Chapter 3, Problem 13A

Determine dimensions A, B, C, D, E, F, G, H, and I of the plate in Figure 3-7. All dimensions are in inches.

A = ______.
B = ______.
C = ______.
D = ______.
E = ______.
F = ______.
G = ______.
H = ______.
I = ______.

To determine

(A)

Dimension for part A of the plate.

Answer to Problem 13A

Dimension for part A of the tapered pin is, $\frac{15}{32}$

Explanation of Solution

Given:

Part dimensions of a tapered pin

Calculation:

Calculation for A

  $\begin{array}{l}2\frac{3}{8}-1\frac{29}{32}\\ \frac{19}{8}-\frac{61}{32}\\ \end{array}$

First of all, we calculate the least common multiple (LCM) for given denominators (8 and 32).

The least common multiple (LCM) for given denominators (8 and 32) is 32.

Hence, the least common denominator is 32.

Now, we subtract the given digits.

  $\begin{array}{l}\frac{19}{8}-\frac{61}{32}\\ =\frac{(19\times 4)-(61\times 1)}{32}\\ =\frac{76-61}{32}\\ =\frac{15}{32}\end{array}$

Hence the subtraction of given digits is $\frac{15}{32}$

To determine

(B)

Dimension for part B of the plate.

Answer to Problem 13A

Dimension for part B of the tapered pin is, $\frac{21}{32}$

Explanation of Solution

Given:

Part dimensions of a tapered pin

Calculation:

Calculation for B

  $\begin{array}{l}1\frac{29}{32}-1\frac{1}{4}\\ \frac{61}{32}-\frac{5}{4}\end{array}$

First of all, we calculate the least common multiple (LCM) for given denominators (32 and 4).

The least common multiple (LCM) for given denominators (32 and 4) is 32.

Hence, the least common denominator is 32.

Now, we subtract the given digits:

  $\begin{array}{l}\frac{61}{32}-\frac{5}{4}\\ =\frac{(61\times 1)-(5\times 8)}{32}\\ =\frac{61-40}{32}\\ =\frac{21}{32}\end{array}$

Hence, the subtraction of given digits is $\frac{21}{32}$

To determine

(C)

Dimension for part C of the plate.

Answer to Problem 13A

Dimension for part C of the tapered pin is, $\frac{7}{16}$

Explanation of Solution

Given:

Part dimensions of a tapered pin

Calculation:

Calculation for C

  $\begin{array}{l}1\frac{1}{4}-\frac{13}{16}\\ \frac{5}{4}-\frac{13}{16}\end{array}$

First, we calculate the least common multiple (LCM) for given denominators (4 and 16).

The least common multiple (LCM) for given denominators (4 and 16) is 16.

Hence, the least common denominator is 16.

Now, we subtract the given digits.

  $\begin{array}{l}\frac{5}{4}-\frac{13}{16}\\ =\frac{(5\times 4)-(13\times 1)}{16}\\ =\frac{20-13}{16}\\ =\frac{7}{16}\end{array}$

Hence, the subtraction of given digits is $\frac{7}{16}$

To determine

(D)

Dimension for part D of the plate

Answer to Problem 13A

The dimensions of the given figure is $\frac{15}{32}$

Explanation of Solution

Given:

Dimension of A, B,C and D given in figure

Calculation:

Calculation for D

  $\begin{array}{l}2\frac{17}{32}-2\frac{1}{16}\\ \frac{81}{32}-\frac{33}{16}\end{array}$

First of all, we calculate the least common multiple (LCM) for given denominators (32 and 16).

The least common multiple (LCM) for given denominators (32 and 16) is 32.

Hence, the least common denominator is 32.

Now, we subtract the given digits:

  $\begin{array}{l}\frac{81}{32}-\frac{33}{16}\\ =\frac{81\times 1-33\times 2}{32}\\ =\frac{81-66}{32}\\ =\frac{15}{32}\end{array}$

Hence, the subtraction of given digits is $\frac{15}{32}$

To determine

(E)

Dimension for part E of the plate.

