Download Percentage and Ratios

120104c
Welder
Percentage and Ratios
Trade Math
First Period
Table of Contents
Objective One ............................................................................................................................................... 2 Expressing Two Quantities as a Ratio ...................................................................................................... 2 Expressing Two Ratios as a Proportion .................................................................................................... 5 Objective One Exercise............................................................................................................................... 10 Objective Two............................................................................................................................................. 14 Converting Fractions and Percents ......................................................................................................... 14 Converting Decimals and Percents ......................................................................................................... 16 Objective Two Exercise .............................................................................................................................. 17 Objective Three ........................................................................................................................................... 21 Solving Problems with Percents ............................................................................................................. 21 Objective Three Exercise ............................................................................................................................ 23 Self-Test ...................................................................................................................................................... 25 Self-Test Answers ....................................................................................................................................... 31 Objective One Exercise Answers................................................................................................................ 33 Objective Two Exercise Answers ............................................................................................................... 34 Objective Three Exercise Answers ............................................................................................................. 35 NOTES
Percentage and Ratios
Rationale
Why is it important for you to learn this skill?
Being able to solve problems involving percentage and ratios is a necessary skill when
working in the trades. For example, you must know how to calculate the composition of
steel, composition of alloys, scrap rate, alignment tolerances and discounts. Ratios can
also help you to solve many different problems in your daily routine, such as the number
of teeth on gears or the scale on a blueprint drawing.
Outcome
When you have completed this module, you will be able to:
Solve problems involving percentage and ratios.
Objectives
1. Calculate ratio problems: two quantities in the form of a ratio and two ratios in the
form of a proportion.
2. Convert between fractions, decimals and percent.
3. Solve percent problems.
Introduction
This module addresses how to solve various problems involving percentages and ratios. It
explains how to express two quantities in the form of a ratio and two ratios in the form of
a proportion to solve trade-related problems. It also addresses how to convert between
fractions and percents, how to convert between decimals and percents and how to solve
percent problems.
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Objective One
When you have completed this objective, you will be able to:
Calculate ratio problems: two quantities in the form of a ratio and two ratios in the form
of a proportion.
Expressing Two Quantities as a Ratio
A ratio is a comparison of two quantities. You must always compare the same things,
such as hours to hours, cm to cm and welds to welds. For example, you can compare the
number of teeth on machinery gears or compare time worked, dollars spent or workers
hired. When you compare two quantities, you must give them the same units. If they are
not in the same units, convert one or the other so they are in like units. Generally, this
requires converting the larger units to equivalent smaller units, such as converting feet to
inches. You should also express ratios in lowest terms.
The three ways to state a ratio are:
1. to use words and numbers (such as the ratio of 5 to 10),
2. to use a colon (such as 5:10) and
3. to use a fraction (such as 510).
When you express the ratio 5:10 in a fraction, the 5 becomes the numerator and the 10
becomes the denominator (510).
Sometimes you can simplify a ratio. For example, 1248 = 14 or 1:4.
To simplify the ratio of 50 cents to 3 dollars, you would first convert 3 dollars to cents so
that you are comparing cents to cents (like units).
3 dollars = 300 cents
50 cents to 300 cents = 50300 = 16 or 1:6
You must keep the units in the same order as they appear in the problem. You are
comparing the ratio of 50 cents to 3 dollars, not 3 dollars to 50 cents.
To express the ratio of 5 feet to 15 inches in lowest terms, follow these steps.
1. Convert 5 feet to inches so you compare inches to inches.
1 foot = 12 inches
5 feet = 60 inches
2. The ratio is now 60 inches to 15 inches, which is 6015 = 41 or 4:1.
Reducing the Ratio
In most cases, you should reduce the ratio so that one of the units in the ratio is 1. First,
divide the small unit into the large unit to determine if the result is a whole number. If the
result is a whole number, then you can use 1 as the smaller unit in the ratio. However,
this may not always be practical. For example, you can express 2:3 as 1:112 (by dividing
each term by 2) and 4:7 as 1:134 (by dividing each term by 4), but it may be more
practical to leave the ratios as 2:3 and 4:7, respectively.
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To express the ratio 658 inches to 106 inches in simplest form, follow these steps.
1. Divide 106 inches by 658 inches.
NOTES
106  658 = 106  538 = 106 x 853 = 84853= 16
2. Write the ratio as 1 to 16, 1:16 or 116.
NOTE
In some cases, when you divide the small unit into the larger unit, the
result is not a whole number. You must then write the ratio with both
units as whole numbers larger than 1.
Example 1
The length of an object on a blueprint is 338 inches and the actual length of the object is
16 inches. To determine how many times larger is the actual length compared to the
blueprint length, follow these steps.
1. Express the ratio of 16 inches to 338 inches in simplest form using whole
numbers.
2. Divide 16 inches by 338 inches to see if the result is a whole number.
16  338 = 16  278 = 16 x 827 = 12827 = 42027
3. The division is not a whole number, so you do not have 1 as one of the numbers
in the ratio.
4. Convert 42027 to an improper fraction and reduce to express the ratio.
42027 = 12827
5. Use whole numbers for both units to determine the ratio.
128
27 or 128:27
6. Take the improper fraction 12827 and express it with 1 as the denominator.
7. Divide 128 by 27. The result is 4.740 with the decimal 0.740 repeating.
8. Round to the nearest one-hundredth. The result is 4.74.
9. The actual length of the object is just less than 434 times the length of the
blueprint dimension.
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Example 2
A cubic foot of water weighs approximately 62.39 lb and a cubic foot of ice weighs
approximately 57.5 lb. Use the ratio of ice:water to express the ratio first with 1 as the
numerator and then with 1 as the denominator. Round to the nearest thousandth.
1. Determine the ratio of the weights of ice to water.
Ice:water = 57.5:62.39 = 57.562.39
2. Convert the fraction 57.562.39 so the numerator is 1. Divide both numerator and
denominator by 57.5.
57.5 57.5
1


