a: \( b=3: 7 \) \( b: 0=21: 22 \) Work out \( a: 0 \) Give your anewer in its simplest form.

To solve for \( a: 0 \) given \( b = 3: 7 \) and \( b: 0 = 21: 22 \), we begin by determining the value of \( b \) in the first ratio. If we let \( b = 3k \) and some additional term, for instance, \( a \) is represented proportionally to \( b \). Next, explore the second ratio, \( b: 0 = 21: 22 \). If \( b = 21m \) and \( 0 = 22m \), we can express \( b \) in terms of \( a \) then. By substituting the known values in these ratios, we ultimately arrive at \( a: 0 \). One way to calculate it is by defining a common variable for each ratio and simplifying it back to \( a: 0 \). After some calculations and simplifications, we find that \( a: 0 = 9: 22 \). Hence the simplest form of \( a: 0 \) is \( 9: 22 \).