Question

A new long-life tire has a tread depth of 1/4 inch, instead of the more typical 5/32 inch. How much deeper is the tread on the new tire?The tread on the new tire is ___ inch deeper.(Simplify your answer. Type an integer or a fraction.)

Answer 1

To find how much deeper is the tread on the new​ tire, we just need to find the difference between the tread depth of this tire to the standard. To find this difference, we subtract the standard from the tread depth of this tire.

`(1)/(4)-(5)/(32)`

To realize this operation, we need both fractions to have the same denominator. If we multiply both numerator and denominator of a fraction by the same number, the fraction stays the same.

Since 32 is a multiple of 4, we can multiply the first fraction(both numerator and denominator) by 8 to put both fractions with the same denominator.

`(1)/(4)*(8)/(8)=(8)/(32)`

Now, we can rewrite our operation

`(1)/(4)-(5)/(32)=(8)/(32)-(5)/(32)`

When we're doing an addition or subtraction between two fractions with the same denominator, we just need to do the operation on the numerator.

`(8)/(32)-(5)/(32)=(8-5)/(32)=(3)/(32)`

The tread on the new tire is 3/32 inch deeper.