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

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:

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

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 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 try to find the lowest common multiple between 6 and 10

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

In this case, the lowest common multiple is 30

Now let's multiply each number by an appropriate factor to reach the multiple of 30

We will multiply the first number by 3

We will multiply the second number by 5

$\frac{5\times3}{10\times3}-\frac{1\times5}{6\times5}=\frac{15}{30}-\frac{5}{30}$

Now let's subtract:

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

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:

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

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:

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