Common Denominators: More than two fractions

Let's try to find the least common multiple (LCM) between 2, 8, and 4

To find the least common multiple, we need to find a number that is divisible by 2, 8, and 4

In this case, the least common multiple is 8

Now we'll multiply each fraction by the appropriate number to reach a denominator of 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{4\times4}{2\times4}-\frac{6\times1}{8\times1}-\frac{1\times2}{4\times2}=\frac{16}{8}-\frac{6}{8}-\frac{2}{4}$

Now let's subtract:

$\frac{16-6-2}{8}=\frac{10-2}{8}=\frac{8}{8}$

We'll solve the fraction in the following way:

$\frac{8}{8}=\frac{1}{1}=1$

We must first identify the lowest common denominator between 5 and 10.

In order to determine 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.

We will then proceed to 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

$\frac{4\times2}{5\times2}-\frac{2\times1}{10\times1}-\frac{1\times2}{5\times2}=\frac{8}{10}-\frac{2}{10}-\frac{2}{10}$

Finally we'll combine and obtain the following:

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

Let's try to find the lowest common denominator between 6, 3, and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 3, and 12

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 1

We'll multiply the second fraction by 4

We'll multiply the third fraction by 2

$\frac{10\times1}{12\times1}-\frac{1\times4}{3\times4}-\frac{2\times2}{6\times2}=\frac{10}{12}-\frac{4}{12}-\frac{4}{12}$

Now let's subtract:

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

Let's divide both numerator and denominator by 2 and we get:

$\frac{2:2}{12:2}=\frac{1}{6}$

To solve the expression $\frac{1}{2} - \frac{2}{8} + \frac{1}{4}$, we must first find a common denominator for the fractions involved.

Step 1: Identify a common denominator. The denominators are 2, 8, and 4. The smallest common multiple of these numbers is 8.

Step 2: Convert each fraction to have the common denominator of 8.

• The fraction $\frac{1}{2}$ can be written as $\frac{4}{8}$ because $1 \times 4 = 4$ and $2 \times 4 = 8$.
• The fraction $\frac{2}{8}$ is already expressed with 8 as the denominator.
• The fraction $\frac{1}{4}$ can be written as $\frac{2}{8}$ because $1 \times 2 = 2$ and $4 \times 2 = 8$.

Step 3: Substitute these equivalent fractions back into the original expression:

$\frac{4}{8} - \frac{2}{8} + \frac{2}{8}$

Step 4: Perform the subtraction and addition following the order of operations:

• Subtract: $\frac{4}{8} - \frac{2}{8} = \frac{2}{8}$
• Add: $\frac{2}{8} + \frac{2}{8} = \frac{4}{8}$

Step 5: Simplify the result:

$\frac{4}{8}$ simplifies to $\frac{1}{2}$ by dividing the numerator and denominator by 4.

Therefore, the value of the expression is $\frac{1}{2}$.

Let's try to find the least common multiple (LCM) between 2, 8, and 4

To find the least common multiple, we need to find a number that is divisible by 2, 8, and 4

In this case, the least common multiple is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{1\times4}{2\times4}-\frac{3\times1}{8\times1}+\frac{2\times2}{4\times2}=\frac{4}{8}-\frac{3}{8}+\frac{4}{8}$

Now we'll subtract and then add:

$\frac{4-3+4}{8}=\frac{1+4}{8}=\frac{5}{8}$

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

We'll multiply the third fraction by 2

$\frac{3\times2}{5\times2}-\frac{1\times1}{10\times1}-\frac{1\times2}{5\times2}=\frac{6}{10}-\frac{1}{10}-\frac{2}{10}$

Now let's subtract:

$\frac{6-1-2}{10}=\frac{5-2}{10}=\frac{3}{10}$

Let's try to find the lowest common denominator between 6 and 4 and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 4, and 12

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

We'll multiply the third fraction by 1

$\frac{5\times2}{6\times2}-\frac{2\times3}{4\times3}-\frac{1\times1}{12\times1}=\frac{10}{12}-\frac{6}{12}-\frac{1}{12}$

Now let's subtract:

$\frac{10-6-1}{12}=\frac{4-1}{12}=\frac{3}{12}$

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

In order to identify the lowest common denominator, we need to find a number that is divisible by both 10 and 5.

In this case, the common denominator is 10.

