Determine whether the following ratios are equivalent: 126 trucks to 42 cars and 252 trucks to 84 cars.
The first ratio is 126 to 42 and the second ratio is 252 to 84. If the two ratios are equivalent, we’ll be able to multiply both sides of the ratio by the same number. 42 multiplied by two is equal to 84 and 126 multiplied by two is 252.
This means that in the second ratio both numbers are double the numbers in the first ratio. We are, therefore, able to say, “Yes, the two ratios 126 to 42 and 252 to 84 are equivalent.”
In some other questions, we might be asked to write this ratio in its simplest form. In order to do this, we need to divide the left- and the right-hand side by the same number. We can do this in one step or in a multistep process.
Dividing both sides of the ratio 126 to 42 by two gives us 63 to 21. Dividing both sides of this ratio by three gives us 21 to seven as 63 divided by three is 21 and 21 divided by three is equal to seven. Finally, dividing both sides of this ratio by seven gives us the simplified ratio three to one.
The ratio 126 to 42 can be simplified to the ratio three to one. We could also have done this in one step by dividing the left- and the right-hand side by 42. 126 divided by 42 is three and 42 divided by 42 is equal to one.