Question

Which statement about the answer to this problem is most accurate? ​45−34=120​ The answer 120 is reasonable because ​45​ and 34​ are both closer to 1 than they are to 12, making the difference close to 0. The answer 120 is not reasonable because ​45​ is closer to 1 than to ​12​, and ​34​ is closer to 0 than to ​12​, making the difference close to 12. ​ The answer 120 is reasonable because both fractions are closer to 12 than they are to 1, making the difference close to 0. The answer​120​is not reasonable because ​45​ is closer to ​12​ than to 1, and ​34​ is closer to 0 than to ​12, making the difference close to​ ​12​.

Answer 1

A. The answer 1/20 is reasonable because ​4/5​ and 3/4​ are both closer to 1 than they are to 1/2, making the difference close to 0.

Explanation:

Given:
`(4)/(5)` -
`(3)/(4)`

Solving this,

`(4)/(5)` -
`(3)/(4)`

the lowest common multiple is 20, so that:

=
`(16 - 15)/(20)`

=
`(1)/(20)`

converting the fractions to decimal,

`(4)/(5)` = 0.8

`(3)/(4)` = 0.75

so that,

0.8 - 0.75

= 0.05

`(1)/(20)` = 0.05

It can be observed that the fractions,
`(4)/(5)` and
`(3)/(4)`, are closer to 1, so that the answer,
`(1)/(20)`, is close to 0.