Simply frac 2 frac 2 3 times 1 frac 1 2 4 frac ... - JAMB Mathematics 2024 Question

We are tasked with simplifying the expression:

\(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)

Step 1: Convert all mixed fractions to improper fractions

• \(2\frac{2}{3} = \frac{(3 \times 2) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}\)
• \(1\frac{1}{2} = \frac{(2 \times 1) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}\)
• \(4\frac{4}{5} = \frac{(5 \times 4) + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5}\)

The expression becomes:

\(\frac{\frac{8}{3} \times \frac{3}{2}}{\frac{24}{5}}\)

Step 2: Simplify the numerator

\(\frac{8}{3} \times \frac{3}{2} = \frac{8 \times 3}{3 \times 2} = \frac{24}{6} = 4\)

So the expression becomes:

\(\frac{4}{\frac{24}{5}}\)

Step 3: Simplify the division of fractions

Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:

\(\frac{4}{\frac{24}{5}} = 4 \times \frac{5}{24}\)

\(= \frac{4 \times 5}{24} = \frac{20}{24}\)

Step 4: Simplify the fraction

\(\frac{20}{24}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:

\(\frac{20}{24} = \frac{20 \div 4}{24 \div 4} = \frac{5}{6}\)

Answer: \(\frac{5}{6}\)