= 1:1.085
62.39 57.5 1.085
3. The ratio of ice to water is approximately 1 to 1.085.
4. Use the same ratio and make the denominator equal to1.
57.5 62.39
0.922

=
= 0.922:1
1
62.39 62.39
The ratio of ice to water is also approximately 0.922 to 1.
Example 3
A mild steel trailer frame weighs 500 lb. Determine the weight of the trailer if the
manufacturer uses aluminum instead of steel. A cubic inch of steel weighs approximately
0.2835 lb and a cubic inch of aluminum weighs approximately 0.098 lb. Use the ratio of
steel:aluminum to express the ratio first with 1 as the numerator and then with 1 as the
denominator. Round to the nearest thousandth.
1. Determine the ratio of the weights of steel to aluminum.
Steel:aluminum = 0.2835:0.098 = 0.28350.098.
2. Convert the fraction 0.28350.098 so the numerator is 1. Divide both numerator
and denominator by 0.2835.
0.2835 0.2835
1


= 1:0.346
0.098 0.2835 0.346
3. The ratio of steel to aluminum is approximately 1:0.346.
4. Use the same ratio and make the denominator equal to 1.
0.2835 0.098 2.893


= 2.893:1
0.098 0.098
1
The ratio of steel to aluminum is also approximately 2.893:1.
NOTE
You can find the comparable weight of aluminum by multiplying
500 lb by 0.346 or dividing 500 lb by 2.893. In either case, your
answer is approximately 173 lb.
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NOTES
Expressing Two Ratios as a Proportion
A proportion is a statement that says two ratios are equal. Since a proportion has two
ratios, it has four terms. A proportion problem requires that you solve for one of the
missing terms. You use the concept of equivalent fractions to find the missing term. Two
of the more common ways of stating a proportion are:
1. fractional form (such as 23 = 812) and
2. proportional form (such as 2:3::8:12).
A ratio is a comparison of two quantities or terms, which must have the same units. When
creating the proportion using two ratios, you must ensure that the units are the same in
each ratio.
Direct Proportions
When you compare ratios in a proportion, you must realize that, if the numerator in one
ratio is smaller than the denominator, then the numerator in the second ratio must also be
smaller than the denominator (such as 2 lb40 lb = 7 dollars140 dollars).
This concept is true whether dealing with direct proportions or indirect proportions. A
direct proportion occurs when increasing one quantity (or number) increases the other
quantity (or number) by the same ratio and decreasing one quantity decreases the other
quantity by the same ratio. For example, the cost of labour increases as the number of
welders on a project increases or the cost of your fuel per week decreases as you use your
machine less. These are direct proportions in which the two compared ratios increase or
decrease simultaneously.
When establishing the ratios, you should set up the equations with similar units in each
ratio and place small numbers in the numerator and large numbers in the denominator.
You may place large numbers in the numerator and small numbers in the denominator or
vice versa; however, you must ensure that you place them the same way every time.
large
large
small
small
=
or
=
small
small
large
large
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Example 1
Determine the cost of 16 boxes of welding rods if 5 boxes cost $85.00.
1. You know that 16 boxes will cost more than 5 boxes, so $85.00 is the small
dollars in one ratio.
small boxes
small dollars
=
large boxes
large dollars
5 boxes
85 dollars
=
16 boxes
n dollars
2. Find the unknown value, n dollars. Determine the equivalent fraction to 516 with
85 as the numerator. Rewrite the proportion with the numbers only.
85
5
=
16
n
3. Cross-multiply. Multiply 5 by n and multiply 16 by 85. Keep the unknown value,
n, on the left side of the equation.
5 x n = 16 x 85
4. Divide both sides of the equation by 5 to isolate the variable n.
5 x n 16 x 85

