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Solution: Here for the given question the ratio is between the number of students taking Math class and the number of students taking English class.

The first ratio given is

Number of students Math : English = 50 : 75

Simplifying the ratio gives 2 : 3.

The second ratio given is

Number of students Math : English = 30 : 45

Simplifying the ratio gives 2 : 3.

Therefor the two ratios are equivalent.

Solution: Here the given ratio is 48 : 96.

Here the numbers 48 and 96 are divisible by 2.

Simplifying the ratio gives 24 : 48.

The ratio is further divisible by 3.

Simplifying the ratio gives 8 : 16

The ratio is further divisible by 8.

Simplifying the ratio gives 1 : 2

Hence the simplified form of the given ratio is 1 : 2