Measurement and Unit Conversions Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 3

Soru 41Soru →

A technician is cutting copper wire for electrical installations. Each installation requires $45$ centimeters of wire. How many meters of wire are needed to complete $20$ installations?

0.9

9

90

90,000

Cevabı ve açıklamayı göster

Cevap: $9$

Cevap

The correct answer is

9

meters.

First, calculate the total length of wire needed by multiplying the requirement for one installation (

45

cm) by the number of installations (

20

), which equals

900

cm. To convert centimeters to meters, divide by the conversion factor of

100

(since

1

meter =

100

centimeters). Dividing

900

by

100

results in exactly

9

meters.

Adım Adım Çözüm

1

Calculate the total amount of wire needed in centimeters.

45 \times 20 = 900

centimeters

To find the overall length required before converting to the requested unit.

2

Convert the total length from centimeters to meters.

900 \div 100 = 9

meters

Because there are

100

centimeters in

1

meter, divide the centimeter value by

100

.

Anahtar Kavram

To convert from a smaller metric unit (centimeters) to a larger metric unit (meters), divide by the appropriate power of ten (in this case, 100).

Soru 42Soru →

A pharmacist is filling $5$ identical prescriptions for a liquid medication. If each prescription requires $120$ milliliters of the medication, how many liters of medication are dispensed in total?

Cevabı ve açıklamayı göster

Cevap: 0.6

Cevap

0.6 Liters

To find the total amount of medication, first multiply the

5

prescriptions by the

120

milliliters needed for each, which equals

600

milliliters. Because the question asks for the answer in liters, and there are

1000

milliliters in

1

liter, divide the

600

milliliters by

1000

. This gives the final answer of

0.6

liters.

Adım Adım Çözüm

1

Calculate the total required volume in milliliters.

600

mL

Since there are

5

prescriptions and each needs

120

milliliters, multiplying them gives the total amount of medication in the initial unit.

2

Convert the total volume from milliliters to liters.

0.6

Liters

The prefix 'milli-' means one-thousandth. To convert from a smaller unit (milliliters) to a larger base unit (liters), divide by

1000

.

Anahtar Kavram

Multi-step metric system conversions between milli-prefixed units and base units.

Soru 43Soru →

Read the scenario below and calculate the required measurement. Enter your numerical answer in the blank.

Aşağıdaki boşlukları doldurun

On a navigational chart, the scale indicates that

\frac{1}{2}

inch represents

5

miles. If the distance between two marker buoys on the chart is

3

inches, the actual distance between the buoys is miles.

Cevabı ve açıklamayı göster

Cevap

The actual distance between the buoys is 30 miles.

The correct answer is found by setting up a proportion or determining the unit rate. Since a half-inch represents 5 miles, doubling both values shows that a full inch represents 10 miles. Multiplying the 3 inches measured on the chart by 10 miles per inch gives an actual distance of 30 miles.

Adım Adım Çözüm

1

Determine the actual distance represented by a full inch on the chart.

Since

\frac{1}{2}

inch represents

5

miles,

1

full inch represents

10

miles (

5 \times 2 = 10

).

Finding the unit rate (miles per 1 inch) makes it easier to scale up to the full measurement.

2

Multiply the chart distance by the unit rate to find the actual distance.

3 \text{ inches} \times 10 \text{ miles/inch} = 30 \text{ miles}

.

Applying the calculated unit rate to the measured distance on the chart yields the real-world distance.

Anahtar Kavram

Using map scale proportions to calculate actual distance

Tahmini Süre:45s

Soru 44Soru →

A county maintenance crew is installing reflective markers along a newly paved road that is exactly $1$ mile long. They completed the work over three days. On the first day, they marked $\frac{1}{4}$ of a mile. On the second day, they marked $\frac{1}{6}$ of a mile. On the third day, they marked a section measuring $300$ yards, $1$ foot, and $8$ inches. What is the length of the road that still needs markers, in feet and inches?

2,178

feet and

4

inches

3,322

feet and

4

inches

2,978

feet and

4

inches

2,778

feet and

4

inches

Cevabı ve açıklamayı göster

Cevap: $2,178$ feet and $4$ inches

Cevap

The remaining length of the road that needs markers is

2,178

feet and

4

inches.

