If a:b = 2:3, b:c = 4:3 and c:d= 2:3 then find a:b:c:d.

To find the ratio a:b:c:d, we need to multiply the corresponding values of the ratios given.

Step 1: We have a:b = 2:3. Let's keep it as it is for now.

Step 2: We have b:c = 4:3. But we need to adjust this ratio so that the value of 'b' in this ratio and the value of 'b' in the a:b ratio are the same. To do this, we can multiply both sides of the b:c ratio by 3/4. This gives us b:c = 3:2.25.

Step 3: We have c:d = 2:3. But we need to adjust this ratio so that the value of 'c' in this ratio and the value of 'c' in the b:c ratio are the same. To do this, we can multiply both sides of the c:d ratio by 2.25/2. This gives us c:d = 2.25:3.375.

Step 4: Now we can write down the combined ratio a:b:c:d. This is done by writing down the values of a, b, c, and d from the adjusted ratios. This gives us a:b:c:d = 2:3:2.25:3.375.

Step 5: To simplify this ratio, we can multiply all parts by 4 to remove the decimal. This gives us a:b:c:d = 8:12:9:13.5.

Step 6: To further simplify this ratio, we can multiply all parts by 2 to remove the decimal. This gives us a:b:c:d = 16:24:18:27.

So, the ratio a:b:c:d is 16:24:18:27.