Subtraction of Fractions: The common denominator is smaller than the product of the denominators

In this question, we need to find a common denominator.

However, we don't have to multiply the denominators by each other as there is a lowest common denominator: 12.

$\frac{3\times3}{3\times4}$

$\frac{1\times2}{6\times2}$

$\frac{9}{12}-\frac{2}{12}=\frac{9-2}{12}=\frac{7}{12}$

We must first identify the lowest common denominator between 4 and 10.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 10.

In this case, the common denominator is 20.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 20

We'll multiply the first fraction by 2

We'll multiply the second fraction by 5

$\frac{4\times2}{10\times2}-\frac{1\times5}{4\times5}=\frac{8}{20}-\frac{5}{20}$

Finally we'll combine and obtain the following:

$\frac{8-5}{20}=\frac{3}{20}$

Let's first identify the lowest common denominator between 10 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 10 and 6.

In this case, the common denominator is 30.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 30.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 5

$\frac{7\times3}{10\times3}-\frac{2\times5}{6\times5}=\frac{21}{30}-\frac{10}{30}$

Now let's subtract:

$\frac{21-10}{30}=\frac{11}{30}$

Let's first identify the lowest common denominator between 6 and 10.

To determine the lowest common denominator, we need to find a number that is divisible by both 6 and 10.

In this case, the common denominator is 30.

Now we'll proceed to multiply each fraction by the appropriate number to reach the denominator 30.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 5

$\frac{8\times3}{10\times3}-\frac{2\times5}{6\times5}=\frac{24}{30}-\frac{10}{30}$

Now let's subtract:

$\frac{24-10}{30}=\frac{14}{30}$

Let's first identify the lowest common denominator between 4 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 6.

In this case, the common denominator is 12.

Let's proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 2

$\frac{1\times3}{4\times3}-\frac{1\times2}{6\times2}=\frac{3}{12}-\frac{2}{12}$

Now let's subtract:

$\frac{3-2}{12}=\frac{1}{12}$

Let's first identify the lowest common denominator between 4 and 6

To determine the lowest common denominator, we need to find a number that is divisible by both 4 and 6.

In this case, the common denominator is 12.

Now we'll proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 3

$\frac{5\times2}{6\times2}-\frac{2\times3}{4\times3}=\frac{10}{12}-\frac{6}{12}$

Now let's subtract:

$\frac{10-6}{12}=\frac{4}{12}$

To solve this problem, we'll perform the following steps:

• Step 1: Find the Least Common Denominator (LCD) of $3$ and $9$.
• Step 2: Convert each fraction to have the LCD as its denominator.
• Step 3: Subtract the numerators of the converted fractions.
• Step 4: Simplify the resulting fraction if needed.

Let's proceed with the steps:

Step 1: The denominators of the given fractions are $3$ and $9$. The LCD of $3$ and $9$ is $9$ since $9$ is the smallest multiple that both $3$ and $9$ divide into evenly.

Step 2: Convert each fraction to have a denominator of $9$.

$\frac{2}{3}$ can be converted to an equivalent fraction with the denominator $9$ by multiplying the numerator and denominator by 3:

$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$

The second fraction $\frac{4}{9}$ already has the denominator $9$, so it remains unchanged.

Step 3: Subtract the fractions: $\frac{6}{9} - \frac{4}{9}$.

Since the denominators are now the same, subtract the numerators:

$6 - 4 = 2$

The resulting fraction is $\frac{2}{9}$.

Step 4: Check if there is a need to simplify. The fraction $\frac{2}{9}$ is already in its simplest form.

Thus, the solution to the problem is $\frac{2}{9}$.

To solve this problem, we will follow these steps:

• Step 1: Simplify the initial fraction $\frac{2}{4}$.
• Step 2: Find a common denominator for $\frac{1}{2}$ and $\frac{1}{6}$.
• Step 3: Convert the fractions to have the common denominator.
• Step 4: Subtract the fractions.
• Step 5: Simplify the resulting fraction.

Let's work through these steps:

Step 1: Simplify $\frac{2}{4} = \frac{1}{2}$.

