Solve the Fraction Subtraction: 8/5 - 2/15 - 2/3 Step-by-Step

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:

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