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

Let's try to find the lowest common denominator between 4 and 10

To find 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

Now we'll 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

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

Now let's subtract:

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

Let's try to find the lowest common denominator between 10 and 6

To find 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

Now we'll 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 try to find the lowest common denominator between 4 and 6

To find 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 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 try to find the lowest common denominator between 4 and 6

To find 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 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 try to find the lowest common denominator between 6 and 10

To find 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 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:

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

In this question, we need to find a common denominator.
However, we don't have to multiply the denominators by each other,
there is a lower common denominator: 12.

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

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

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