All Operations in Fractions: Only addition and subtraction

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 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 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:

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