If x : y = \(\frac{1}{4} : \frac{3}{8}\) and y : z = \(\frac{1}{3} : \frac{4}{9}\), find x : z

To find x : z, we need to have a common ratio between x, y, and z. We can use the given ratios to find a common ratio involving all three. Since x : y = 1/4 : 3/8, we can simplify this ratio by multiplying both terms by 8 to get: x : y = 2 : 3 Similarly, since y : z = 1/3 : 4/9, we can simplify this ratio by multiplying both terms by 3 to get: y : z = 1 : 4/3 Now we have a common ratio of y between the two ratios. We can use this common ratio to find x : z by multiplying the two simplified ratios: x : y = 2 : 3 y : z = 1 : 4/3 Multiplying these ratios gives: x : z = (2/3) * (1/(4/3)) = 2/4 = 1/2 Therefore, x : z = 1 : 2. In summary, x : z = 1 : 2.