5
5
n
16 x 85
5
n  272
5. 16 boxes of rods cost $272.00.
When you have a proportion (two ratios with an equal sign), you always cross-multiply.
You multiply where there is a number both in the numerator and in the denominator
across from it, and then divide by the third number. This procedure gives you the value of
the unknown number.
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Example 2
To calculate how many times greater a load with a 1-inch diameter rod can carry than a
1
2-inch diameter rod, follow these steps.
1. You have to find the cross-sectional area of each rod before you can set up the
proportion. The formula to find the area of a circle is A = r2. The radius is 12
diameter and  = 3.1416.
 Area of large rod = 3.1416 x (12)2 = 0.7854 inch2
 Area of small rod = 3.1416 x (14)2 = 0.19635 inch2
2. Give the small rod an arbitrary load value of 1. Use a proportion to find the load
value of the large rod (n).
small area small load value
=
large area
large load value
0.19635
1
=
0.7854
n
3. Cross-multiply and divide to solve for n.
n x 0.19635  0.7854
n  4.0
4. A 1-inch diameter rod carries a load 4 times as heavy as a 1/2-inch diameter rod.
Indirect Proportion
In an indirect proportion, an increase in one quantity causes a decrease in the other
quantity or a decrease in one quantity causes an increase in the other quantity. For
example, as the number of welders on a job increases, the amount of time it takes to
complete the job decreases.
When establishing an indirect proportion, you use the same structure as with direct
proportion so that you have small numbers in the numerator and large numbers in the
denominator. You must always express each ratio in the same units.
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Example 1
A crew of 12 welders can complete a fabrication job in 8 hours. If they must complete the
same job in 3 hours, calculate how many welders must work. The welders are one ratio
and the hours are the other ratio. The small hours (3) and large hours (8) make the hours
ratio.
small welders
small hours
large welders = large hours
1.
2. It will take more welders to finish a job more quickly, so 12 welders is the small
number in the welders ratio.
12 welders 3 hours
n welders = 8 hours
3. Cross-multiply and divide.
3 x n  12 x 8
n
12 x 8
 32
3
It will take 32 welders to complete the same job in 3 hours.
Example 2
If the 10-inch pulley turns at 60 rpm (Figure 1), calculate fast the 2-inch pulley turns.
Figure 1 - Pulley ratio.
1. The smaller pulley or gear must rotate faster than the large one, so write the ratio
this way.
small pulley
small rpm
large pulley = large rpm
2. Since the 10-inch pulley turns slower, the 60 rpm associated with the 10-inch
pulley is the small rpm in the ratio.
2
60
10 = n
3. Cross-multiply and divide.
n = 300 rpm
The small pulley turns at 300 rpm while the large pulley turns at 60 rpm.
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NOTES
NOTE
When solving indirect proportion problems, always consider if your
answer should be more or less when reading the problem. This helps
you know if you have made a mistake after solving the problem.
Example 3
If the small gear in Figure 2 has 8 teeth and turns at 30 rpm, calculate how fast the large
gear with 20 teeth turns? Use the following steps.
Figure 2 - Gear ratio.
Since the small gear is turning faster, the 30 rpm is the large rpm in the ratio.
small rpm small teeth
=
large rpm large teeth
n
8

