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Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 19

Achievement Review—Section One - all with Video Answers

Educators

Chapter Questions

Problem 1

Express each of the following fractions as equivalent fractions as indicated.
a. $\frac{3}{8}=\frac{?}{32}$
b. $\frac{7}{10}=\frac{?}{100}$
c. $\frac{1}{4}=\frac{?}{64}$
d. $\frac{9}{16}=\frac{?}{128}$

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Problem 2

Express each of the following mixed numbers as improper fractions.
a. $3 \frac{1}{5}$
b. $2 \frac{9}{10}$
c. $5 \frac{3}{4}$
d. $13 \frac{3}{8}$
e. $6 \frac{9}{32}$

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00:52

Problem 3

Express each of the following improper fractions as mixed numbers.

a. $\frac{5}{2}$
b. $\frac{21}{5}$
c. $\frac{75}{4}$
d. $\frac{115}{32}$
e. $\frac{329}{64}$

Erika Bustos
Erika Bustos
Numerade Educator
00:52

Problem 4

Express each of the following fractions as a fraction in lowest terms.
a. $\frac{8}{16}$
b. $\frac{12}{100}$
c. $\frac{30}{32}$
d. $\frac{18}{64}$
e. $\frac{28}{128}$

Erika Bustos
Erika Bustos
Numerade Educator
02:18

Problem 5

Express the fractions in each of the following sets as equivalent fractions having the least common denominator
a. $\frac{1}{4^{\prime}}, \frac{3}{16}, \frac{9}{32}$
c. $\frac{7}{10}, \frac{3}{4}, \frac{9}{25}, \frac{13}{20}$
b. $\frac{7}{16}, \frac{5}{32}, \frac{9}{64}$

Lauren Shelton
Lauren Shelton
Numerade Educator

Problem 6

Add or subtract each of the following values. Express the answers in lowest terms.

a. $\frac{1}{8}+\frac{5}{8}$
b. $\frac{7}{16}+\frac{15}{16}$
c. $\frac{5}{8}+\frac{13}{32}$
d. $3 \frac{7}{10}+\frac{49}{100}$
e. $\frac{9}{32}+\frac{1}{4}+\frac{21}{64}$
f. $\frac{11}{16}-\frac{7}{16}$
g. $\frac{17}{20}-\frac{3}{5}$
h. $\frac{49}{64}-\frac{3}{8}$
i. $6-\frac{11}{16}$
j. $13 \frac{1}{8}-9 \frac{7}{32}$

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08:36

Problem 7

Multiply or divide each of the following values. Express the answers in lowest terms.
a. $\frac{1}{2} \times \frac{5}{8}$
b. $\frac{3}{4} \times \frac{4}{5} \times \frac{2}{3}$
c. $5 \frac{7}{32} \times \frac{3}{8}$
d. $3 \frac{1}{10} \times 8 \frac{1}{4}$
e. $\frac{3}{16} \times 20 \times 5 \frac{1}{2}$
f. $\frac{3}{10} \div \frac{2}{5}$
g. $\frac{14}{15} \div \frac{7}{25}$
h. $16 \div \frac{1}{3}$
i. $2 \frac{17}{32} \div \frac{9}{24}$
j. $2 \frac{29}{32} \div 8 \frac{3}{4}$

Debasish Das
Debasish Das
Numerade Educator
02:09

Problem 8

Perform each of the indicated combined operations.
a. $\frac{3}{4}+\frac{5}{16}-\frac{3}{8}$
b. $20 \frac{1}{2}+3 \frac{3}{8} \times \frac{1}{8}$
c. $\frac{3}{5} \times \frac{7}{8}+3 \frac{3}{4}$
d. $\left(18-5 \frac{3}{4}\right) \div \frac{1}{2}+3 \frac{7}{8}$
e. $\frac{16-4 \frac{1}{2}}{\frac{1}{2}+2 \frac{1}{8}}$
f. $\frac{5 \frac{1}{4} \times \frac{1}{2}}{6 \div 3 \frac{3}{4}}$

Brittany Scott
Brittany Scott
Numerade Educator
02:33

Problem 9

How many complete pieces can be blanked from a strip of aluminum 72 inches long if each stamping requires $1 \frac{3}{8}$ inches of material plus an allowance of $\frac{3}{4}$ inch at one end of the strip?

Mukesh Devi
Mukesh Devi
Numerade Educator

Problem 10

How many inches of bar stock are needed to make 30 spacers each $1 \frac{3}{16}$ inches long? Allow $\frac{1}{8}$ inch waste for each spacer.

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Problem 11

A shaft is turned at 200 revolutions per minute with a tool feed of $\frac{1}{32}$ inch per revolution. How many minutes does it take to cut a distance of 50 inches along the shaft?

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Problem 12

A shop order calls for 1800 steel pins each $1 \frac{5}{8}$ inches long. If $\frac{3}{16}$ inch is allowed for cutting off and facing each pin, how many complete 10 -foot lengths of stock are needed for the order?

