will first simplify each fraction.

First, $\frac{3}{4}$ is already in simplest form since the GCD of 3 and 4 is 1.

Now, for the fraction $\frac{6}{8}$, we find the GCD of 6 and 8, which is 2. Simplifying $\frac{6}{8}$ by dividing both the numerator and the denominator by 2 gives:

$\frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Both fractions, $\frac{3}{4}$ and $\frac{6}{8}$, simplify to $\frac{3}{4}$.

Since they simplify to the same form, they are equivalent:

$\frac{3}{4} = \frac{6}{8}$

Therefore, the correct missing sign is $\boxed{=}$.

$=$

To solve this problem, we follow these steps:

• Simplify each fraction to its simplest form.

• Compare the simplified fractions to determine their relationship.

Let's simplify the fractions:

$\frac{2}{5}$ is already in its simplest form since 2 and 5 have no common factors other than 1.

For $\frac{6}{15}$, find the greatest common factor (GCF) of 6 and 15, which is 3.

Divide both the numerator and the denominator by their GCF:

$\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Now both fractions simplify to $\frac{2}{5}$.

Since the fractions $\frac{2}{5}$ and $\frac{2}{5}$ are equal, we use the symbol $=$.

Therefore, the correct symbol to fill in the blank is$$ = $$.