Step 2: Identify the least common denominator (LCD) for $\frac{1}{2}$ and $\frac{1}{6}$. The denominators are 2 and 6, and the LCM of 2 and 6 is 6.

Step 3: Convert both fractions to have this common denominator.
$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
$\frac{1}{6} = \frac{1}{6}$ (already with the correct denominator).

Step 4: Subtract the fractions:
$\frac{3}{6} - \frac{1}{6} = \frac{3 - 1}{6} = \frac{2}{6}$.

Step 5: Simplify the resulting fraction $\frac{2}{6}$. Find the greatest common divisor (GCD) of 2 and 6, which is 2, and divide both numerator and denominator by 2:
$\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}$.

Therefore, the solution to the problem is $\frac{1}{3}$.

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

• Step 1: Identify and find the least common denominator (LCD) of the denominators 4 and 6.
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Subtract the numerators of the converted fractions.
• Step 4: Simplify the result, if possible.

Now, let's work through each step:

Step 1: The denominators are 4 and 6. The LCD of 4 and 6 is 12, since 12 is the smallest number divisible by both 4 and 6.

Step 2: Convert each fraction to this common denominator.
- Convert $\frac{2}{4}$ to have a denominator of 12. We multiply both the numerator and denominator by 3:
$\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}$.
- Convert $\frac{2}{6}$ to have a denominator of 12. We multiply both the numerator and denominator by 2:
$\frac{2}{6} = \frac{2 \times 2}{6 \times 2} = \frac{4}{12}$.

Step 3: Subtract the fractions:
$\frac{6}{12} - \frac{4}{12} = \frac{6 - 4}{12} = \frac{2}{12}$.

Step 4: Simplify the result:
The fraction $\frac{2}{12}$ simplifies to $\frac{1}{6}$ by dividing both numerator and denominator by their greatest common divisor, which is 2.

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

To solve the problem $\frac{2}{4} - \frac{2}{6}$, let's follow these steps:

• Step 1: Find the least common denominator (LCD) for the fractions. The denominators are 4 and 6, and the LCM of 4 and 6 is 12.
• Step 2: Convert each fraction to an equivalent fraction with a denominator of 12.

First, convert $\frac{2}{4}$:

$\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}$

Next, convert $\frac{2}{6}$:

$\frac{2}{6} = \frac{2 \times 2}{6 \times 2} = \frac{4}{12}$

• Step 3: Subtract the fractions with the common denominator.

$\frac{6}{12} - \frac{4}{12} = \frac{6 - 4}{12} = \frac{2}{12}$

• Step 4: Simplify the result, if possible.

$\frac{2}{12}$ simplifies to $\frac{1}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

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

To solve the problem of subtracting the fractions $\frac{3}{4}$ and $\frac{1}{6}$, we follow these steps:

• First, identify the least common denominator (LCD) of the given fractions' denominators. The numbers 4 and 6 have an LCD of 12.
• Next, convert each fraction to have this common denominator.

The fraction $\frac{3}{4}$ is converted by determining what number we multiply 4 by to get 12 (which is 3). Thus, multiply both the numerator and the denominator by 3:
$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.

The fraction $\frac{1}{6}$ is converted by determining what number we multiply 6 by to get 12 (which is 2). Hence, multiply both the numerator and the denominator by 2:
$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$.

• Now that both fractions have the common denominator, subtract the numerators:

$\frac{9}{12} - \frac{2}{12} = \frac{9 - 2}{12} = \frac{7}{12}$.

The solution is the fraction $\frac{7}{12}$.

In conclusion, the answer to this problem is $\frac{7}{12}$.

To solve the problem $\frac{3}{4} - \frac{3}{6}$, follow these steps:

Step 1: Identify the denominators: 4 and 6.

Step 2: Find the Least Common Multiple (LCM) of 4 and 6. The LCM of 4 and 6 is 12, as 12 is the smallest number that both 4 and 6 divide into evenly.

Step 3: Convert each fraction to an equivalent fraction with a denominator of 12:
$\frac{3}{4}$ needs to be converted. Multiply both the numerator and denominator by 3 to obtain $\frac{9}{12}$.
$\frac{3}{6}$ also needs conversion. Multiply both the numerator and denominator by 2 to obtain $\frac{6}{12}$.