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01:14

Problem 13

Compute dimensions $A, B, C, D$, and $E$ of the support bracket shown in Figure 19-1. All dimensions are given in inches.
A =
B =
C =
D =
E =

Mitchell Cutler
Mitchell Cutler
Numerade Educator
00:53

Problem 14

Write each of the following numbers as words.
a. 0.6
b. 0.74
c. 0.147
d. 0.0086
e. 4.208
f. 16.0419

Ronald Prasad
Ronald Prasad
Numerade Educator
00:46

Problem 15

Write each of the following words as decimal fractions or mixed decimals.
a. three tenths
b. twenty-six thousandths
c. nine and twenty-six thousandths
d. five and eighty-one ten-thousandths

Erika Bustos
Erika Bustos
Numerade Educator
02:02

Problem 16

Round each of the following numbers to the indicated number of decimal places.
a. 0.596 (2 places)
b. 5.0463 (3 places)
c. 0.80729 (4 places)
d. 7.0005 (3 places)

Gregory Higby
Gregory Higby
Numerade Educator
00:52

Problem 17

Express each of the following common fractions as decimal fractions. Where necessary,
round the answers to 3 decimal places.
a. $\frac{3}{4}$
b. $\frac{7}{8}$
c. $\frac{2}{3}$
d. $\frac{2}{25}$
e. $\frac{13}{20}$

Erika Bustos
Erika Bustos
Numerade Educator
00:34

Problem 18

Express each of the following decimal fractions as common fractions in lowest terms.
a. 0.7
b. 0.525
c. 0.007
d. 0.915
e. 0.0075

Dale Sanford
Dale Sanford
Numerade Educator
06:30

Problem 19

Add or subtract each of the following values.
a. 0.875 1 0.712
b. 5.004 1 0.92 1 0.5034
c. 0.006 1 12.3 1 0.0009
d. 2.99 1 6.015 1 0.1003
e. 23 1 0.0007 1 0.007 1 0.4
f. 0.879 2 0.523
g. 0.1863 2 0.0419
h. 5.400 2 5.399
i. 0.009 2 0.0068
j. 14.001 2 13.999

Ly Tran
Ly Tran
Numerade Educator
03:40

Problem 20

Multiply or divide each of the following values. Round the answer to 4 decimal places where necessary.
a. $0.923 \times 0.6$
f. $0.85 \div 0.39$
b. $3.63 \times 2.30$
g. $0.100 \div 0.01$
c. $4.81 \times 0.07$
h. $4.016 \div 0.03$
d. $0.005 \times 0.180$
i. $123 \div 0.665$
e. $12.123 \times 0.001$
j. $0.0098 \div 5.036$

Ronald Prasad
Ronald Prasad
Numerade Educator
02:20

Problem 21

Raise each of the following values to the indicated powers.
a. $2.6^2$ $\qquad$
b. $0.50^3$ $\qquad$
c. $0.006^2$ $\qquad$
d. $\left(\frac{3}{5}\right)^2$ $\qquad$
e. $\left(\frac{20.8}{6.5}\right)^3$

Erin Kearney
Erin Kearney
Numerade Educator
01:02

Problem 22

Determine the roots of each of the following values as indicated.
a. $\sqrt{49}$ $\qquad$
b. $\sqrt[3]{64}$ $\qquad$
c. $\sqrt{\frac{36}{81}}$ $\qquad$
d. $\sqrt{46.83+17.17}$
e. $\sqrt{39.2 \times 1.25}$

Lily An
Lily An
Numerade Educator
02:02

Problem 23

Determine the square roots of each of the following values to the indicated number of decimal places.
a. $\sqrt{379}(2$ places) $\qquad$
b. $\sqrt{0.8736}$ ( 3 places) $\qquad$
c. $\sqrt{\frac{2}{5}}$ (3 places)
d. $\sqrt{93.876-47.904}$ (3 places)

Gregory Higby
Gregory Higby
Numerade Educator
00:52

Problem 24

Find the decimal or fraction equivalents of each of the following numbers using the decimal equivalent table.
a. $\frac{5}{8}$ $\qquad$
b. $\frac{17}{32}$ $\qquad$
c. $\frac{21}{64}$ $\qquad$
d. 0.65625 $\qquad$
e. 0.671875 $\qquad$

Erika Bustos
Erika Bustos
Numerade Educator
01:01

Problem 25

Determine the nearer fractional equivalents of each of the following decimals using
the decimal equivalent table.
a. 0.465
b. 0.769
c. 0.038
d. 0.961

James Kiss
James Kiss
Numerade Educator
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Problem 26

Solve each of the following combined operations expressions. Round answers to 2 decimal places.
a. $0.4321+10.870 \div 3.43 \times 0.93$ $\qquad$ c. $35.98 \div \sqrt{6.35-4.81}$
b. $(12.60 \div 3-0.98)^2 \times 3.60$ $\qquad$ d. $6 \times\left(\frac{\sqrt{81} \times 4.03}{3.30 \times 2.75}\right)-1.7^2$

Ronald Prasad
Ronald Prasad
Numerade Educator

Problem 27

The basic form of an ISO Metric Thread is shown in Figure 19-2. Given a thread pitch of 1.5 millimeters, compute thread dimensions A, B, C, D, E, and F to 3 decimal places.
A =
B =
C =
D =
E =
F =

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Problem 28

A combination of gage blocks is selected to provide a total thickness of 0.4573 inch. One block 0.250 inch thick and one block 0.118 inch thick are selected. What is the required thickness of the remaining blocks?

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Problem 29

A piece of round stock is being turned to a 17.86 -millimeter diameter. A machinist measures the diameter of the piece as 18.10 millimeters. What depth of cut should be made to turn the piece to the required diameter?

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02:01

Problem 30

A plate 57.20 millimeters thick is to be machined to a thickness of 44.10 millimeters. The plate is to be rough cut with the last cut a finish cut 0.30 millimeter deep. If each rough cut is 3.20 millimeters deep, how many rough cuts are required?

Catheryn Taylor
Catheryn Taylor
Numerade Educator

Problem 31

A shaft is turned in a lathe at 120 revolutions per minute. The cutting tool advances 0.030 inch per revolution. How long is the length of cut along the shaft at the end of 3.50 minutes?

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