To find the remaining distance, all measurements must be converted to a common unit (feet and inches). The total road is

5,280

feet. The first two days account for

\frac{1}{4} \times 5,280 = 1,320

feet and

\frac{1}{6} \times 5,280 = 880

feet. The third day accounts for

300 \times 3 = 900

feet, plus

1

foot and

8

inches, totaling

901

feet

8

inches. The total completed is

1,320 + 880 + 901 \text{ ft } 8 \text{ in} = 3,101 \text{ feet } 8 \text{ inches}

. Subtracting this from

5,280

feet (written as

5,279

feet

12

inches for borrowing) leaves exactly

2,178

feet and

4

inches.

Adım Adım Çözüm

1

Convert the total road length from miles to feet.

1 \text{ mile} = 5,280 \text{ feet}

.

Establishing a standard unit (feet) is necessary to evaluate the remaining length accurately.

2

Calculate the exact distance completed on the first and second days in feet.

Day 1:

\frac{1}{4} \times 5,280 = 1,320 \text{ feet}

. Day 2:

\frac{1}{6} \times 5,280 = 880 \text{ feet}

.

Converting the fractional mile measurements into feet allows them to be added to the other measurements.

3

Convert the third day's distance entirely into feet and inches.

300 \text{ yards} = 300 \times 3 = 900 \text{ feet}

. Adding the rest:

900 \text{ ft} + 1 \text{ ft} + 8 \text{ in} = 901 \text{ feet } 8 \text{ inches}

.

All components of the third day's work must be in the common feet/inches format to find the total sum.

4

Sum the completed distances from all three days.

1,320 \text{ ft} + 880 \text{ ft} + 901 \text{ ft } 8 \text{ in} = 3,101 \text{ feet } 8 \text{ inches}

.

This provides the total length of the road that has already been marked.

5

Subtract the total completed distance from the total road length.

5,280 \text{ ft } 0 \text{ in} - 3,101 \text{ ft } 8 \text{ in}

. Borrow

1

foot (

12

inches):

5,279 \text{ ft } 12 \text{ in} - 3,101 \text{ ft } 8 \text{ in} = 2,178 \text{ feet } 4 \text{ inches}

.

Subtracting the completed work from the total length yields the final remaining measurement required.

Anahtar Kavram

Multi-step conversion between US customary linear units (miles, yards, feet, inches) and fraction operations.

Soru 45Soru →

A regional transit map uses a scale where $1$ inch represents exactly $4$ miles. If two train stations are drawn $5.5$ inches apart on this map, what is the actual physical distance between them?

1.375

miles

2.2

miles

9.5

miles

22

miles

Cevabı ve açıklamayı göster

Cevap: $22$ miles

Cevap

The actual distance between the two train stations is

22

miles.

The map scale provides a direct ratio: every

1

inch corresponds to

4

miles. To determine the actual distance, the map distance must be multiplied by this scale factor. Calculating

5.5 \times 4

yields

22

miles.

Adım Adım Çözüm

1

Identify the provided map scale and the measured map distance.

The scale is

1

inch =

4

miles. The map distance is

5.5

inches.

Establishing the known values is necessary to set up the correct conversion calculation.

2

Multiply the map distance by the scale factor to find the actual distance.

5.5 \times 4 = 22

miles.

Because each single inch represents

4

actual miles, multiplying the total inches by

4

scales the measurement up to real-world size.

Anahtar Kavram

Applying a basic linear map scale to find actual distances using direct multiplication.

Soru 46Soru →

A metal fabricator starts with a single steel rod that measures exactly $4$ yards and $2$ feet in length. From this rod, they cut $7$ identical segments, each measuring exactly $1$ foot and $5$ inches long. Assuming no material is lost during the cutting process, how many inches of the steel rod remain?

Cevabı ve açıklamayı göster

Cevap: 49

Cevap

49 inches

The correct answer is found by converting all lengths into inches (

4

yards

= 144

in,

2

feet

= 24

in, Total

= 168

in), finding the total length of the cut pieces (

7 \times 17

in

= 119

in), and subtracting the cuts from the total (

168 - 119 = 49

inches).

