Question

What are the ratios of 5/4 inches to 2/3 inch in fraction and simplest form.

Answer 1

Fraction is
`(15)/(8)`

Simplest form is
`(15)/(8)`

Explanation:

Given : the ratios of
`(5)/(4)` inches to
`(2)/(3)` inch

We have write the given ratio in fraction and simplest form

The given ratios
`(5)/(4)` inches to
`(2)/(3)` inch can be written mathematically as
`((5)/(4))/((2)/(3))`

`\mathrm{Divide\:fractions}:\quad ((a)/(b))/((c)/(d))=(a\cdot \:d)/(b\cdot \:c)`

`=(5\cdot \:3)/(4\cdot \:2)`

Thus, fraction is
`(15)/(8)`

Since, numerator and denominator do not have any term common so fraction is the simplest form also,

Thus, simplest form is
`(15)/(8)`

Answer 2

The thing with ratios is you need to have the same units of measurement before simplifying it. But in our given, both has the same unit of measurement so it is easy to find it.

So 5/4 inches: 2/3 inches

Get the lcd of these two fractions which is 12, then multiply this to the lcd.

5/4 x 12: 2/3 x 12

15: 4 would be the simplest form.