Step 4: Subtract the fractions:
$\frac{9}{12} - \frac{6}{12} = \frac{3}{12}$.

Step 5: Simplify the resulting fraction if possible.
The fraction $\frac{3}{12}$ can be simplified to $\frac{1}{4}$ by dividing both the numerator and the denominator by their greatest common divisor, 3.

Therefore, the solution to the problem is $\frac{1}{4}$.

To solve the problem $\frac{3}{5} - \frac{3}{10}$, follow these steps:

• Step 1: Find the common denominator:

The denominators are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10, so our common denominator is 10.

• Step 2: Convert each fraction to have the common denominator:

Convert $\frac{3}{5}$ to a fraction with a denominator of 10:

Multiply both the numerator and denominator of $\frac{3}{5}$ by 2 to get $\frac{6}{10}$.

Note: $\frac{3}{10}$ already has the common denominator of 10, so it remains unchanged.

• Step 3: Perform the subtraction:

Subtract $\frac{3}{10}$ from $\frac{6}{10}$:

$\frac{6}{10} - \frac{3}{10} = \frac{6 - 3}{10} = \frac{3}{10}$.

Therefore, the solution to the problem is $\frac{3}{10}$.

To solve the problem of subtracting the fraction $\frac{6}{10}$ from $\frac{4}{5}$, follow these steps:

Step 1: Identify the least common multiple (LCM) of the denominators 5 and 10.
The LCM of 5 and 10 is 10.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 10.
- The fraction $\frac{4}{5}$ can be converted to have a denominator of 10 by multiplying both the numerator and the denominator by 2. Thus, $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$.
- The fraction $\frac{6}{10}$ already has the denominator of 10, so it remains $\frac{6}{10}$.

Step 3: Subtract the second fraction from the first.
Subtract the numerators while keeping the common denominator: $\frac{8}{10} - \frac{6}{10} = \frac{8 - 6}{10} = \frac{2}{10}$.

Step 4: Simplify the resulting fraction.
The fraction $\frac{2}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: $\frac{2}{10} = \frac{2 \div 2}{10 \div 2} = \frac{1}{5}$.

Therefore, the solution to the problem is $\frac{1}{5}$, which corresponds to choice number 2.

To solve this problem, let's go step by step:

• Step 1: Identify the Least Common Denominator (LCD).
  • The denominators are 6 and 9.
  • The multiples of 6 are 6, 12, 18, 24, ...
  • The multiples of 9 are 9, 18, 27, 36, ...
  • The smallest common multiple is 18.
• Step 2: Rewrite the fractions with the common denominator of 18.
  • $\frac{4}{6}$ can be converted by finding an equivalent fraction with a denominator of 18: $\frac{4 \times 3}{6 \times 3} = \frac{12}{18}$.
  • $\frac{3}{9}$ can be converted similarly: $\frac{3 \times 2}{9 \times 2} = \frac{6}{18}$.
• Step 3: Subtract the two fractions.
  • Subtract the numerators: $12 - 6 = 6$.
  • The result is $\frac{6}{18}$.
• Step 4: Simplify the resulting fraction.
  • $\frac{6}{18}$ simplifies to $\frac{1}{3}$ by dividing both the numerator and the denominator by 6.

Therefore, the solution to the problem is $\frac{1}{3}$.

To solve the problem $\frac{5}{10} - \frac{1}{4}$, we need to subtract two fractions. We will accomplish this by finding a common denominator.

Let's begin by finding the least common multiple (LCM) of the denominators 10 and 4:

• List the multiples of 10: 10, 20, 30, 40, ...
• List the multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
• The smallest common multiple is 20, so 20 is the least common denominator.

Now, convert both fractions to have the common denominator of 20:

• For $\frac{5}{10}$, multiply both the numerator and the denominator by 2 to get an equivalent fraction: $\frac{5 \times 2}{10 \times 2} = \frac{10}{20}$.
• For $\frac{1}{4}$, multiply both the numerator and the denominator by 5 to get an equivalent fraction: $\frac{1 \times 5}{4 \times 5} = \frac{5}{20}$.