Answer to Problem 13A

The dimensions of the given figure is $\frac{9}{32}$

Explanation of Solution

Given:

Dimension of A, B,C and D given in figure

Calculation:

Calculation for E

  $\begin{array}{l}1\frac{3}{8}-1\frac{3}{32}\\ \frac{11}{8}-\frac{35}{32}\end{array}$

First of all, we calculate the least common multiple (LCM) for given denominators (8 and 32).

The least common multiple (LCM) for given denominators (32 and 16) is 32.

Hence, the least common denominator is 32.

Now, we subtract the given digits.

  $\begin{array}{l}\frac{11}{8}-\frac{35}{32}\\ =\frac{11\times 4-35\times 1}{32}\\ =\frac{44-35}{32}\\ =\frac{9}{32}\end{array}$

Hence, the subtraction of given digits is $\frac{9}{32}$

To determine

(F)

Dimension for part F of the plate.

Answer to Problem 13A

The dimensions of the given figure is $\frac{5}{16}$

Explanation of Solution

Given:

Dimension of A, B,C and D given in figure.

Calculation:

Calculation for F

  $\frac{13}{16}-\frac{1}{2}$

First of all, we calculate the least common multiple (LCM) for given denominator (16,2).

The least common multiple (LCM) for given denominators 16

Now we subtract the given digits

  $\begin{array}{l}\frac{13}{16}-\frac{1}{2}\\ =\frac{13\times 1-1\times 8}{16}\\ =\frac{13-8}{16}\\ =\frac{5}{16}\end{array}$

Hence, the subtraction of given digits is $\frac{5}{16}$

To determine

(G)

Dimension for part G of the plate.

Answer to Problem 13A

The dimensions of the given figure is $\frac{39}{32}$

Explanation of Solution

Given:

Dimension of A, B,C and D given in figure

Calculation:

Calculation for G

  $\begin{array}{l}2\frac{1}{32}-\frac{13}{16}\\ \frac{65}{32}-\frac{13}{16}\end{array}$

First of all, we calculate the least common multiple (LCM) for given denominator (16,32).

The least common multiple (LCM) for given denominator 32.

Now, we subtract the given digits:

  $\begin{array}{l}\frac{65}{32}-\frac{13}{16}\\ =\frac{65\times 1-13\times 2}{32}\\ =\frac{65-26}{32}\\ =\frac{39}{32}\end{array}$

Hence, the subtraction of given digits is $\frac{39}{32}$

To determine

(H)

Dimension for part H of the plate.

Answer to Problem 13A

The dimensions of the given figure is $\frac{33}{64}$

Explanation of Solution

Given:

Dimension of A, B, C and D given in figure.

Calculation:

Calculation for H:

  $\begin{array}{l}1\frac{17}{32}-1\frac{1}{64}\\ \frac{49}{32}-\frac{65}{64}\end{array}$

First of all, we calculate the least common multiple (LCM) for given denominator (32,64).

The least common multiple (LCM) for given denominator 64.

Now, we subtract the given digits:

  $\begin{array}{l}\frac{49}{32}-\frac{65}{64}\\ =\frac{49\times 2-65\times 1}{64}\\ =\frac{98-65}{64}\\ =\frac{33}{64}\end{array}$

Hence, the subtraction of given digits is $\frac{33}{64}$

To determine

(I)

Dimension for part I of the plate.

Answer to Problem 13A

The dimensions of the given figure is $\frac{19}{32}$

Explanation of Solution

Given:

Dimension of A, B, C and D given in figure.

Calculation:

Calculation for I

  $2\frac{23}{32}-2\frac{1}{8}$

  $\frac{87}{32}-\frac{17}{8}$

First of all, we calculate the least common multiple (LCM) for given denominator (32,8).

The least common multiple (LCM) for given denominator 32.

Now, we subtract the given digits:

  $\begin{array}{l}\frac{87}{32}-\frac{17}{8}\\ =\frac{87\times 1-17\times 4}{32}\\ =\frac{87-68}{32}\\ =\frac{19}{32}\end{array}$

Hence, the subtraction of given digits is $\frac{19}{32}$