Simply $\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}$

To solve this expression, we need to convert the mixed fractions into improper fractions, perform the multiplication, and then divide by the denominator.

1. Analyze the question

We are given the expression:

2. Explain the concept

To work with mixed fractions, follow these steps:

• Convert to improper fractions: Multiply the whole number by the denominator and add the numerator. Place this over the original denominator.
• Multiply fractions: Multiply the numerators together and the denominators together.
• Divide fractions: Multiply the first fraction by the reciprocal (flipped version) of the second fraction.

3. Show the solution

Step 1: Convert all mixed fractions to improper fractions.

• $2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{8}{3}$
• $1\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$
• $4\frac{4}{5} = \frac{(4 \times 5) + 4}{5} = \frac{24}{5}$

Step 2: Substitute these into the expression.

Step 3: Simplify the numerator.

Step 4: Divide by the denominator. Now we have:

To divide by a fraction, multiply by its reciprocal:

Step 5: Reduce the fraction to its simplest form. Divide both the numerator and denominator by their highest common factor, which is 4:

4. Identify the answer

Comparing our result to the given options, we find that $\frac{5}{6}$ matches option C.

5. Exam Tip

When multiplying fractions, always look for common factors in the numerators and denominators to cancel them out before you multiply. For example, in Step 3, you could have cancelled the '3's immediately, leaving you with $\frac{8}{2} = 4$. This saves time and reduces the risk of calculation errors!