Comparing Fractions Practice Problems & Worksheets

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 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 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 $\frac{1}{3} \lt \frac{2}{3}$.

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: $\frac{3}{10} > \frac{1}{10}$.