Comparing Fractions - Examples, Exercises and Solutions

To solve this problem, follow these steps:

• Identify the two fractions: $\frac{6}{7}$ and $\frac{3}{7}$.

• Since both fractions have a common denominator, compare the numerators directly: 6 and 3.

• Determine that the numerator 6 is greater than 3.

• Based on this comparison, the fraction $\frac{6}{7}$ is greater than $\frac{3}{7}$.

• Thus, the correct sign to fill in the blank is $>$.

The correct answer to the problem is $>$.

To solve the problem, we will compare two fractions: $\frac{2}{8}$ and $\frac{7}{8}$.

Both fractions have the same denominator (8), which allows us to directly compare the numerators. Therefore, we need only consider the values of the numerators to understand the relationship between the two fractions.

• Step 1: Identify the numerators. For $\frac{2}{8}$, the numerator is 2. For $\frac{7}{8}$, the numerator is 7.
• Step 2: Compare the numerators. We observe that $2 < 7$.

Since 2 is less than 7, it follows that $\frac{2}{8}$ is less than $\frac{7}{8}$.

Therefore, the correct sign to place between $\frac{2}{8}$ and $\frac{7}{8}$ is $<$.

The solution to the problem is $<$.

To solve this problem, we need to determine which of the two fractions, $\frac{3}{10}$ and $\frac{1}{10}$, is greater. Since both fractions have the same denominator, the larger fraction will be the one with the larger numerator.

We'll follow these steps:

• Step 1: Identify the numerators of the two fractions. For $\frac{3}{10}$, the numerator is 3. For $\frac{1}{10}$, the numerator is 1.
• Step 2: Compare the numerators. Since 3 is greater than 1, this means that $\frac{3}{10}$ is greater than $\frac{1}{10}$.

Therefore, the correct mathematical sign to fill in the blank is $>$.

Thus, the complete inequality is: $\frac{3}{10} > \frac{1}{10}$.

The correct answer is choice 2: $\frac{3}{10} > \frac{1}{10}$.

To compare fractions with the same denominator, focus on the numerators:

• Given fractions: $\frac{5}{9}$ and $\frac{3}{9}$
• Since both fractions have the same denominator (9), we only need to compare the numerators.
• Numerator of the first fraction is 5, and the numerator of the second fraction is 3.
• Since 5 is greater than 3, $\frac{5}{9}$ is greater than $\frac{3}{9}$.

Therefore, the missing sign that correctly compares the two fractions is $>$, so the correct statement is:

$\frac{5}{9} > \frac{3}{9}$.

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

• Step 1: Identify the given fractions, $\frac{4}{7}$ and $\frac{1}{7}$.
• Step 2: Note that both fractions share the same denominator of 7.
• Step 3: Compare the numerators of the fractions, 4 and 1.

Now, let's work through each step:
Step 1: The problem provides us with the fractions $\frac{4}{7}$ and $\frac{1}{7}$.
Step 2: We can compare the numerators directly since the denominators are the same. The numerators are 4 and 1, respectively.
Step 3: Since 4 is greater than 1, $\frac{4}{7}$ is greater than $\frac{1}{7}$.

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

To find the correct comparison sign for the fractions $\frac{1}{3}$ and $\frac{2}{3}$, follow these logical steps:

• Step 1: Look at the fractions $\frac{1}{3}$ and $\frac{2}{3}$. Both fractions have the same denominator, which is 3.
• Step 2: Identify the numerators of the fractions. The numerator of $\frac{1}{3}$ is 1, and the numerator of $\frac{2}{3}$ is 2.
• Step 3: Compare these numerators. Since 1 is less than 2, we deduce that $\frac{1}{3} \lt \frac{2}{3}$.

Therefore, the missing sign to correctly complete the expression $\frac{1}{3} ☒ \frac{2}{3}$ is $\lt$. Thus, the solution to the problem is $\frac{1}{3} \lt \frac{2}{3}$.

Let's solve the problem step-by-step:

Both fractions in the problem, $\frac{7}{4}$ and $\frac{2}{4}$, have the same denominator. This allows us to directly compare their numerators.

The numerators are 7 and 2, respectively. Therefore, we need to determine whether 7 is less than, greater than, or equal to 2.

Comparing 7 and 2:

• $7 > 2$

Since 7 is greater than 2, it follows that:

• $\frac{7}{4} > \frac{2}{4}$

The correct inequality symbol to fill in the blank is $>$.

Thus, the solution to the problem is $\frac{7}{4} > \frac{2}{4}$.

Therefore, the correct choice from the available options is choice 2: $>$.

To solve this problem, we need to compare two fractions with the same denominator and determine the appropriate comparison sign:

• Step 1: Notice that both fractions, $\frac{2}{5}$ and $\frac{6}{5}$, have the same denominator, $5$.
• Step 2: Focus on comparing the numerators of both fractions: $2$ and $6$.
• Step 3: Since $2$ is less than $6$, it follows that the fraction $\frac{2}{5}$ is less than $\frac{6}{5}$.

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

The missing sign is $<$.

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:

$\frac{2 \div 2}{4 \div 2} = \frac{1}{2}$

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 solve this problem, we'll follow these steps:

• Step 1: Simplify each fraction.
• Step 2: Compare the simplified fractions.

Now, let's work through each step:
Step 1: Simplify the fractions.
- The fraction $\frac{1}{9}$ is already in its simplest form.
- The fraction $\frac{3}{27}$ can be simplified by dividing both the numerator and the denominator by 3, resulting in $\frac{1}{9}$.

Step 2: Compare the simplified fractions.
Both simplified fractions are $\frac{1}{9}$ and $\frac{1}{9}$, which are equal.

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

We need to compare the fractions $\frac{2}{8}$ and $\frac{4}{16}$. To do this, we'll simplify each fraction to see if they are equal or if one is greater than the other.

Step 1: Simplify $\frac{2}{8}$
To simplify, find the greatest common divisor (GCD) of 2 and 8, which is 2. Divide the numerator and denominator by this GCD:
$\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$

Step 2: Simplify $\frac{4}{16}$
Similarly, find the GCD of 4 and 16, which is 4. Divide both the numerator and denominator by this GCD:
$\frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4}$

Both fractions simplify to $\frac{1}{4}$. Thus, they are equal.

Conclusion:
Since the simplified forms of both fractions are equal, the correct sign to fill in is $=$.

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

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 $=$.