$\frac{99}{144} \times \frac{96}{88}$
The objective is to compute and simplify the product of two fractions: \(\frac{99}{144} \times \frac{96}{88}\). To simplify this multiplication, we can either simplify each fraction individually before multiplying them or combine them into a single fraction and then simplify. Simplifying first is generally more efficient.
First, we look at the fraction \(\frac{99}{144}\). Notice that both the numerator and the denominator are divisible by 9:
\[\frac{99}{144} = \frac{9 \times 11}{9 \times 16} = \frac{11}{16}\]
Next, we look at the fraction \(\frac{96}{88}\). Notice that both the numerator and the denominator are divisible by 8:
\[\frac{96}{88} = \frac{8 \times 12}{8 \times 11} = \frac{12}{11}\]
Now, we multiply the simplified fractions together:
\[\frac{11}{16} \times \frac{12}{11}\]
We can cancel the factor of 11 from the numerator of the first fraction and the denominator of the second fraction:
\[\frac{\cancel{11}}{16} \times \frac{12}{\cancel{11}} = \frac{12}{16}\]
Finally, we simplify \(\frac{12}{16}\) by dividing both the numerator and denominator by their greatest common divisor, which is 4:
\[\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\]
Thus, the product of the two fractions is \(\boxed{\frac{3}{4}}\).
In everyday scenarios, multiplying fractions occurs when scaling recipes or adjusting measurements. For example, if a recipe calls for \(\frac{99}{144}\) of a cup of flour and you need to scale it by a factor of \(\frac{96}{88}\) due to a batch size change, you would compute \(\frac{99}{144} \times \frac{96}{88} = \frac{3}{4}\) cup of flour. Mastering this allows for quick adjustments in cooking, construction, or any situation involving proportional measurements.