Adım Adım Çözüm

1

Convert the total initial length of the steel rod into inches.

4

yards

= 144

inches;

2

feet

= 24

inches. Total

= 168

inches.

Converting to the smallest unit (inches) at the beginning prevents errors when subtracting later.

2

Convert the length of a single cut segment into inches.

1

foot

= 12

inches;

12 + 5 = 17

inches per segment.

The length of each cut segment must be in the same base unit as the total rod.

3

Calculate the total length of steel used for all

7

segments.

7 \times 17

inches

= 119

inches.

This determines the total amount of material that will be removed from the original rod.

4

Subtract the total used length from the initial rod length.

168

inches

- 119

inches

= 49

inches.

Subtracting the removed material from the starting material gives the final remaining length.

Anahtar Kavram

Converting multi-unit US Customary linear measurements to a common base unit to perform arithmetic operations.

Soru 47Soru →

A park director is planning a new $3 \frac{1}{2}$ -mile nature trail. The first segment of the trail is a dirt path that covers exactly $1 \frac{1}{4}$ miles. The second segment consists of $1,500$ yards of crushed gravel. The final segment is a continuous wooden boardwalk leading back to the visitor center. What is the length of the wooden boardwalk in feet?

7,380

6,060

11,380

10,380

Cevabı ve açıklamayı göster

Cevap: $7,380$

Cevap

The wooden boardwalk is

7,380

feet long.

To find the missing segment, all given measurements must be converted to a common unit (feet). A length of

3 \frac{1}{2}

miles is equal to

18,480

feet,

1 \frac{1}{4}

miles is equal to

6,600

feet, and

1,500

yards is equal to

4,500

feet. Subtracting the two known segments (

6,600 + 4,500 = 11,100

feet) from the total (

18,480

feet) yields the final segment length of

7,380

feet.

Adım Adım Çözüm

1

Convert the total length of the trail from miles to feet.

3 \frac{1}{2} \times 5,280 = 18,480

feet

Because the final answer must be in feet, it is best to establish the total boundary constraint in the target unit.

2

Convert the length of the dirt path from miles to feet.

1 \frac{1}{4} \times 5,280 = 6,600

feet

All segments must be in the same unit to perform addition and subtraction.

3

Convert the length of the crushed gravel segment from yards to feet.

1,500 \times 3 = 4,500

feet

There are

3

feet in

1

yard, so multiplying yards by

3

gives the measurement in feet.

4

Subtract the lengths of the first two segments from the total trail length to find the boardwalk length.

18,480 - (6,600 + 4,500) = 18,480 - 11,100 = 7,380

feet

The trail consists of three contiguous parts, so removing the known parts from the whole leaves the unknown final part.

Anahtar Kavram

Multi-step conversion of standard US Customary linear units (miles and yards) to a common base unit (feet) to solve for an unknown segment.

Soru 48Soru →

A communications technician is preparing four different runs of fiber optic cable for an office building installation. To organize the work, the technician must sort the cable runs from shortest to longest.

Run 1: $115$ yards and $2$ feet
Run 2: $4,188$ inches
Run 3: $\frac{1}{15}$ of a mile
Run 4: $350$ feet and $6$ inches

Arrange the cable runs in order from shortest to longest.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from shortest to longest is: Run 1, Run 2, Run 4, and Run 3.

By converting all lengths to a common unit (feet), we can directly compare them. Run 1 is

347

feet, Run 2 is

349

feet, Run 4 is

350.5

feet, and Run 3 is

352

feet. Ordering these from smallest to largest yields the correct sequence: Run 1, Run 2, Run 4, Run 3.

Adım Adım Çözüm

1

Convert the length of Run 1 into feet.

347

feet

Since

1

yard equals

3

feet, multiply

115

yards by

3

to get

345

feet. Add the additional

2

feet for a total of

347

feet.

2

Convert the length of Run 2 into feet.

349

feet

Since

1

foot equals

12

inches, divide

4,188

inches by

12

to get

349

feet.

3

Convert the length of Run 3 into feet.

