6 8/15 - 4,21/45

To calculate the expression \(6 \frac{8}{15} - 4\frac{21}{45}\), you need to perform the subtraction of the two mixed numbers. First, make sure that the fractions have a common denominator.

The fractions \( \frac{8}{15} \) and \( \frac{21}{45} \) do not currently share a common denominator. However, the denominator 45 is a multiple of 15, so we can easily convert \( \frac{8}{15} \) to a fraction with a denominator of 45 by finding an equivalent fraction.

To convert \( \frac{8}{15} \) to a denominator of 45, we multiply the numerator and denominator by the same number (in this case, 3).

\( \frac{8}{15} \) = \( \frac{8 \times 3}{15 \times 3} \) = \( \frac{24}{45} \)

Now, we have two mixed numbers with the same denominator:

\(6 \frac{24}{45} - 4\frac{21}{45}\)

Next, you subtract the whole numbers and fractions separately:

Subtracting the whole numbers: 6 - 4 = 2

Subtracting the fractions: \( \frac{24}{45} - \frac{21}{45} = \frac{3}{45} \)

However, \( \frac{3}{45} \) can be simplified since 3 is the greatest common divisor of 3 and 45. So when we divide both the numerator and the denominator by 3:

\( \frac{3}{45} = \frac{3 \div 3}{45 \div 3} \) = \( \frac{1}{15} \)

Now, combine the results of the whole number subtraction and the simplified fraction:

2 + \( \frac{1}{15} \) = \( 2 \frac{1}{15} \)

Thus, the final answer is \( 2 \frac{1}{15} \).