30 20
n  12
The large gear turns at 12 rpm.
Proportional Form
You commonly write proportions in proportional form or fractional form. An example of
the proportional form is 2:3::8:12. The two outside terms (2 and 12) are the extremes and
the two inside terms (3 and 8) are the means. The product of the means equals the
products of the extremes. If a ratio is in this format, you can use this rule to solve it. For
example, to solve the proportion M:8::6:24, follow these steps.
1. Write the proportion this way.
M x 24 = 8 x 6
2. Divide both sides of the equation by 24.
M=2
3. State the proportional form M:8::6:24 in the fractional form.
6
M
=
8
24
4. Cross-multiply.
M x 24 = 8 x 6
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Objective One Exercise
Answer the following questions.
Two Quantities as a Ratio
1. Express the following ratios in their simplest form.
a) $10 to 25¢
b) 3 feet to 1 yard
c) 3 minutes to 1 hour
d) 6 feet to 144 inches
e) 5 days to 6 weeks
2. Express the two lengths of the flat bar in Figure 3 as a ratio.
Figure 3 - Lengths of flat bar expressed as a ratio.
3. A journeyman welder can weld 75 structural beam splice joints per 40-hour week.
His apprentice can weld one beam every 80 minutes. What is the ratio of the minutes
spent by the journeyman as compared to the apprentice when welding one beam
splice joint?
4. Determine the ratio of the speed of gear A to the speed of gear B, if gear A turns at
84 rpm and gear B turns at 14 rpm.
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5. The compression ratio of a gasoline engine is the ratio of cylinder volume at the
bottom of the stroke to the volume at the top of the stroke. If a cylinder of an engine
has a full volume of 575 cm3 at the bottom of the stroke and 67 cm3 at the top
(Figure 4), what is the compression ratio? Express your answer to three decimal
places.
NOTES
Figure 4 - Engine compression ratio.
6. A gallon of water weighs approximately 10 lb and a gallon of diesel fuel weighs
approximately 7.55 lb. What is the ratio of the weight of water to the weight of diesel
fuel? Express your answer to two decimal places.
Two Ratios as a Proportion
1. Solve the proportion for the unknown in the following problems.
B
5
a)
=
8
24
b)
80 60
=
r
5
c)
10 0 .4
=
m
36
d)
0 .3
0 .2
=
24
a
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NOTES
2. The cost of 150 feet of 58 inch steel rod is $45.00. How much does 535 feet of the
same rod cost?
3. A stack of 40 steel plates weighs 2000 lb. How much would a stack of 25 of the same
plates weigh?
4. If a welder can do 72 fillet welds in an 8-hour day, how many can she do in
20 minutes?
5. A pump that discharges 4.5 gal/min can fill a tank in 22 hours. How long will it take
to fill the same tank if you use a pump discharging 12 gal/min?
6. If it takes 10 welders 9 days to construct a steel tank, how long will it take 6 welders
to construct the tank?
7. A belt connects two pulleys (Figure 5). If the 45 cm pulley rotates at 1850 rpm, how
fast will the 60 cm pulley turn?
Figure 5 - Pulleys.
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8. Three automatic spot welding machines perform 16 500 welds per 8-hour day. How
long will it take five machines to complete 33 000 welds?
NOTES
9. The hydrostatic pressure in a storage tank increases directly with depth. If the
pressure is 4.33 psi at the bottom of the tank at a depth of 10 feet, what is the pressure
at the bottom of the tank if it is 39 feet high and completely filled?
10. Figure 6 illustrates two gears that work together. The smaller gear rotates at 450 rpm.
If the larger gear has 24 teeth and the smaller gear has 16 teeth, how fast does the
larger one rotate?
Figure 6 - Gear set.
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NOTES
Objective Two
When you have completed this objective, you will be able to:
Convert between fractions, decimals and percent.
Converting Fractions and Percents
To convert fractions to percent and percent to fractions, you must first have an
understanding of what percent means. Percent means per one hundred or out of one
hundred. The % symbol following a number means that specific quantity out of one
hundred. If you score 85% on a 100-question test, you have correctly answered
85 questions out of 100. You can express 100% of something as 100/100 or 1.
Converting a Fraction to a Percent
In order to convert a fraction to a percent, you must first change the fraction to a decimal.
Divide the numerator by the denominator and carry the result to two or more decimal
places. Then, multiply by 100 and add a percent sign (multiply by 100%). For example,
to change 4960 to a percent rounded to two decimals, follow these steps.
1. 49  60 = 0.816666666 repeating.
2. Multiply by 100, round to two decimals and add a % sign.
3. The answer is 81.67%.
You can also multiply the numerator by 100 and then divide by the denominator and add
a percent sign (4900  60 = 81.67%).
Example
To change a mixed number to a percent, you must first convert the mixed number to an
improper fraction. For example, to change 537 to a percent, follow these steps.
1. Convert 537 to an improper fraction. You can either multiply by 100 and then
divide by 7 or divide by 7 and then multiply by 100. It does not change the
answer.
5
3
38
=
7
7
2. Multiply 38 by 100, divide by 7 and add a percent sign.
3800  7 = 542.86% (rounded to two decimal places)
3. Convert back to a mixed number to get 54267%.
You can also solve this problem another way. Since 5 is equal to 500%, convert 3/7 to a
percent and add it to 500% to get 5426/7%.
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NOTES
Converting a Percent to a Fraction
To change a percent to a fraction, follow these steps.
1. Start with a fraction that has a denominator of 100 (per one hundred).
2. Drop the percent sign and use that number as the numerator.
3. If the percent is a fraction or a mixed number, such as 14% or 1212%, convert to
an improper fraction.
4. When you have the percent in fractional form, remove the percent sign, multiply
the denominator by 100 and reduce it to its lowest terms, if possible. You then
have a fraction equal to the original percent.
For example, 40% is converted to a fraction reduced to its lowest terms like this.
40% =
40
2
=
100
5
Once you have a proper fraction, you must reduce the fraction to its lowest terms. If the
numerator is a decimal, you must make an equivalent fraction so that the numerator is a
whole number. You may have to multiply both numerator and denominator by 10, 100 or
1000.
The following are additional examples.
7.8
78
39
=
=
.
500
100 1000