352

feet

Since

1

mile equals

5,280

feet, divide

5,280

by

15

(or multiply by

\frac{1}{15}

) to get

352

feet.

4

Convert the length of Run 4 into feet.

350.5

feet

Since

6

inches is exactly

\frac{1}{2}

of a foot, the measurement is

350.5

feet.

5

Compare the standardized lengths and order them from shortest to longest.

Run 1 (

347

ft) < Run 2 (

349

ft) < Run 4 (

350.5

ft) < Run 3 (

352

ft)

Comparing all measurements in a common unit (feet) reveals the final correct sequence.

Anahtar Kavram

Converting mixed US Customary linear units (inches, feet, yards, miles) to a single common unit to compare their lengths.

Soru 49Soru →

An awning installer is measuring canvas fabric for two separate storefronts. The first storefront requires a continuous fabric length of $1 \frac{3}{4}$ yards. The second storefront requires a length of $2 \frac{1}{2}$ yards. What is the total length of canvas required for both storefronts, expressed in feet and inches?

4

feet

3

inches

10

feet

3

inches

11

feet

0

inches

12

feet

9

inches

Cevabı ve açıklamayı göster

Cevap: $12$ feet $9$ inches

Cevap

12

feet

9

inches

The correct answer is derived by first successfully adding the two mixed fractions (

1 \frac{3}{4} + 2 \frac{1}{2}

) to find a total of

4 \frac{1}{4}

yards. Converting this length to feet requires multiplying by

3

, yielding

12 \frac{3}{4}

feet. Finally, the remaining

\frac{3}{4}

of a foot is converted to inches by multiplying by

12

, resulting in exactly

12

feet and

9

inches.

Adım Adım Çözüm

1

Add the two yardage amounts together by finding a common denominator.

1 \frac{3}{4} + 2 \frac{2}{4} = 3 \frac{5}{4} = 4 \frac{1}{4}

yards.

To find the total amount of canvas needed, the fractional values must be combined correctly.

2

Convert the total yards into feet by multiplying by 3.

4 \frac{1}{4} \times 3 = \frac{17}{4} \times 3 = \frac{51}{4} = 12 \frac{3}{4}

feet.

Because there are 3 feet in 1 yard, multiplying the yardage by 3 gives the equivalent measurement in feet.

3

Convert the fractional portion of the foot into inches by multiplying by 12.

\frac{3}{4} \times 12 = \frac{36}{4} = 9

inches. The final combined measurement is

12

feet

9

inches.

Standard linear measurements require any fraction of a foot to be expressed in inches (12 inches = 1 foot).

Anahtar Kavram

Converting Mixed Customary Linear Units

Soru 50Soru →

A combat engineer platoon is constructing a defensive barrier. They use $15$ sandbags to reinforce a specific section. If each filled sandbag weighs exactly $42$ pounds and $12$ ounces, what is the total weight of the sandbags used for this section, in pounds?

Cevabı ve açıklamayı göster

Cevap: 641.25

Cevap

641.25

The correct calculation requires first establishing the exact weight of a single sandbag in pounds. Because there are

16

ounces in

1

pound,

12

ounces converts to

0.75

pounds (

12 \div 16

). Adding this to the base

42

pounds yields

42.75

pounds per sandbag. Multiplying this decimal weight by the

15

sandbags results in exactly

641.25

pounds.

Adım Adım Çözüm

1

Convert the ounce portion of the sandbag weight into pounds.

12 \text{ oz} \div 16 \text{ oz/lb} = 0.75 \text{ lbs}

To perform accurate arithmetic operations in a single unit, the mixed US Customary unit must be standardized into pounds.

2

Calculate the total weight of one sandbag in pounds.

42 \text{ lbs} + 0.75 \text{ lbs} = 42.75 \text{ lbs}

Combines the converted ounce value with the existing pound value to find the exact decimal weight of a single unit.

3

Multiply the single sandbag weight by the total number of sandbags.

42.75 \text{ lbs} \times 15 = 641.25 \text{ lbs}

Finds the aggregate weight for all

15

sandbags used in the section.

Anahtar Kavram

Converting mixed US Customary weight units (pounds and ounces) to a single decimal unit and calculating aggregate weight.

