Question

Alex, Kenny, Chris, and Donna all live on the same street as their school, which runs from east to west.

-Alex lives 5 5/10 blocks to the west
-Kenny lives 4 5/20 blocks to the east
-Chris lives 2 15/20 blocks to the west
-Donna lives 6 5/10 blocks to the east

Use a number line to find how far each house is from every other house:

How far is Alex from Kenny?

How far is Alex from Chris?

How far is Alex from Donna?

How far is Kenny from Chris?

How far is Kenny from Donna?

How far is Chris from Donna?

What is the value of each space on the number line? Why?

Answer 1

We are given that,

Alex lives
`5(5)/(10)` =
`(11)/(2)` blocks to the west

Kenny lives
`4(5)/(20)` =
`(17)/(4)` blocks to the east

Chris lives
`2(15)/(20)` =
`(11)/(4)` blocks to the west

Donna lives
`6(5)/(10)` =
`(13)/(2)` blocks to the east

So, according to the locations, we get the number line as below.

Now, we have,

1. How far is Alex from Kenny?

Distance between Alex and Kenny =
`(17)/(4)+(11)/(2)=(39)/(4)`

That is, Alex is
`(39)/(4)` blocks to the east of Kenny.

2. How far is Alex from Chris?

Distance between Alex and Chris =
`(-11)/(4)-(-11)/(2)=(11)/(4)`

That is, Alex is
`(11)/(4)` blocks to the east of Chris.

3. How far is Alex from Donna?

Distance between Alex and Donna =
`(13)/(2)+(11)/(2)` = 12

That is, Alex is 12 blocks to the east of Donna.

4. How far is Kenny from Chris?

Distance between Kenny and Chris =
`(17)/(4)+(11)/(4)` = 7

That is, Kenny is 7 blocks to the west of Chris.

5. How far is Kenny from Donna?

Distance between Kenny and Donna =
`(13)/(2)-(17)/(4)=(9)/(4)`

That is, Kenny is
`(9)/(4)` blocks to the east of Donna.

6. How far is Chris from Donna?

Distance between Chris and Donna =
`(13)/(2)+(11)/(4)=(37)/(4)`

That is, Chris is
`(37)/(4)` blocks to the east of Donna.

Further, we need to find the value of each space in the number line.

As, we have that value of each space in the number line are given by,

Between Alex and Chris =
`(11)/(4)`

Between Chris and School =
`(11)/(4)`

Between School and Kenny =
`(17)/(4)`

Between Kenny and Donna =
`(9)/(4)`