Measuring, One Step Worksheet Downloads - One Less Thing - Free Printable

Problem Overview:

The task involves measuring the positions of letters (A through L) on a 1/16-inch ruler and expressing the measurements in lowest terms. The ruler is marked in inches, with each inch divided into 16 equal parts (1/16-inch increments).

Solution Approach:

1. Understand the Ruler Scale:
- Each inch is divided into 16 equal parts.
- The markings represent fractions of an inch: \( \frac{1}{16}, \frac{2}{16}, \frac{3}{16}, \ldots, \frac{15}{16} \).
- Simplify fractions to their lowest terms (e.g., \( \frac{2}{16} = \frac{1}{8} \)).

2. Identify the Position of Each Letter:
- Measure the distance from the zero mark to each letter.
- Express the measurement as a fraction of an inch in its lowest terms.

3. Simplify Fractions:
- Reduce fractions like \( \frac{4}{16} \) to \( \frac{1}{4} \), \( \frac{6}{16} \) to \( \frac{3}{8} \), etc.

Step-by-Step Measurement:

#### Top Ruler (Reference):
The top ruler shows how each inch is divided into 16 parts. This will help us understand the scale for the bottom ruler.

#### Bottom Ruler (Measurements):
We will measure the position of each letter (A through L) relative to the zero mark.

1. Letter A:
- Position: Just past the 1-inch mark.
- Measurement: \( 1 + \frac{1}{16} = 1 \frac{1}{16} \).

2. Letter B:
- Position: Slightly beyond the 1-inch mark.
- Measurement: \( 1 + \frac{3}{16} = 1 \frac{3}{16} \).

3. Letter C:
- Position: Near the middle of the second inch.
- Measurement: \( 1 + \frac{7}{16} = 1 \frac{7}{16} \).

4. Letter D:
- Position: Close to the end of the second inch.
- Measurement: \( 1 + \frac{15}{16} = 1 \frac{15}{16} \).

5. Letter E:
- Position: Just past the 2-inch mark.
- Measurement: \( 2 + \frac{1}{16} = 2 \frac{1}{16} \).

6. Letter F:
- Position: Slightly beyond the 2-inch mark.
- Measurement: \( 2 + \frac{3}{16} = 2 \frac{3}{16} \).

7. Letter G:
- Position: Near the middle of the third inch.
- Measurement: \( 2 + \frac{7}{16} = 2 \frac{7}{16} \).

8. Letter H:
- Position: Close to the end of the third inch.
- Measurement: \( 2 + \frac{15}{16} = 2 \frac{15}{16} \).

9. Letter I:
- Position: Just past the 3-inch mark.
- Measurement: \( 3 + \frac{1}{16} = 3 \frac{1}{16} \).

10. Letter J:
- Position: Slightly beyond the 4-inch mark.
- Measurement: \( 4 + \frac{3}{16} = 4 \frac{3}{16} \).

11. Letter K:
- Position: Near the middle of the fifth inch.
- Measurement: \( 5 + \frac{7}{16} = 5 \frac{7}{16} \).

12. Letter L:
- Position: Close to the end of the sixth inch.
- Measurement: \( 6 + \frac{15}{16} = 6 \frac{15}{16} \).

Final Answers:

\[
\begin{aligned}
&\text{A: } 1 \frac{1}{16} \\
&\text{B: } 1 \frac{3}{16} \\
&\text{C: } 1 \frac{7}{16} \\
&\text{D: } 1 \frac{15}{16} \\
&\text{E: } 2 \frac{1}{16} \\
&\text{F: } 2 \frac{3}{16} \\
&\text{G: } 2 \frac{7}{16} \\
&\text{H: } 2 \frac{15}{16} \\
&\text{I: } 3 \frac{1}{16} \\
&\text{J: } 4 \frac{3}{16} \\
&\text{K: } 5 \frac{7}{16} \\
&\text{L: } 6 \frac{15}{16} \\
\end{aligned}
\]

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
&\text{A: } 1 \frac{1}{16} \\
&\text{B: } 1 \frac{3}{16} \\
&\text{C: } 1 \frac{7}{16} \\
&\text{D: } 1 \frac{15}{16} \\
&\text{E: } 2 \frac{1}{16} \\
&\text{F: } 2 \frac{3}{16} \\
&\text{G: } 2 \frac{7}{16} \\
&\text{H: } 2 \frac{15}{16} \\
&\text{I: } 3 \frac{1}{16} \\
&\text{J: } 4 \frac{3}{16} \\
&\text{K: } 5 \frac{7}{16} \\
&\text{L: } 6 \frac{15}{16} \\
\end{aligned}
}
\]