Soru 51Soru →

A disaster relief team is assembling emergency survival kits. Each kit must contain exactly $15$ ounces of high-energy rations. If the team receives a bulk shipment of $2.4$ tons of these rations, what is the total number of complete kits they can assemble?

320

2,560

3,200

5,120

Cevabı ve açıklamayı göster

Cevap: $5,120$

Cevap

The team can assemble exactly 5,120 complete survival kits.

To find the number of kits, the total weight must be converted to the same unit as the kit requirement. Converting

2.4

tons to pounds yields

4,800

pounds (using

2,000

pounds per ton). Converting

4,800

pounds to ounces yields

76,800

ounces (using

16

ounces per pound). Dividing the total

76,800

ounces by

15

ounces per kit results in exactly

5,120

kits.

Adım Adım Çözüm

1

Convert the total weight of the shipment from tons to pounds.

2.4 \times 2,000 = 4,800

pounds

There are 2,000 pounds in 1 US ton, which is the first step in moving toward the required unit of ounces.

2

Convert the total weight from pounds to ounces.

4,800 \times 16 = 76,800

ounces

There are 16 ounces in 1 pound. The total supply must be in the same units as the individual kit requirement to calculate the number of kits.

3

Divide the total ounces available by the ounces required for one kit.

76,800 \div 15 = 5,120

kits

Dividing the total mass of rations by the mass per kit determines how many complete kits can be created.

Anahtar Kavram

To divide a bulk quantity into smaller parts, all measurements must be converted to the same unit using standard US customary weight conversions (1 ton = 2,000 pounds; 1 pound = 16 ounces).

Soru 52Soru →

A scrap metal recycling facility is preparing four different compacted bales of aluminum for transport. Arrange the following bales in order from the lightest to the heaviest weight.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from lightest to heaviest is: the

38,400

-ounce bale, the

2,450

-pound bale, the

1.25

-ton bale, and the

1

-ton and

600

-pound bale.

By converting all weights to a single common unit (pounds), we find the sequence is

2,400

lbs,

2,450

lbs,

2,500

lbs, and

2,600

lbs. This establishes the correct order from lightest to heaviest.

Adım Adım Çözüm

1

Convert the weight of the

38,400

-ounce bale to pounds.

38,400 \div 16 = 2,400

pounds.

Since there are

16

ounces in a pound, dividing the total ounces by

16

converts the weight to pounds, providing a common unit for comparison.

2

Evaluate the weight of the second bale.

The weight is already provided in pounds:

2,450

pounds.

No conversion is necessary for this item.

3

Convert the weight of the

1.25

-ton bale to pounds.

1.25 \times 2,000 = 2,500

pounds.

Since there are

2,000

pounds in a US short ton, multiplying the ton value by

2,000

gives the weight in pounds.

4

Convert the weight of the mixed-unit bale (

1

ton and

600

pounds) to pounds.

1 \times 2,000 = 2,000

pounds. Adding the extra

600

pounds results in

2,000 + 600 = 2,600

pounds.

Convert the ton portion to pounds first, then add the remaining pounds to find the total.

5

Compare all four weights in pounds and sequence them from lightest to heaviest.

2,400

lbs

<

2,450

lbs

<

2,500

lbs

<

2,600

lbs.

Ordering the standardized numerical values determines the correct sequence of the items.

Anahtar Kavram

Converting between ounces, pounds, and US short tons to compare varying weights.

Soru 53Soru →

A military dining facility is using a recipe for a large batch of stew that requires $2.5$ pounds of beef. A chef is scaling up the recipe and needs to prepare $40$ batches for an upcoming event. The beef is purchased from a wholesale supplier at a cost of $\$0.60$ per ounce. What is the total cost of the beef required for all $40$ batches?

\$3.75

\$60

\$960

\$9,600

Cevabı ve açıklamayı göster

Cevap: $\$960$

Cevap

The total cost of the beef required is

\$960

.

First, find the total weight in pounds by multiplying the number of batches by the weight per batch (

40 \times 2.5 = 100

pounds). Next, convert the pounds to ounces by multiplying by

16

since there are

16

ounces in a pound (

100 \times 16 = 1,600

ounces). Finally, multiply the total ounces by the cost per ounce (

1,600 \times \$0.60

) to get the total cost of

\$960

.

