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Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 4

Multiplication of Common Fractions and Mixed Numbers - all with Video Answers

Educators


Chapter Questions

01:08

Problem 1

Express $\frac{1}{3}, \frac{2}{5}, \frac{5}{6}$, and $\frac{4}{9}$ as equivalent fractions having the lowest common denominator.

Julie Silva
Julie Silva
Numerade Educator
02:15

Problem 2

Add $\frac{1}{3}+\frac{2}{5}+\frac{5}{6}+\frac{4}{9}$.

Luke P
Luke P
Numerade Educator
00:51

Problem 3

Reduce $\frac{36}{45}$ to lowest terms.

Alex Ryder
Alex Ryder
Numerade Educator
02:02

Problem 4

Determine the length $A$ in Figure 4-3. All dimensions are in inches.
Figure 4-3 can't copy

Liuxi Sun
Liuxi Sun
Numerade Educator

Problem 5

Determine the length of the template in Figure 4-3. All dimensions are in inches.
Figure 4-3 can't copy

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Problem 6

Determine the length $B$ in Figure 4-3. All dimensions are in inches.
Figure 4-3 can't copy

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08:36

Problem 7

Multiply the fractions in Exercises 7 through 9. Reduce to lowest terms where necessary.
a. $\frac{2}{3} \times \frac{1}{6}$ _______
b. $\frac{1}{2} \times \frac{1}{4}$ _______
c. $\frac{5}{8} \times \frac{13}{64}$ _______

Debasish Das
Debasish Das
Numerade Educator
09:07

Problem 8

Multiply the fractions in Exercises 7 through 9. Reduce to lowest terms where necessary.
a. $\frac{3}{4} \times \frac{3}{5} \times \frac{2}{3}$ _______
b. $7 \times \frac{9}{14} \times 3$ _______
c. $\frac{7}{15} \times \frac{3}{8} \times \frac{5}{7}$ _______

Debasish Das
Debasish Das
Numerade Educator

Problem 9

Multiply the fractions in Exercises 7 through 9. Reduce to lowest terms where necessary.
a. $\frac{5}{4} \times \frac{2}{3}$ _______
b. $4 \times \frac{7}{8} \times \frac{5}{21}$ _______
c. $\frac{5}{9} \times 3 \times \frac{4}{15}$ _______

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Problem 10

Determine dimensions A, B, C, D, and E of the template shown in Figure 4-4.
All dimensions are in inches.
Figure 4-4 can't copy
A = _______
B = _______
C = _______
D = _______
E = _______

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Problem 11

A special washer-faced nut is shown in Figure 4-5. All dimensions are in inches.
Figure 4-5 can't copy
a. Determine the distance across flats.
Distance across flats $=\frac{55}{64} \times$ Distance across corners _______
b. Determine the washer thickness.
Washer thickness $=\frac{1}{8} \times$ Total thickness _______

Rashmi Sinha
Rashmi Sinha
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Problem 12

The Unified Thread may have either a flat or rounded crest or root (Figure 4-6). If the sides of the Unified Thread are extended, a sharp V-thread is formed (Figure 4-7). In Figure 4-7, H is the height of a sharp V-thread. The pitch, P, is the distance between two adjacent threads.
Figure 4-7 can't copy
Find dimensions A, B, and C as indicated.
a. $\mathrm{H}=\frac{7^{\prime \prime}}{16^{\prime}}$ A = _______ $\quad$ B = _______
b. $\mathrm{H}=\frac{3^{\prime \prime}}{8^{\prime}}$ A = _______ $\quad$ B = _______
c. $\mathrm{H}=\frac{15^{\prime \prime}}{16}$, A = _______ $\quad$ B = _______
d. $\mathrm{H}=\frac{21^{\prime \prime}}{32^{\prime}}$, A = _______ $\quad$ B = _______
e. $\mathrm{H}=\frac{3^{\prime \prime}}{4^{\prime}}$, A = _______ $\quad$ B = _______
f. $P=\frac{1^{\prime \prime}}{4^{\prime}}$ C = _______
g. $P=\frac{3^{\prime \prime}}{32}$ C = _______
h. $P=\frac{1^{\prime \prime}}{20^{\prime}}$, C = _______
i. $\quad \mathrm{P}=\frac{1^{\prime \prime}}{28^{\prime}}$ C = _______
j. $\quad P=\frac{3^{\prime \prime}}{16^{\prime}}$ C = _______

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08:36

Problem 13

Multiply these mixed numbers. Reduce to lowest terms where necessary.
a. $1 \frac{2}{3} \times 6 \frac{3}{10}$ _______
b. $3 \frac{5}{16} \times 7 \frac{3}{4}$ _______
c. $4 \frac{5}{8} \times 2 \frac{1}{2}$ _______
d. $1 \frac{2}{3} \times 10 \frac{1}{4} \times \frac{3}{8}$ _______
e. $2 \frac{3}{32} \times 3 \times \frac{1}{8}$ _______
f. $2 \frac{2}{3} \times 2 \frac{2}{3} \times 5 \frac{1}{4}$ _______

Debasish Das
Debasish Das
Numerade Educator

Problem 14

How many inches of drill rod are required in order to make 20 drills each $3 \frac{3^{\prime \prime}}{16}$ long?
Allow $\frac{3^{\prime \prime}}{32}$ waste for each drill.

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01:20

Problem 15

A hole is cut in a rectangular metal plate as shown in Figure 4-8. To find the area of a rectangle, multiply the length by the width. Determine the area of the plate after the hole has been removed. All dimensions are in inches. The area will be in square inches.
Figure 4-8 can't copy

Vicki Stebbins
Vicki Stebbins
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01:20

Problem 16

Six identical square holes are cut in a rectangular metal plate as shown in Figure 4-9. To find the area of a rectangle, multiply the length by the width. Determine the area of the plate after the holes have been removed. All dimensions are in inches. The area will be in square inches.
Figure 4-9 can't copy

Vicki Stebbins
Vicki Stebbins
Numerade Educator