To determine which of the given pairs of ratios are equal, we can convert each ratio to its simplest form and compare them.
a) 1:16 and 2:8
The ratio 1:16 is already in its simplest form. The ratio 2:8 can be simplified by dividing both sides by 2, resulting in 1:4. Since 1:16 is not equal to 1:4, these ratios are not equal.
b) 2:32 and 4:8
The ratio 2:32 can be simplified by dividing both sides by 2, resulting in 1:16. The ratio 4:8 can be simplified by dividing both sides by 4, resulting in 1:2. Since 1:16 is not equal to 1:2, these ratios are not equal.
c) 1:64 and 4:16
The ratio 1:64 is already in its simplest form. The ratio 4:16 can be simplified by dividing both sides by 4, resulting in 1:4. Since 1:64 is not equal to 1:4, these ratios are not equal.
d) 1:16 and 4:64
The ratio 1:16 is already in its simplest form. The ratio 4:64 can be simplified by dividing both sides by 4, resulting in 1:16. Since both ratios are now 1:16, these ratios are equal.
Conclusion: Among the options given, the ratios that are equal to each other are d) 1:16 and 4:64.