Adım Adım Çözüm

1

Calculate the total amount of beef needed in pounds.

40 \times 2.5 = 100

pounds

To find the total weight required, multiply the number of batches by the weight per batch.

2

Convert the total weight from pounds to ounces.

100 \times 16 = 1,600

ounces

The cost is given per ounce, so the total weight must be converted to ounces. There are

16

ounces in a pound.

3

Calculate the total cost by multiplying the total ounces by the cost per ounce.

1,600 \times \$0.60 = \$960

Multiplying the total number of ounces by the price per ounce yields the total cost.

Anahtar Kavram

Unit conversions for US customary weight and calculating total costs

Soru 54Soru →

A cargo master is preparing an air drop bundle. The bundle contains $64$ identical medical supply boxes. Each box weighs exactly $6$ pounds and $4$ ounces. The parachute and rigging equipment add an additional $125$ pounds to the total load. What is the total combined weight, in pounds, of the fully rigged bundle?

Cevabı ve açıklamayı göster

Cevap: 525

Cevap

525

The correct answer is found by first converting the weight of each medical box entirely into pounds. Since there are

16

ounces in a pound,

4

ounces is equal to

\frac{4}{16}

or

0.25

pounds, making each box

6.25

pounds. Multiplying this weight by the

64

boxes gives a total medical supply weight of

400

pounds. Adding the

125

pounds for the parachute and rigging equipment gives a final total weight of

525

pounds.

Adım Adım Çözüm

1

Convert the fractional ounces into pounds.

4 ounces = 0.25 pounds, making each box 6.25 pounds.

To standardize the unit of measurement to pounds before calculating the total weight.

2

Calculate the total weight of all medical boxes.

64 boxes × 6.25 lbs/box = 400 lbs.

To find the aggregate weight of the payload.

3

Add the weight of the rigging equipment.

400 lbs + 125 lbs = 525 lbs.

The question asks for the total combined weight of the fully rigged bundle.

Anahtar Kavram

US Customary Weight Measurement Conversions

Soru 55Soru →

A groundskeeping crew is preparing a specialized liquid fertilizer. The instructions state to mix $4$ fluid ounces of the concentrated fertilizer for every $3$ quarts of water. If the crew uses $12$ gallons of water, how many cups of concentrated fertilizer must they add?

2

8

16

64

Cevabı ve açıklamayı göster

Cevap: $8$

Cevap

The crew must add

8

cups of concentrated fertilizer.

The correct answer is found by first converting the

12

gallons of water to quarts (

12 \times 4 = 48

quarts) so that it matches the ratio. Using the given rate, find the required concentrate:

(48 \div 3) \times 4 = 64

fluid ounces. Finally, convert the fluid ounces to cups by dividing by the conversion factor (

8

fluid ounces per cup), resulting in

8

cups.

Adım Adım Çözüm

1

Convert the total amount of water from gallons to quarts.

12 \text{ gallons} \times 4 \text{ quarts/gallon} = 48 \text{ quarts}

The mixing ratio is given in terms of quarts, so the total water volume must match this unit before applying the proportion.

2

Calculate the total fluid ounces of concentrate needed for the water.

(\frac{48 \text{ quarts}}{3 \text{ quarts}}) \times 4 \text{ fluid ounces} = 16 \times 4 = 64 \text{ fluid ounces}

This scales the ratio up to the actual volume of water being used to find the total amount of concentrate required.

3

Convert the fluid ounces of concentrate into cups.

64 \text{ fluid ounces} \div 8 \text{ fluid ounces/cup} = 8 \text{ cups}

The question specifically asks for the final answer in cups, requiring a final conversion.

Anahtar Kavram

Multi-step volume conversions and proportional scaling

Soru 56Soru →

An auto detailing shop keeps different formulations of car wash soap in various containers. To properly inventory their stock, the manager asks a technician to arrange $4$ containers based on their capacity.

Arrange the following containers in order from the smallest volume to the largest volume.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from smallest to largest is:

5

quarts,

11

pints,

1.5

gallons, and

200

fluid ounces.

