To determine the simplest form of the ratio [tex]\(40:16\)[/tex], we need to simplify it by dividing both terms by their greatest common divisor (GCD).
1. Find the GCD of 40 and 16:
- Factors of 40: [tex]\(1, 2, 4, 5, 8, 10, 20, 40\)[/tex]
- Factors of 16: [tex]\(1, 2, 4, 8, 16\)[/tex]
- The greatest common divisor is the largest factor that both numbers share, which in this case is [tex]\(8\)[/tex].
2. Simplify the ratio by dividing both terms by the GCD:
[tex]\[ \text{Numerator: } \frac{40}{8} = 5 \][/tex]
[tex]\[ \text{Denominator: } \frac{16}{8} = 2 \][/tex]
So, the simplest form of the ratio [tex]\(40:16\)[/tex] is [tex]\(5:2\)[/tex].
3. Compare with the given choices:
- A. [tex]\(20:8\)[/tex]
- B. [tex]\(10:4\)[/tex]
- C. [tex]\(5:4\)[/tex]
- D. [tex]\(5:2\)[/tex]
- E. [tex]\(10:8\)[/tex]
The correct choice is D, which matches the simplified form [tex]\(5:2\)[/tex].
Hence, the simplest form of the ratio [tex]\(40:16\)[/tex] is [tex]\(\boxed{5:2}\)[/tex].