As a fraction reduced to its lowest terms, 7.8% =

As a fraction reduced to its lowest terms, 0.03% =

As a fraction reduced to its lowest terms,

25
1
25
1
1
x
=
=
.
As a fraction reduced to its lowest terms, 12 % =
2
2
100
200 8

As a fraction reduced to its lowest terms, 107
.03
3
=
.
100 10 000
1
1
1
1
%=
x
=
.
4
4
100
400
1
215
1
215 43
%=
x
=
=
=
2
2
100
200 40
3
. You can first reduce 215200 to its lowest terms of 4340 and then convert it to a
40
mixed number of 13/40.
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Converting Decimals and Percents
To convert a decimal to a percent or a percent to a decimal, you either multiply by 100 or
divide by 100.
Converting a Decimal to a Percent
To convert a decimal to a percent, you must multiply by 100 and add a percent sign. In
other words, you move the decimal point two places to the right and add a percent sign. If
you multiply by 10 or any multiple of 10, you move the decimal point as many places to
the right as there are zeroes in the multiplier (in this case, two decimal places because
you are multiplying by 100).
These are several examples of the process.
 To convert 0.001 to a percent, 0.001 x 100 = 0.1%.
 To convert 0.2584 to a percent, 0.2584 x 100 = 25.84%.
 To convert 3.5 to a percent, 3.5 x 100 = 350% = 350.0%
When there are not enough numbers to move the decimal two places to the right, you
must add enough zeroes to make it possible. Also, if the decimal ends up at the end of the
number, do not write it. A decimal point is just the separator between the whole and
fractional parts of a number.
Converting a Percent to a Decimal
To convert a percent to a decimal, you remove the percent sign and move the decimal
point two places to the left. By moving the decimal point two places to the left, you are
actually dividing by 100. For example, 0.67% as a decimal is 0.0067.
If you divide by 10 or multiples of 10, you move the decimal point as many places to the
left as there are zeroes in the divisor (in this case, two decimal places because you are
dividing by 100). You can also remove the percent sign, divide by 100, change the
fraction so there is no decimal in the numerator and then convert the fraction to a
decimal.
For example, 16.6% =
16.6
166
=
= 0.166.
100 1000
In cases where the percent is a fraction or a mixed number, first change the fraction to a
decimal.
219
For example, 219% =
= 2.19.
100
These are other examples of converting percentages to decimals.

