Question

1. (overline{nq})

diagram: points q, p, n on a line. segment qp is 1 in., segment pn is (1\frac{1}{4}) in.

Explanation:

Step1: Identify the segments

We have segment \( QP = 1 \) in and \( PN = 1\frac{1}{4} \) in. To find \( NQ \), we need to add these two segments since \( NQ = QP + PN \).

Step2: Convert mixed number to improper fraction

\( 1\frac{1}{4}=\frac{4\times1 + 1}{4}=\frac{5}{4} \)

Step3: Add the lengths

\( QP = 1=\frac{4}{4} \), so \( NQ=\frac{4}{4}+\frac{5}{4}=\frac{4 + 5}{4}=\frac{9}{4}=2\frac{1}{4} \)

Answer:

\( 2\frac{1}{4} \) inches