Question

What numbers are a distance of 34 unit from 18 on a number line?

Select the locations on the number line to plot the points.

Answer 1

`(7)/(8) \textsf{ and } -(5)/(8)`

Explanation:

To find numbers that are
`(3)/(4)` units distance from
`\displaystyle (1)/(8)` , add and subtract
`(3)/(4)` to and from
`\displaystyle (1)/(8)`

One of the points is at
`\displaystyle (1)/(8) + (3)/(4)` units away and the other at
`\displaystyle (1)/(8) - (3)/(4)` units away

1. Compute
   `\displaystyle (1)/(8) + (3)/(4) :`
   
   
   `\mathrm{For}\:(3)/(4):\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:2`:
   
   
   `(3)/(4)=(3\cdot \:2)/(4\cdot \:2)=(6)/(8)`
   
   
   `\displaystyle (1)/(8) + (3)/(4) = (1)/(8)+(6)/(8) = (7)/(8)`
   
2. Compute
   `(1)/(8)-(3)/(4)`
   Again for
   `(3)/(4):\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:2`
   
   `(3)/(4)=(3\cdot \:2)/(4\cdot \:2)=(6)/(8)`
   
   
   `(1)/(8)-(3)/(4) = (1-6)/(8) = (-5)/(8)`