1
0.0625
% = 0.0625% =
= 0.000625.
100
16

11.125
1
11 % = 11.125% =
= 0.11125.
8
100

1
365.25
365 % = 365.25% =
= 3.6525.
4
100
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Objective Two Exercise
Answer the following questions.
Converting Between Fractions and Percents
1. Express 1825 as a percent.
2. Express 30105 as a percent. (Round to two decimal places.)
3. Express 7818 as a percent.
4. Express each of the following fractions and mixed numbers as a percent.
25
a)
21
b)
2
9
c)
5
70
d)
2
30
e) 114
5. Express 130% as a mixed number.
6. Express 8313% as a common fraction.
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7. Express each of the following percents as a common fraction or mixed number.
a) 8%
b) 40%
c) 2%
d) 1623%
e) 8712%
f) 1258%
8. Express 78% as a common fraction.
9. Express each of the following as a percent.
a)
1
2
b)
3
4
c)
1
6
d)
3
5
10. Express each of the following percents as a common fraction or mixed number.
a) 614%
b) 3313%
c) 8356%
d) 147%
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Converting Between Decimals and Percents
1. Convert 0.07 to a percent.
2. Convert 2.3 to a percent.
3. Convert 0.125 to a percent.
4. Convert each of the following to a percent.
a) 0.01
b) 0.065
c) 0.12
d) 1.963
5. Convert 1.35 to a percent.
6. Convert 4.8% to a decimal.
7. Convert 37.5% to a decimal.
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NOTES
8. Convert 0.12% to a decimal.
9. Express each of the following as a decimal.
a) 0.2%
b) 0.43%
c) 5%
d) 84%
e) 93.4%
10. Convert 28.37 % to a decimal.
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Objective Three
When you have completed this objective, you will be able to:
Solve percent problems.
Solving Problems with Percents
Percent means per one hundred and you can express them as decimals or fractions. When
working with percentage, you can have three types of problems.
 You have to find a number that represents a percent of another number (such as
20% of 540).
 You have to find the percent that one number is of another number (such as the
percent that 37 is of 97).
 You have to find the whole number (such as the whole number if 63 represents
only 25%).
In all three types of problems, you can set up two ratios as a proportion, cross-multiply
and divide to solve the problem.
1. The first ratio should be a percent with 100 as the denominator.
2. Write the second ratio so that the equality is true according to the wording of the
problem.
Example 1
What is 20% of 540? In this example, 540 is 100%. Also, any number following the word
of is the denominator in the ratio. You can use a proportion to solve this type of problem
as shown.
20%
n

