Express the ratio 42 minutes to 0.1 hours in its simplest form.
The two parts of this ratio have been given using different units. One side is expressed in minutes. And the other side is expressed in hours. In order to express this ratio in its simplest form, we need to convert both sides to the same unit.
What is 0.1 hours in minutes? Well, one hour is equal to 60 minutes. We could approach this conversion in two different ways. We could keep the 0.1 as a decimal and work out 0.1 multiplied by 60. This is equivalent to working out 0.1 multiplied by 10 multiplied by six. 0.1 multiplied by 10 is just one. So this is equivalent to one multiplied by six, which is six.
The second approach would be to use fractions if you’re more comfortable working with these than decimals. 0.1 is equivalent to one tenth. To find what one-tenth of 60 minutes is, we need to divide by 10. 60 divided by 10 is equal to six. So using whichever method you’re more comfortable with, we’ve shown that 0.1 hours is equivalent to six minutes.
So the ratio of 42 minutes to 0.1 hours can be written instead as 42 minutes to six minutes. The units on the two sides of the ratio are now the same. So they can be cancelled out. We’re left with a ratio of 42 to six. But this isn’t yet in its simplest form. 42 and six both have a common factor of six. So both parts of the ratio can be divided by six. The ratio in its simplest form is seven to one.