Operations with Fractions

To solve the problem $\frac{1}{3} - \frac{1}{5}$, we follow these steps:

First, we need to find a common denominator for the fractions $\frac{1}{3}$ and $\frac{1}{5}$. The denominators are 3 and 5, and their least common multiple (LCM) is 15.

We will convert each fraction to an equivalent fraction with the denominator 15:

• To convert $\frac{1}{3}$ to a fraction with denominator 15, multiply both the numerator and the denominator by 5: $\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$
• To convert $\frac{1}{5}$ to a fraction with denominator 15, multiply both the numerator and the denominator by 3: $\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

Now that both fractions have the same denominator, we can subtract the numerators:

Therefore, the solution to the problem is $\frac{2}{15}$.

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

• Step 1: Find the common denominator for the fractions $\frac{2}{4}$ and $\frac{1}{3}$.
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Perform the subtraction and simplify if necessary.

Now, let's work through these steps:

Step 1: The denominators are $4$ and $3$. The common denominator is the product $4 \times 3 = 12$.

Step 2: Convert each fraction:
$\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}$
$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Step 3: Subtract the fractions with a common denominator:
$\frac{6}{12} - \frac{4}{12} = \frac{6 - 4}{12} = \frac{2}{12}$

Finally, simplify $\frac{2}{12}$. The greatest common divisor of 2 and 12 is 2, so:
$\frac{2}{12} = \frac{2 \div 2}{12 \div 2} = \frac{1}{6}$

Therefore, the solution to the problem is $\frac{1}{6}$.

To solve the subtraction of fractions $\frac{3}{5} - \frac{1}{2}$, we will follow these steps:

• Step 1: Find the least common multiple (LCM) of the denominators 5 and 2. The LCM of 5 and 2 is 10.
• Step 2: Convert each fraction to have a denominator of 10.
• Step 3: Subtract the converted fractions.
• Step 4: Simplify the result if necessary.

Now, let's work through each step in detail:

Step 1: The LCM of 5 and 2 is 10, since 10 is the smallest number that both 5 and 2 divide into evenly.

Step 2: Convert each fraction to have a denominator of 10.

For $\frac{3}{5}$:
Multiply numerator and denominator by 2 to get $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$.

For $\frac{1}{2}$:
Multiply numerator and denominator by 5 to get $\frac{1 \times 5}{2 \times 5} = \frac{5}{10}$.

Step 3: Subtract the fractions:

$\frac{6}{10} - \frac{5}{10} = \frac{6 - 5}{10} = \frac{1}{10}$.

Step 4: There is no further simplification needed for $\frac{1}{10}$ as it is already in its simplest form.

Therefore, the solution to the problem is $\frac{1}{10}$.

The correct answer, choice (4), is $\frac{1}{10}$.

To solve the problem of subtracting $\frac{1}{4}$ from $\frac{3}{5}$, we need a common denominator.

First, find the least common denominator (LCD) of 5 and 4, which is 20. This is done by multiplying the denominators: $5 \times 4 = 20$.

Next, convert each fraction to an equivalent fraction with the denominator of 20:

• For $\frac{3}{5}$: Multiply both numerator and denominator by 4 to get $\frac{3 \times 4}{5 \times 4} = \frac{12}{20}$.
• For $\frac{1}{4}$: Multiply both numerator and denominator by 5 to get $\frac{1 \times 5}{4 \times 5} = \frac{5}{20}$.

Now perform the subtraction with these equivalent fractions:

$\frac{12}{20} - \frac{5}{20} = \frac{12 - 5}{20} = \frac{7}{20}$

The resulting fraction, $\frac{7}{20}$, is already in its simplest form.

Therefore, the solution to the subtraction $\frac{3}{5} - \frac{1}{4}$ is $\frac{7}{20}$.

Checking against the multiple-choice answers, the correct choice is the first one: $\frac{7}{20}$.

To solve the subtraction of fractions $\frac{3}{5} - \frac{1}{3}$, follow these steps:

• Step 1: Find the Least Common Denominator (LCD)
  The denominators are 5 and 3. The least common multiple of 5 and 3 is 15. Thus, the common denominator will be 15.
• Step 2: Convert fractions to have the same denominator
  For $\frac{3}{5}$, multiply both the numerator and the denominator by 3 to get:
  $\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$.
  For $\frac{1}{3}$, multiply both the numerator and the denominator by 5 to get:
  $\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}$.
• Step 3: Subtract the numerators
  Now subtract the equivalent fractions:
  $\frac{9}{15} - \frac{5}{15} = \frac{9 - 5}{15} = \frac{4}{15}$.
• Step 4: Simplify the fraction
  The fraction $\frac{4}{15}$ is already in its simplest form.

Thus, the solution to the problem is $\frac{4}{15}$.