100% 540
n x 100  20 x 540
n  108
You can also change 20% to a decimal (0.20) and multiply by 540 to solve. You can
replace the of with a multiplication sign, so 20% of 540 becomes 0.20 x 540 = 108.
Example 2
37 is what percent of 97?
1. 37 is an unknown percent and 97 is 100%.
n%
37
=
100% 97
2. Cross-multiply and divide to solve for n.
n = 38.14% (rounded to two decimal places)
3. 37 is 38.14% of 97.
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Example 3
63 is 25% of what number?
1. You have an unknown 100% amount because 63 is 25%.
25%
63
=
n
100%
2. Solve for n by cross-multiplying and dividing.
n = 252
3. 63 is 25% of 252.
Example 4
You purchased a new pair of work boots for $230.05, which included 7% sales tax. How
much did you pay in sales tax?
You cannot simply find 7% of $230.05 because you calculate the sales tax on the selling
price and $230.05 is the selling price plus sales tax. You must find the selling price first.
1. 107% is $230.05 (100% cost + 7% sales tax). Find the dollar value that is 100%.
n
100%
=
107% 230.05
2. Cross-multiply and divide to find the selling price.
n = $215.00
3. Find the sales tax.
$230.05 - $215.00 = $15.05
or
7% of $215.00 = $15.05
Pay special attention to these types of problems. If you had solved for 7% of $230.05,
you would have the incorrect answer of $16.10.
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Objective Three Exercise
1. What is 12% of 600?
2. What is 214% of 4000 rods?
3. A welder receives an increase of 634% in her hourly rate, which is currently $25.80
per hour. What is her new hourly rate?
4. A certain grade of braze welding rod is 60% copper, 39% zinc and 1% tin. If this
welding rod weighs 130 lb, determine the weight of each individual metal.
5. 3.5 is what percent of 69? (Round to two decimal places).
6. 0.84 is what percent of 96?
7. You purchase a truck for $1800.00 and later sell it at a profit of $400.00. What is the
percent profit based on the selling price?
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8. A rig welder had a total income of $223 000.00 for one year's operation and will
make a net profit of $68 000.00. What percent of the total income was net profit?
9. 30 is 1212% of _________.
10. 20 is 0.5% of __________.
11. A welding shop purchases a pallet of wire. They receive a 22% discount for
purchasing in bulk and save $410.00.
a) What was the original list price?
b) What was the actual purchase price?
12. A journeyman welder had $119.54 deducted from his wages. If this was 2% of his
wages, how much did he earn?
13. If a journeyman welder received a raise of 3.5% and is currently earning $26.52/hr,
what was her original rate of pay?
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Self-Test
1. Braze welding rod contains approximately 35 copper. What percent is copper?
a) 30%
b) 50%
c) 60%
d) 75%
2. Hydrogen sulphide in concentrations of only 700 parts per million may cause death.
What is 700 ppm as a percentage?
a) 0.7%
b) 0.07%
c) 0.007%
d) 0.0007%
3. A welding shop employs 20 welders and four are first-year apprentices. What percent
of the welders are first-year apprentices?
a) 4%
b) 8%
c) 16%
d) 20%
4. In a class of 30 welding students, four students are left-handed. What percent of
students are right-handed? (Round to the nearest whole percent.)
a) 87%
b) 26%
c) 13%
d) 4%
5. A certain type of stainless steel contains 38% chromium. What fraction of the alloys
is chromium?
a) 38
b) 34
c) 3850
d) 1950
6. A 0.40% carbon steel is classed as a medium carbon steel. What is the fractional
portion of carbon in this steel?
a) 25
b) 125
c) 1250
d) 1400
7. A chromium-nickel steel that contains 1212% nickel has what fractional portion of
nickel?
a) 18
b) 112
c) 1125
d) 125100
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8. A cast iron with 2.0% carbon contains what fractional portion of carbon?
a) 150
b) 1500
c) 110
d) 15
9. Express 0.002 as a percent.
a) 0.02%
b) 0.20%
c) 2.0%
d) 20%
10. Express 0.98 as a percent.
a) 0.98%
b) 9.8%
c) 98%
d) 980%
11. Express 140.3 as a percent.
a) 1.403%
b) 14.03%
c) 1403%
d) 14030%
12. Express 1.125 as a percent.
a) 112.5%
b) 125%
c) 112%
d) 1125%
13. A third-year apprentice's wage is 90% of the journeyman rate. Express this as a
decimal.
a) 0.009
b) 0.09
c) 0.9
d) 9.0
14. A certain type of aluminum is alloyed with 0.12% manganese. Express this as a
decimal.
a) 0.012
b) 0.0012
c) 0.00012
d) 1.2
15. Express 230% as a decimal.
a) 2300
b) 23.0
c) 2.30
d) 0.23
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16. The percentage of elongation in a tensile test is 1912%. Express this as a decimal.
a) 19.5
b) 1.95
c) 0.19
d) 0.195
NOTES
17. The ratio of 71.25 inches to 23.75 feet is:
a) 3:1.
b) 4:1.
c) 1:3.
d) 1:4.
18. A journeyman welder can weld 120 lengths of pipe per 40-hour week while his
apprentice can weld one pipe every half hour. What is the ratio of the journeyman's
rate of work to the apprentice's rate of work?
a) 1.5:1
b) 3:1
c) 2:1
d) 2:3
19. Determine the ratio of the speed of gear A to the speed of gear B if gear A turns at
120 revolutions per minute and gear B turns at 18 revolutions per second.
a) 20:3
b) 18:1
c) 1:9
d) 1:6 23
20. On a shop drawing, the length of a pipe is 238 inches. The actual length of the pipe is
12 feet 8 inches long. What is the ratio of the blueprint length to the actual length?
a) 1:32
b) 1:64
c) 1:6
d) 1:24
