Question

.
Which ratio is proportional to 64 to 44?

16 to 11

32 to 11

32 to 20

16 to 22

Answer 1

To find which ratio is proportional to 64 to 44, we can simplify the original ratio and then check the given options.

1. Simplifying the ratio 64 to 44:
\[
\frac{64}{44} = \frac{64 \div 4}{44 \div 4} = \frac{16}{11}
\]

Now we have established that 64 to 44 simplifies to 16 to 11.

2. We will compare 16 to 11 with the other options to see if they are equivalent:

- **16 to 11:** This is the same as the simplified version of 64 to 44.
- **32 to 11:** To check proportion we could cross multiply:
\[
16 \times 11 = 176 \quad \text{and} \quad 32 \times 11 = 352 \quad \text{(not proportional)}
\]
- **32 to 20:**
\[
16 \times 20 = 320 \quad \text{and} \quad 32 \times 11 = 352 \quad \text{(not proportional)}
\]
- **16 to 22:**
\[
16 \times 22 = 352 \quad \text{and} \quad 32 \times 11 = 352 \quad \text{(proportional)}
\]

Therefore, the ratios that are **proportional** to 64 to 44 is **16 to 11** and also **16 to 22**.

However, **the most straightforward and simplest form that matches directly is 16 to 11**.

Thus, the correct proportionate ratio is **16 to 11**.