Read the numbers at points R and S on the number line. Which statement is true?

Class 7Rational NumbersRational Numbers

A $\frac{- 4}{3} > \frac{- 1}{3}$
B $\frac{- 2}{3} < \frac{- 1}{3}$
C $\frac{- 4}{3} < \frac{- 1}{3}$
D $\frac{4}{3} > \frac{1}{3}$

Step-by-Step Solution

Each unit is cut into thirds. R is 4 thirds left of 0, so R

= \frac{- 4}{3}

; S

= \frac{- 1}{3}

. On a number line the number further to the left is smaller, so

\frac{- 4}{3} < \frac{- 1}{3}

Answer: C)

\frac{- 4}{3} < \frac{- 1}{3}

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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