21. If a cup of coffee costs $0.75 and a dozen doughnuts cost $4.50, what is the ratio of
the cost of a cup of coffee to the cost of a dozen doughnuts?
a) 1:6
b) 1:60
c) 1:12
d) 2:1
22. If a welder can do 128 fillet welds in an 8-hour day, how many can she weld in
15 minutes?
a) 16
b) 12
c) 8
d) 4
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23. If a joint 712-feet long requires 40 spot welds, how many welds do you use on a joint
that is 12 feet 412 inches long if you use the same spacing?
a) 40
b) 66
c) 90
d) 148
24. A welding contractor charges $3500 for a job that took 3 welders working 38 hours
each to complete. What should the contractor charge, at the same rate, for a job that
requires 5 welders for 43 hours each?
a) $3960.53
b) $5833.33
c) $6600.88
d) $1855.81
25. If it takes 7 workers 38 hours to fabricate a steel tank, how long will it take 11
workers, working at the same rate, to do the same job?
a) 24.18 hours
b) 59.71 hours
c) 32.18 hours
d) 28.11 hours
26. Seven ironworkers can produce parts for a skid shack in 1312 hours. How many
ironworkers do you need if they must finish the job in 3112 hours?
a) 13
b) 9
c) 6
d) 3
27. How many times greater a load does a 112-inch diameter rod carry than a 12-inch
diameter rod? (The formula to find the area of a circle is A = r2.)
a) 3
b) 6
c) 9
d) 12
28. A welding project costs $8000.00 and requires 4 welders working for 54 hours. How
many hours would it take 6 welders to do the same job working at the same rate?
a) 81 hours
b) 63 hours
c) 36 hours
d) 24 hours
29. A crew of 16 welders can complete a fabrication job in 9 hours. If they must
complete the same job in 4 hours, how many welders do you require to do the work?
a) 36
b) 7
c) 32
d) 13
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30. A welder who earns $14.50 per hour obtains a 9.5% raise. Calculate his new hourly
rate.
a) $15.50
b) $15.88
c) $16.95
d) $19.55
NOTES
31. A welding shop receives a discount of 1212% off the regular price of $426.00 for a
pedestal grinder. Calculate the price the shop paid to the nearest cent.
a) $413.50
b) $400.00
c) $353.25
d) $372.75
32. Phosphor bronze contains 0.3% phosphorous. Find the number of pounds of
phosphorous in 600 lb of phosphor bronze.
a) 1.8 lb
b) 18.0 lb
c) 3.0 lb
d) 6.0 lb
33. A welding machine priced at $9500.00 has a sales tax of $570.00. What is the
percentage of sales tax?
a) 0.06%
b) 0.6%
c) 6.0%
d) 6.6%
34. If you receive 10 pairs of damaged welding goggles out of an order of 200 pairs,
what percentage is damaged?
a) 0.5%
b) 5%
c) 10%
d) 20%
35. A contractor estimates that a job will cost her $4560.00 for material and labour. If her
contract price is $5800.00, what is her percentage of profit based on cost?
a) 78.6%
b) 27.2%
c) 21.4%
d) 12.4%
36. If you paid $347.75 for a new photoelectric welding helmet that included 7% sales
tax, what was the list price of the helmet?
a) $323.41
b) $325.00
c) $330.75
d) $335.45
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37. After receiving a 4.5% raise, your salary is $16.86 per hour. What was your salary
before the raise?
a) $15.86
b) $15.90
c) $16.10
d) $16.13
38. After purchasing 10 new welders, a tank fabrication shop increased its annual
production by 25%. If annual production increased by 63 tanks, what was their old
annual production?
a) 252 tanks
b) 263 tanks
c) 315 tanks
d) 360 tanks
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Self-Test Answers
1. c) 60%
2. b) 0.07%
3. d) 20%
4. a) 87%
50
5. d)
19
6. c)
1
250
7. a)
1
8
8. a)
1
50
9. b) 0.20%
10. c) 98%
11. d) 14030%
12. a) 112.5%
13. c) 0.9
14. b) 0.0012
15. c) 2.30
16. d) 0.195
17. d) 1:4.
18. a) 1.5:1
19. c) 1:9
20. b) 1:64
21. a) 1:6
22. d) 4
23. b) 66
24. c) $6600.88
25. a) 24.18 hours
26. d) 3
27. c) 9
28. c) 36 hours
29. a) 36
30. b) $15.88
31. d) $372.75
32. a) 1.8 lb
33. c) 6.0%
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34. b) 5%
35. b) 27.2%
36. b) $325.00
37. d) $16.13
38. a) 252 tanks
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Objective One Exercise Answers
Check your answers.
Two Quantities as a Ratio
1. a)
b)
c)
d)
e)
40:1
1:1
1:20
1:2
5:42 or 1:8.4
2. 1:6
3. 1:2.5
4. 6:1
5. 8.582:1
6. 1.32:1
Two Ratios as a Proportion
1. a)
b)
c)
d)
B = 15
r = 6. 6
m = 900
a = 16
2. $160.50
3. 1250 lb
4. 3 fillet welds
5. 8.25 hours
6. 15 days
7. 1387.5 rpm
8. 9.6 hrs
9. 16.887 psi
10. 300 rpm
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Objective Two Exercise Answers
Check your answers.
Converting Between Fractions and Percents
1. 72%
2. 28.57%
3. 433. 3 %
4. a)
b)
c)
d)
e)
84%
22. 2 %
7.143%
6. 6 %
125%
5. 1310
6.
5
6
7. a)
b)
c)
d)
e)
f)
8.
7
25
5
1
50
1
6
7
8
101
800
2
2
800
9. a)
b)
c)
d)
50%
75%
16. 6 %
60%
10. a) 116
b) 13
c) 503600
d) 147100
Converting Between Decimals and Percents
1. 7.0%
2. 230.0%
3. 12.5%
4. a)
b)
c)
d)
1%
6.5%
12%
196.3%
5. 135%
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6. 0.048
7. 0.375
8. 0.0012
9. a)
b)
c)
d)
e)
0.002
0.0043
0.05
0.84
0.934
10. 0.2837
Objective Three Exercise Answers
1. 72
2. 90 rods
3. $27.54/hr
4. 78 lb of copper, 50.7 lb of zinc and1.3 lb of tin
5. 5.07%
6. 0.875%
7. 18.1 8 %
8. 30.49%
9. 30 is 121/2% of 240.
10. 20 is 0.5% of 4000.
11. a) list price = $1863.64
b) purchase price = $1453.64
12. $5977.00
13. $25.62/hr
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Module Number 120104c
Version 6.0