Since the exercise mentions a number line, draw one. Since

*d* >

*a*, label the left end of the number line with

*d* and the right end with

*a*. The values of

*b* and

*c* will be between

*a* and

*d*:

Start with the relationship between

*c*,

*a*, and

*d*. Since

*c* is twice as far from

*a* as it is from

*d*,

the segment between

*a* and

*d* is divided into 3 pieces – two pieces between

*c* and

*a* and one piece between

*d* and

*c*. Each piece is 1/3 of

*d* to

*a*.

The relationship between

*b*,

*c*, and

*a* says that

*b* is twice as far from

*c* as it is from

*a*. This

means the segment between

*a* and

*c* is divided into 3 pieces.

The segment between

*c* and

*a* was 2/3 of the segment between

*d* and

*a*. Dividing 2/3 into 3 pieces makes each piece (2/3) / 3 = 2/9.

So

*d* –

*b* (the length of the segment between

*d* and

*b*) makes 7/9 of

*d* –

*a* (the length of the segment between

*d* and

*a*).