Chapter 1, Problem 1A

Write the fractional part that each length, A through F, represents of the total shown on the scale in Figure 1-3.

A = .
B = .
C = .
D = .
E = .
F = .

To determine

Evaluate the fractional part length of A, B, C, D, E and F.

Answer to Problem 1A

The fractional part length of A, B, C, D, E and F are $\frac{3}{32}$, $\frac{7}{32}$, $\frac{3}{8}$, $\frac{19}{32}$, $\frac{27}{32}$ and $1$ respectively.

Explanation of Solution

Given:

All the dimensions are shown in below Fig:

   

Concept used:

Fraction of the each part can determine with given expression.

  $\text{Fraction}\text{=}\frac{n}{N}$   .... (1)

Here, length of each part is $n$ and total length is $N$.

Calculation:

From below Fig:

   

Fraction A is calculated as:

Substitute $3$ for $n$ and $32$ for $N$.

  $\text{A=}\frac{3}{32}$

Fraction B is calculated as:

Substitute $7$ for $n$ and $32$ for $N$.

  $\text{B =}\frac{7}{32}$

Fraction C is calculated as:

Substitute $12$ for $n$ and $32$ for $N$.

  $\begin{array}{l}\text{C =}\frac{12}{32}\\ \text{C }=\frac{3}{8}\end{array}$

Fraction D is calculated as:

Substitute $19$ for $n$ and $32$ for $N$.

  $\text{D =}\frac{19}{32}$

Fraction E is calculated as:

Substitute $27$ for $n$ and $32$ for $N$.

  $\text{E =}\frac{27}{32}$

Fraction F is calculated as:

Substitute $32$ for $n$ and $32$ for $N$.

  $\begin{array}{l}\text{F =}\frac{32}{32}\\ \text{F =1}\end{array}$

Thus, the fractional part length of A, B, C, D, E and F are $\frac{3}{32}$, $\frac{7}{32}$, $\frac{3}{8}$, $\frac{19}{32}$, $\frac{27}{32}$ and $1$ respectively.

Conclusion:

The fractional part length of A, B, C, D, E and F are $\frac{3}{32}$, $\frac{7}{32}$, $\frac{3}{8}$, $\frac{19}{32}$, $\frac{27}{32}$ and $1$ respectively.