33/32*24/11

To simplify the expression \( \frac{33}{32} \times \frac{24}{11} \), you can multiply the numerators together and the denominators together:

\[ \frac{33 \times 24}{32 \times 11} \]

Calculating the numerator:

\[ 33 \times 24 = 792 \]

Calculating the denominator:

\[ 32 \times 11 = 352 \]

So, the expression becomes:

\[ \frac{792}{352} \]

Now, you can simplify this fraction. Both 792 and 352 can be divided by their greatest common divisor (GCD), which is 16:

\[ \frac{792 \div 16}{352 \div 16} = \frac{49.5}{22} \text{ (but it's normally not preferred to leave it like that)} \]

It's more useful, or you can continue reducing:

\[ 792 = 2^3 \times 3^2 \times 11, \quad 352 = 2^5 \times 11 \]

So common factors are \(2^3 \times 11\):

Reduced gives \( \frac{49.5}{22} \).

An alternative is to multiply prior to simplification:

Find if there are cancellations:

33 and 11 can simplify (33 = 3 * 11) so gives:

\[ \frac{3 \times 24}{32} = \frac{72}{32} \]

72 and 32 can be reduced to:

\[ \frac{72 \div 8}{32 \div 8} = \frac{9}{4} \]

So, the simplified form of \( \frac{33}{32} \times \frac{24}{11} \) is \( \frac{9}{4} \).