Final answer:
The number you can multiply both quantities in the ratio 2 to 10 by to get the ratio 4 to 20 is 2, as dividing the terms of the new ratio by the corresponding terms of the original ratio yields 2 in both cases.
Step-by-step explanation:
To find the number you can multiply both quantities in the ratio 2 to 10 by to obtain the ratio 4 to 20, you can set up a proportion or simply observe the multiplication pattern between the numbers in the ratios.
For the first term of the ratio, we do: 4 ÷ 2 = 2.
For the second term of the ratio, we do: 20 ÷ 10 = 2.
Both terms of the original ratio are being multiplied by the same number, which in this case is 2, to get the new ratio.
Therefore, the number by which you can multiply both quantities in the ratio 2 to 10 to get the ratio 4 to 20 is 2.