Fractions and ratios

[Guest]

please explain the missing steps. in particular how is the fraction 8/14 equivalent to the ratio 8:6!!
Change the following fraction to the simplest possible ratio: 8/14
The solution is 4:3. I do not understand the following solution: to solve this problem, you must know how to convert fractions into ratios.
A ratio expresses the relationship between two numbers. For instance, the ratio 2:3 suggests that for every 2 of one thing, there will be 3 of another. This equates to a fraction of 2/5 because there are 5 things total.
The fraction 8/14 is equivalent to the ratio 8:6. To simplify the ratio, divide both sides by the greatest common factor, 2. The simplest form of this ratio is 4:3.

[Jonasmathwork]

Solution : Given 8/14=8/6
which is not true

here the GCF of 8/14 is 2
then we get 4/7

there for 8/14 is equivalent to 4/7

Hope you got your answer

[Guest]

please explain the missing steps. in particular how is the fraction 8/14 equivalent to the ratio 8:6!!
Change the following fraction to the simplest possible ratio: 8/14
The solution is 4:3. I do not understand the following solution: to solve this problem, you must know how to convert fractions into ratios.
A ratio expresses the relationship between two numbers. For instance, the ratio 2:3 suggests that for every 2 of one thing, there will be 3 of another. This equates to a fraction of 2/5 because there are 5 things total.
The fraction 8/14 is equivalent to the ratio 8:6. To simplify the ratio, divide both sides by the greatest common factor, 2. The simplest form of this ratio is 4:3.

A fraction is always a fraction of something that I will call "the whole" A ratio, like "8:6" means that "the whole" has been cut into 8 parts and 6 parts (so a total of 14 parts) and 8 of those parts separated from the other 6.
As this says, 8+ 6= 14 so if two things are in a ratio of 8:6 then one is 8/14= 2(4)/2(7)= 4/7 of the whole. The other is 6/14= 2(3)/2(7)= 3/7 of the whole. Notice that 8/14+ 6/14= 14/14= 1 and that 4/7+ 3/7= 7/7= 1.