By converting every measurement to fluid ounces, we find the exact comparative sizes:

5

quarts equals

160

fluid ounces,

11

pints equals

176

fluid ounces,

1.5

gallons equals

192

fluid ounces, and the final container is exactly

200

fluid ounces. Arranging these calculated amounts from smallest to largest gives the correct sequence.

Adım Adım Çözüm

1

Identify the conversion factors needed to change all units to the smallest unit given, which is fluid ounces.

1 \text{ gallon} = 128 \text{ fluid ounces}

,

1 \text{ quart} = 32 \text{ fluid ounces}

, and

1 \text{ pint} = 16 \text{ fluid ounces}

.

To accurately compare different volumes, they must all be converted to a single common unit.

2

Convert the volume of the quarts container into fluid ounces.

5 \text{ quarts} \times 32 \text{ fluid ounces/quart} = 160 \text{ fluid ounces}

.

Standardizing the unit for accurate comparison.

3

Convert the volume of the pints container into fluid ounces.

11 \text{ pints} \times 16 \text{ fluid ounces/pint} = 176 \text{ fluid ounces}

.

Standardizing the unit for accurate comparison.

4

Convert the volume of the gallons container into fluid ounces.

1.5 \text{ gallons} \times 128 \text{ fluid ounces/gallon} = 192 \text{ fluid ounces}

.

Standardizing the unit for accurate comparison.

5

Compare all four quantities in fluid ounces and order them from smallest to largest.

160 \text{ fl oz} < 176 \text{ fl oz} < 192 \text{ fl oz} < 200 \text{ fl oz}

.

Sorting the standard numerical values provides the final, correct arrangement.

Anahtar Kavram

Converting various US customary volume measurements into a common unit to compare and order capacities.

Tahmini Süre:1m 30s

Soru 57Soru →

A public aquarium needs to treat a $120$ -gallon quarantine tank with a specialized water conditioner. The treatment instructions require $3$ fluid ounces of conditioner for every $4$ gallons of water. The conditioner is sold only in $1$ -quart bottles. If the aquarium purchases the minimum number of full bottles required for the treatment, how many fluid ounces of conditioner will be left over after treating the tank?

0

2

6

38

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

6

The correct answer is

6

. First, calculate the total conditioner needed using the given proportion:

(120 \text{ gallons} \div 4 \text{ gallons}) \times 3 \text{ fluid ounces} = 90 \text{ fluid ounces}

. Next, convert the bottle capacity into fluid ounces so the units match:

1 \text{ quart} = 32 \text{ fluid ounces}

. To find the number of bottles required, divide the total needed by the bottle capacity:

90 \div 32 = 2.8125

. Since the aquarium must purchase full bottles, they will need

3

bottles. The total volume of conditioner purchased is

3 \times 32 = 96

fluid ounces. Finally, subtract the needed amount from the purchased amount to find the leftover volume:

96 - 90 = 6

fluid ounces.

Adım Adım Çözüm

1

Calculate the total fluid ounces of conditioner required for the tank.

90

fluid ounces

The rate is

3

fluid ounces per

4

gallons. For a

120

-gallon tank, calculate

(120 \div 4) \times 3 = 30 \times 3 = 90

.

2

Convert the bottle size from quarts to fluid ounces.

32

fluid ounces per bottle

Standard US Customary capacity conversions state that

1

quart is equal to

32

fluid ounces.

3

Determine the minimum number of full bottles to purchase.

3

bottles

Divide the total needed by the bottle capacity:

90 \div 32 = 2.8125

. Because they must buy full bottles, round up to the next whole number, which is

3

.

4

Calculate the total fluid ounces purchased.

96

fluid ounces

Multiply the number of bottles by the capacity per bottle:

3 \times 32 = 96

.

5

Calculate the leftover volume of conditioner.

6

fluid ounces

Subtract the amount needed from the total amount purchased:

96 - 90 = 6

.

Anahtar Kavram

Calculating liquid capacity required using proportional rates and converting standard US Customary units (quarts to fluid ounces) to determine purchasing requirements and remainders.

