Subtraction of Fractions - Examples, Exercises and Solutions

Let's begin by multiplying the numerator:

$12+8=20$

We should obtain the fraction written below:

$\frac{20}{5}$

Let's now reduce the numerator and denominator by 5 and we should obtain the following result:

$\frac{4}{1}=4$

Let's try to find the lowest common denominator between 5 and 10

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{3\times2}{5\times2}-\frac{3\times1}{10\times1}=\frac{6}{10}-\frac{3}{10}$

Now let's subtract:

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

Let's try to find the least common denominator between 5 and 10

To find the least common denominator, we need to find a number that is divisible by both 5 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{4\times2}{5\times2}-\frac{5\times1}{10\times1}=\frac{8}{10}-\frac{5}{10}$

Now let's subtract:

$\frac{8-5}{10}=\frac{3}{10}$

Let's try to find the least common denominator between 5 and 10

To find the least common denominator, we need to find a number that is divisible by both 5 and 10

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{4\times2}{5\times2}-\frac{3\times1}{10\times1}=\frac{8}{10}-\frac{3}{10}$

Now let's subtract:

$\frac{8-3}{10}=\frac{5}{10}$

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.

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

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

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

Let's try to find the least common denominator between 10 and 5

To find the least common denominator, we need to find a number that is divisible by both 10 and 5

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

$\frac{8\times1}{10\times1}-\frac{1\times2}{5\times2}-\frac{2\times1}{10\times1}=\frac{8}{10}-\frac{2}{10}-\frac{2}{10}$

Now let's subtract:

$\frac{8-2-2}{10}=\frac{6-2}{10}=\frac{4}{10}$

Let's try to find the least common denominator between 10 and 5

To find the least common denominator, we need to find a number that is divisible by both 10 and 5

In this case, the common denominator is 10

Now we'll multiply each fraction by the appropriate number to reach the denominator 10

We'll multiply the first fraction by 1

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

$\frac{4\times1}{10\times1}-\frac{1\times2}{5\times2}-\frac{1\times1}{10\times1}=\frac{4}{10}-\frac{2}{10}-\frac{1}{10}$

Now we'll subtract and get:

$\frac{4-2-1}{10}=\frac{2-1}{10}=\frac{1}{10}$

Let's try to find the least common multiple (LCM) between 5, 15, and 3

To find the least common multiple, we need to find a number that is divisible by 5, 15, and 3

In this case, the least common multiple is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

We'll multiply the third fraction by 5

$\frac{8\times3}{5\times3}-\frac{2\times1}{15\times1}-\frac{2\times5}{3\times5}=\frac{24}{15}-\frac{2}{15}-\frac{10}{15}$

Now let's subtract:

$\frac{24-2-10}{15}=\frac{22-10}{15}=\frac{12}{15}$

Let's divide both numerator and denominator by 3 and we get:

$\frac{12:3}{15:3}=\frac{4}{5}$

Let's try to find the least common denominator between 5 and 15 and 3

To find the least common denominator, we need to find a number that is divisible by 5, 15, and 3

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

We'll multiply the third fraction by 5

$\frac{7\times3}{5\times3}-\frac{2\times1}{15\times1}-\frac{2\times5}{3\times5}=\frac{21}{15}-\frac{2}{15}-\frac{10}{15}$

Now let's subtract:

$\frac{21-2-10}{15}=\frac{19-10}{15}=\frac{9}{15}$

We'll divide both the numerator and denominator by 3 and get:

$\frac{9:3}{15:3}=\frac{3}{5}$