For transforming the ratio 1 to 2 into 3 to 6, apply the operation of multiplication by 3 to both parts of the original ratio. This preserves the proportional relationship between the terms.
To transform the ratio 1 to 2 into the ratio 3 to 6, you can apply the operation of multiplication. Ratios are equivalent if you can obtain one from the other by multiplying or dividing both parts of the ratio by the same nonzero number.
In this case, to go from 1 to 2 to 3 to 6, each part of the ratio needs to be multiplied by 3.
Original ratio: 1 to 2
Multiply both parts by 3: 1 times 3 to 2 times 3 equals 3 to 6
Therefore, the operation applied is multiplication by 3. This is a valid operation because it preserves the proportional relationship between the two parts of the ratio.
In general, to find an equivalent ratio, you can multiply or divide both parts of the original ratio by the same nonzero number. This preserves the relative size of the parts and generates a new ratio that represents the same relationship in different terms.