Let's break this problem down step by step to find the solution.
1. List the Fractions:
We are given the fractions [tex]\( \frac{9}{16}, \frac{7}{8}, \frac{3}{4}, \frac{1}{2} \)[/tex].
2. Multiply the Fractions:
When multiplying fractions, you multiply the numerators together and the denominators together.
[tex]\( \frac{9}{16} \cdot \frac{7}{8} \cdot \frac{3}{4} \cdot \frac{1}{2} \)[/tex]
Let's break it down into steps:
- Multiply [tex]\( \frac{9}{16} \)[/tex] by [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[
\frac{9 \times 7}{16 \times 8} = \frac{63}{128}
\][/tex]
- Then multiply [tex]\( \frac{63}{128} \)[/tex] by [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{63 \times 3}{128 \times 4} = \frac{189}{512}
\][/tex]
- Finally, multiply [tex]\( \frac{189}{512} \)[/tex] by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
\frac{189 \times 1}{512 \times 2} = \frac{189}{1024}
\][/tex]
3. Convert the Result to Decimal:
To better understand the size of the resulting fraction, let's convert [tex]\( \frac{189}{1024} \)[/tex] to a decimal.
- Divide 189 by 1024:
[tex]\[
\frac{189}{1024} \approx 0.1845703125
\][/tex]
Thus, the product of the fractions [tex]\( \frac{9}{16} \cdot \frac{7}{8} \cdot \frac{3}{4} \cdot \frac{1}{2} \)[/tex] is approximately [tex]\( 0.1845703125 \)[/tex].