Soru 58Soru →

A cosmetics laboratory prepares a bulk batch of hand sanitizer containing $3$ gallons and $2$ quarts. The sanitizer will be packaged into small travel bottles that hold $4$ fluid ounces each. How many travel bottles can be completely filled from this batch?

Cevabı ve açıklamayı göster

Cevap: 112

Cevap

112

The correct answer is found by first unifying the entire volume into fluid ounces. Converting the 3 gallons into quarts yields 12 quarts. Adding the extra 2 quarts brings the total to 14 quarts. Because there are 32 fluid ounces in a single quart, you multiply 14 by 32 to determine the batch contains 448 fluid ounces. Dividing this total by the 4-ounce capacity per bottle yields exactly 112 bottles.

Adım Adım Çözüm

1

Convert the gallons portion to quarts.

3 gallons = 12 quarts

Converting to a smaller common unit makes it easier to combine the total volume.

2

Find the total volume in quarts.

12 quarts + 2 quarts = 14 quarts

This gives the complete batch size in a single unit.

3

Convert the total quarts to fluid ounces.

14 quarts × 32 fluid ounces/quart = 448 fluid ounces

The bottles are measured in fluid ounces, so the total volume must match this unit before dividing.

4

Divide the total fluid ounces by the capacity of each bottle.

448 ÷ 4 = 112

This determines the exact number of travel bottles that can be filled.

Anahtar Kavram

Converting mixed US customary volume units (gallons and quarts) to fluid ounces and dividing by a unit rate.

Soru 59Soru →

An industrial pump requires $2$ gallons, $3$ quarts, and $1$ pint of lubricating oil to completely fill its reservoir. If a maintenance technician needs to completely fill the empty reservoirs of $8$ identical pumps, what is the total volume of oil required, in gallons?

21

23

46

92

Cevabı ve açıklamayı göster

Cevap: 23

Cevap

The total volume of oil required is 23 gallons.

To find the total, you must first convert the requirement for one pump into a standard unit:

2

gallons is

8

quarts, plus

3

quarts, plus

1

pint (

0.5

quarts) equals

11.5

quarts per pump. Multiplying

11.5

quarts by

8

pumps yields

92

quarts. Since there are

4

quarts in a gallon, dividing

92

by

4

gives the correct total of

23

gallons.

Adım Adım Çözüm

1

Convert the capacity of one pump into a single unit, such as quarts.

2

gallons =

8

quarts, and

1

pint =

0.5

quarts. Adding these together gives

8 + 3 + 0.5 = 11.5

quarts per pump.

Standardizing all measurements into one unit prevents addition errors and simplifies the multiplication step.

2

Multiply the single-pump volume by the total number of pumps.

11.5

quarts

\times 8

pumps =

92

quarts.

This determines the total volume of oil needed for all the equipment combined.

3

Convert the total volume back into gallons.

92 \div 4 = 23

gallons.

The question specifically asks for the final answer in gallons, and there are

4

quarts in

1

gallon.

Anahtar Kavram

Multiplying mixed US Customary capacity measurements and converting between units.

Soru 60Soru →

A water purification unit processes $450$ liters of water per hour. How many kiloliters of water does it process during an $8$ -hour shift?

3,600,000

3.6

36

3600

Cevabı ve açıklamayı göster

Cevap: $3.6$

Cevap

The water purification unit processes

3.6

kiloliters of water.

The unit processes

450

liters per hour for

8

hours, yielding a total of

3600

liters. Because

1

kiloliter is equal to

1000

liters, dividing

3600

by

1000

results in

3.6

kiloliters.

Adım Adım Çözüm

1

Calculate the total amount of water processed in liters.

450 \times 8 = 3600

liters

The unit processes water at a rate of 450 liters per hour for an 8-hour period.

2

Convert the total volume from liters to kiloliters.

3600 \div 1000 = 3.6

kiloliters

There are 1000 liters in one kiloliter. Converting from a smaller unit (liters) to a larger unit (kiloliters) requires dividing by 1000.

Anahtar Kavram

Metric volume conversions require dividing by powers of 10 when converting to a larger unit. To convert from base units (liters) to kilo- units (kiloliters), divide the value by 1000.

Measurement and Unit Conversions

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram