The blue point is the starting number and the orange arrow is a jump to the right. Which addition does the picture show?

Class 7Rational NumbersRational Numbers

A $\frac{- 5}{4} + \frac{3}{4} = \frac{- 1}{2}$
B $\frac{- 3}{4} + \frac{7}{4} = 1$
C $\frac{- 5}{4} + \frac{7}{4} = \frac{1}{2}$
D $\frac{5}{4} + \frac{7}{4} = 3$

Step-by-Step Solution

Each unit has 4 parts. The start is 5 quarters left of 0:

\frac{- 5}{4}

. The arrow covers 7 small parts:

+ \frac{7}{4}

. It lands 2 quarters right of 0, so

\frac{- 5}{4} + \frac{7}{4} = \frac{2}{4} = \frac{1}{2}

Answer: C)

\frac{- 5}{4} + \frac{7}{4} = \frac{1}{2}

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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