We can now subtract the fractions:

• Subtract the numerators: $\frac{10}{20} - \frac{5}{20} = \frac{10 - 5}{20} = \frac{5}{20}$.

Simplify $\frac{5}{20}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

• So, $\frac{5}{20} = \frac{5 \div 5}{20 \div 5} = \frac{1}{4}$.

Therefore, the solution to the problem is $\frac{1}{4}$.

The correct answer choice is 4, which represents the simplified solution.

We need to subtract the fractions $\frac{5}{10} - \frac{2}{6}$.

Step 1: Find a common denominator for the fractions. The denominators are 10 and 6.

• The Least Common Multiple (LCM) of 10 and 6 is 30.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 30.

• For $\frac{5}{10}$, multiply both the numerator and the denominator by 3 to get $\frac{15}{30}$.
• For $\frac{2}{6}$, multiply both the numerator and the denominator by 5 to get $\frac{10}{30}$.

Step 3: Subtract the fractions:

$\frac{15}{30} - \frac{10}{30} = \frac{15 - 10}{30} = \frac{5}{30}$.

Step 4: Simplify the result:

The fraction $\frac{5}{30}$ can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 5.

$\frac{5}{30} = \frac{5 \div 5}{30 \div 5} = \frac{1}{6}$.

Therefore, the answer to the subtraction $\frac{5}{10} - \frac{2}{6}$ is $\frac{1}{6}$.

To solve the subtraction problem $\frac{5}{8} - \frac{3}{10}$, we first need to find a common denominator for the fractions.

• Step 1: Determine the least common multiple (LCM) of the denominators 8 and 10.

To find the LCM of 8 and 10, list their multiples:

Multiples of 8: $8, 16, 24, 32, 40, \ldots$
Multiples of 10: $10, 20, 30, 40, 50, \ldots$

The smallest common multiple is 40. Therefore, the common denominator is 40.

• Step 2: Adjust each fraction to the common denominator of 40.

Convert $\frac{5}{8}$ to a fraction with a denominator of 40:

$\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}$

Convert $\frac{3}{10}$ to a fraction with a denominator of 40:

$\frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40}$

• Step 3: Subtract the fractions.

Subtract the numerators and place the result over the common denominator:

$\frac{25}{40} - \frac{12}{40} = \frac{25 - 12}{40} = \frac{13}{40}$

The result is $\frac{13}{40}$, which is already in its simplest form.

The solution to the problem is $\frac{13}{40}$.

To solve the problem $\frac{7}{10} - \frac{2}{6}$, we need to follow these steps:

• Find the Least Common Denominator (LCD) for the denominators 10 and 6. The LCD of 10 and 6 is 30.
• Convert each fraction to have the common denominator of 30:
• $\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}$
• $\frac{2}{6} = \frac{2 \times 5}{6 \times 5} = \frac{10}{30}$
• Subtract the two fractions:
• $\frac{21}{30} - \frac{10}{30} = \frac{21 - 10}{30} = \frac{11}{30}$

Therefore, the solution to the problem is $\frac{11}{30}$.

To solve the problem of subtracting $\frac{5}{12}$ from $\frac{7}{8}$, we follow these steps:

• Step 1: Find the least common multiple (LCM) of the denominators 8 and 12. The multiples of 8 are 8, 16, 24, 32, and those of 12 are 12, 24, 36. The smallest common multiple is 24.
• Step 2: Convert each fraction to have a denominator of 24.
  For $\frac{7}{8}$:
  Multiply the numerator and the denominator by 3 to get: $\frac{7 \times 3}{8 \times 3} = \frac{21}{24}$.
  For $\frac{5}{12}$:
  Multiply the numerator and the denominator by 2 to get: $\frac{5 \times 2}{12 \times 2} = \frac{10}{24}$.
• Step 3: Subtract the fractions now that they have the same denominator:
  $\frac{21}{24} - \frac{10}{24} = \frac{21 - 10}{24} = \frac{11}{24}$.
• Step 4: Simplify the fraction if possible. In this case, $\frac{11}{24}$ is already in its simplest form.

Therefore, the result of $\frac{7}{8} - \frac{5}{12}$ is $\frac{11}{24}$.