Let's proceed to multiply each fraction by the appropriate number in order 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

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

Finally let's subtract as follows:

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

Let's try to find the least common denominator between 6, 3, and 12

To find the least common denominator, we need to find a number that is divisible by 6, 3, and 12

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 4

We'll multiply the third fraction by 1

$\frac{3\times2}{6\times2}-\frac{1\times4}{3\times4}-\frac{1\times1}{12\times1}=\frac{6}{12}-\frac{4}{12}-\frac{1}{12}$

Now let's subtract:

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

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

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

Now we'll subtract and get:

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

Let's try to find the lowest common denominator between 6, 4, and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 4, and 12

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

We'll multiply the third fraction by 1

$\frac{5\times2}{6\times2}-\frac{2\times3}{4\times3}-\frac{3\times1}{12\times1}=\frac{10}{12}-\frac{6}{12}-\frac{3}{12}$

Now we'll subtract and get:

$\frac{10-6-3}{12}=\frac{4-3}{12}=\frac{1}{12}$

Let's try to find the least common denominator between 2 and 8 and 4

To find the least common denominator, we need to find a number that is divisible by 2, 8, and 4

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{3\times4}{2\times4}-\frac{5\times1}{8\times1}-\frac{1\times2}{4\times2}=\frac{12}{8}-\frac{5}{8}-\frac{2}{8}$

Now let's subtract:

$\frac{12-5-2}{8}=\frac{7-2}{8}=\frac{5}{8}$

Let's try to find the lowest common denominator between 12, 3, and 6

To find the lowest common denominator, we need to find a number that is divisible by 12, 3, 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 1

We'll multiply the second fraction by 4

We'll multiply the third fraction by 2

$\frac{10\times1}{12\times1}-\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}=\frac{10}{12}-\frac{8}{12}-\frac{2}{12}$

Now let's subtract:

$\frac{10-8-2}{12}=\frac{2-2}{12}=\frac{0}{12}$

We'll divide both the numerator and denominator by 0 and get:

$\frac{0}{12}=0$

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

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

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 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

$\frac{2\times5}{3\times5}+\frac{2\times1}{15\times1}-\frac{4\times3}{5\times3}=\frac{10}{15}+\frac{2}{15}-\frac{12}{15}$

Now we'll add and then subtract:

$\frac{10+2-12}{15}=\frac{12-12}{15}=\frac{0}{15}$

We'll divide both the numerator and denominator by 0 and get:

$\frac{0}{15}=0$

Let's try to find the lowest common multiple of 3, 6 and 12

To find the lowest common multiple, we find a number that is divisible by 3, 6 and 12

In this case, the common multiple is 12

Now let's multiply each number in the appropriate multiple to reach the multiple of 12

We will multiply the first number by 4

We will multiply the second number by 2

We will multiply the third number by 1

$\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}-\frac{6\times1}{12\times1}=\frac{8}{12}-\frac{2}{12}-\frac{6}{12}$

Now let's subtract:

$\frac{8-2-6}{12}=\frac{6-6}{12}=\frac{0}{12}$

We will divide the numerator and the denominator by 0 and get:

$\frac{0}{12}=0$

Let's try to find the least common denominator between 3, 6, and 12

To find the least common denominator, we need to find a number that is divisible by 3, 6, and 12

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 4

We'll multiply the second fraction by 2

We'll multiply the third fraction by 1

$\frac{2\times4}{3\times4}-\frac{1\times2}{6\times2}-\frac{3\times1}{12\times1}=\frac{8}{12}-\frac{2}{12}-\frac{3}{12}$

Now let's subtract:

$\frac{8-2-3}{12}=\frac{6-3}{12}=\frac{3}{12}$

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

$\frac{3:3}{12:3}=\frac{1}{4}$

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:

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

Let's try to find the lowest common denominator between 6, 3, and 12

To find the lowest common denominator, we need to find a number that is divisible by 6, 3, and 12

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 4

We'll multiply the third fraction by 1

$\frac{4\times2}{6\times2}-\frac{1\times4}{3\times4}-\frac{1\times1}{12\times1}=\frac{8}{12}-\frac{4}{12}-\frac{1}{12}$

Now let's subtract:

$\frac{8-4-1}{12}=\frac{4-1}{12}=\frac{3}{12}$

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

$\frac{3:3}{12:3}=\frac{1}{4}$

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

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

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 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

$\frac{1\times5}{3\times5}+\frac{7\times1}{15\times1}-\frac{2\times3}{5\times3}=\frac{5}{15}+\frac{7}{15}-\frac{6}{15}$

Now we'll add and then subtract:

$\frac{5+7-6}{15}=\frac{12-6}{15}=\frac{6}{15}$

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

$\frac{6:3}{15:3}=\frac{2}{5}$

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:

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