Question

Representing bench mark fractions in a number line

Answer 1

A = 1/8

B = 1/4

C = 5/8

D = 7/8

Explanation:

We have a number line between 0 and 1.

First we look at it into two equal intervals. One between 0 and 1/2, and the other between 1/2 and 1.

1/2 is the point before C.

Now we look between 0 and 1/2.

B is the midpoint of this segment.

So B is 1/2*(1/2) = 1/4

A is the midpoint between 0 and B, so 1/2*(1/4) = 1/8

C is the midpoint between 1/2 and 3/4

So

`C-(1)/(2)=(3)/(4)-C`
`2C=(3)/(4)+(1)/(2)`
`2C=(3)/(4)+(2)/(4)`
`2C=(5)/(4)`
`C=(5)/(4)\ast(1)/(2)=(5)/(4\ast2)=(5)/(8)`

D is the midpoint between 3/4 and 1. So

`D-(3)/(4)=1-D`
`2D=1+(3)/(4)`
`2D=(4)/(4)+(3)/(4)`
`2D=(7)/(4)`
`D=(7)/(4)\ast(1)/(2)=(7)/(8)`