Points P and Q are marked on the number line. Which rational number lies between P and Q?

Class 7Rational NumbersRational Numbers

A $\frac{- 5}{8}$
B $\frac{- 1}{8}$
C $\frac{- 3}{4}$
D $\frac{- 3}{8}$

Step-by-Step Solution

= \frac{- 1}{2} = \frac{- 4}{8}

and Q

= \frac{- 1}{4} = \frac{- 2}{8}

. The rational

\frac{- 3}{8}

lies between

\frac{- 4}{8}

and

\frac{- 2}{8} . \frac{- 5}{8}

and

\frac{- 3}{4}

are left of P;

\frac{- 1}{8}

is right of Q.

Answer: D)

\frac{- 3}{8}

Key idea: Rationals on the number line

Every rational number has a place on the number line. Negative rationals on the left of 0, positive on the right. Between any two rationals, you can always find another rational (in fact, infinitely many) — this is called **density**.

Example: between 1/3 and 1/2, the average (1/3 + 1/2)/2 = 5/12 sits in the middle. Between 1/3 and 5/12 there's another rational, and so on, forever.

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