To add the fractions \( \frac{5}{4} + \left(-\frac{2}{4}\right) \) using a number line, follow these steps:
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Locate \( \frac{5}{4} \) on the number line: Since \( \frac{5}{4} \) is equal to \( 1.25 \), you would mark this point between 1 and 2.
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Recognize \( -\frac{2}{4} \): This fraction is equivalent to \( -\frac{1}{2} \) or \( -0.5 \).
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Move left on the number line: From your point at \( \frac{5}{4} \) (or \( 1.25 \)), move \( \frac{2}{4} \) to the left:
- Moving \( \frac{1}{4} \) left takes you to \( 1.0 \),
- Moving another \( \frac{1}{4} \) left takes you to \( 0.75 \) (or \( \frac{3}{4} \)).
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End location: After moving \( \frac{2}{4} \) (or \( 0.5 \)) left from \( 1.25 \), you end up at \( 0.75 \) (or \( \frac{3}{4} \)).
Therefore, \[ \frac{5}{4} + \left(-\frac{2}{4}\right) = \frac{3}{4}. \]
So, the final answer is: \[ \frac{5}{4} + \left(-\frac{2}{4}\right) = \frac{3}{4}. \]