Fractions, Decimals, and Percentages Alıştırma Soruları — ACT — Sayfa 3

Soru 41Soru →

A community theater group allocated a total budget of $\$1,500$ to create costumes for an upcoming production. Exactly $\frac{1}{4}$ of the budget was spent on fabric, $0.30$ of the budget was spent on specialized footwear, and $\frac{1}{5}$ of the budget was spent on sewing accessories. The remaining amount of the budget was spent on theatrical wigs. What amount, in dollars, did the theater group spend on theatrical wigs?

\$300

\$375

\$450

\$975

\$1,125

Cevabı ve açıklamayı göster

Cevap: $\$375$

Cevap

The theater group spent

\$375

on theatrical wigs.

The correct answer of

\$375

is found by determining each individual expense and subtracting their sum from the total budget. Fabric accounts for

\frac{1}{4}

of

\$1,500

, which is

\$375

. Footwear accounts for

0.30

of

\$1,500

, which is

\$450

. Sewing accessories account for

\frac{1}{5}

of

\$1,500

, which is

\$300

. Combined, these three categories equal

\$375 + \$450 + \$300 = \$1,125

. Subtracting

\$1,125

from the total budget of

\$1,500

leaves

\$375

for theatrical wigs.

Adım Adım Çözüm

1

Calculate the dollar amount spent on fabric

\frac{1}{4} \times \$1,500 = \$375

Multiply the fraction representing fabric by the total budget.

2

Calculate the dollar amount spent on footwear

0.30 \times \$1,500 = \$450

Multiply the decimal representing footwear by the total budget.

3

Calculate the dollar amount spent on sewing accessories

\frac{1}{5} \times \$1,500 = \$300

Multiply the fraction representing accessories by the total budget.

4

Sum the three known category expenses

\$375 + \$450 + \$300 = \$1,125

Add the expenses together to determine the total spent before wigs.

5

Subtract the sum of known expenses from the total budget

\$1,500 - \$1,125 = \$375

The remaining portion of the budget is allocated to theatrical wigs.

Anahtar Kavram

Converting fractions and decimals to quantities of a total amount and calculating remaining portions.

Soru 42Soru →

Four numerical values are given below. Arrange these values in order from least to greatest.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from least to greatest is

55\%

,

0.565

,

\frac{4}{7}

, and

\frac{3}{5}

.

Converting each quantity into a decimal format yields

55\% = 0.55

,

0.565 = 0.565

,

\frac{4}{7} \approx 0.5714

, and

\frac{3}{5} = 0.60

. Ordering these decimal values from least to greatest yields

0.55 < 0.565 < 0.5714 < 0.60

, which corresponds to the sequence

55\%, 0.565, \frac{4}{7}, \frac{3}{5}

.

Adım Adım Çözüm

1

Convert the percentage to a decimal.

55\% = \frac{55}{100} = 0.55

Converting all values to decimals provides a uniform scale for direct comparison.

2

Convert the fractions to decimals.

\frac{4}{7} \approx 0.5714

and

\frac{3}{5} = 0.60

Dividing the numerator by the denominator converts each fraction into decimal form.

3

Compare all four decimal values:

0.55

,

0.565

,

0.5714

, and

0.60

.

0.55 < 0.565 < 0.5714 < 0.60

Aligning decimal places shows that

0.5500 < 0.5650 < 0.5714 < 0.6000

.

4

Map the ordered decimal values back to their original forms.

55\% < 0.565 < \frac{4}{7} < \frac{3}{5}

Replacing each decimal with its original representation produces the required sequence.

Anahtar Kavram

Converting fractions, decimals, and percents to a common representation (decimals) to compare and order them.

Soru 43Soru →

At a local bookstore, $40\%$ of the total inventory consists of fiction books. Of the remaining inventory, $\frac{5}{8}$ consists of non-fiction books, and the rest are children's books. If there are $270$ children's books in the bookstore, what is the total number of books in the inventory?

450

675

720

1,200

1,800

Cevabı ve açıklamayı göster

Cevap: $1,200$

Cevap

1,200

Fiction books account for

40\%

of the total inventory, leaving

60\%

as the remaining portion. Since

\frac{5}{8}

of this remainder is non-fiction, the children's books represent the other

\frac{3}{8}

of that

60\%

remainder. Multiplying

\frac{3}{8} \times 0.60 = 0.225

, or

22.5\%

of the total inventory. Given that there are

270

children's books, dividing

270

by

0.225

yields the total inventory of

1,200

books.

Adım Adım Çözüm

1

Determine the fraction of inventory remaining after accounting for fiction books.

Remaining fraction =

100\% - 40\% = 60\% = 0.6 = \frac{3}{5}

Fiction accounts for

40\%

, leaving

60\%

of the total inventory for other genres.

2

Find the fraction of the remaining inventory that consists of children's books.

Children's fraction of remaining =

1 - \frac{5}{8} = \frac{3}{8}

Since

\frac{5}{8}

of the remaining inventory is non-fiction, the rest (

\frac{3}{8}

) must be children's books.

3

Calculate the proportion of the total inventory that children's books represent.

Children's proportion of total =

\frac{3}{8} \times \frac{3}{5} = \frac{9}{40} = 0.225 = 22.5\%

Multiply the fraction of the remainder by the fraction of the total remaining.

4

Set up an equation with total inventory

T

and solve for

T

.

0.225 \times T = 270 \implies T = \frac{270}{0.225} = 1,200

Divide the known count of children's books (

270

) by its fractional share of the total inventory.

Anahtar Kavram

Solving multi-step word problems involving fractions, decimals, and percentages of a whole

Tahmini Süre:1m 15s

Soru 44Soru →

A coffee shop blend initially consists of a $20$ -pound mixture of Arabica and Robusta beans, of which $45\%$ by weight is Arabica. The shop manager adds pure Arabica beans to the mixture to increase the proportion of Arabica beans to $56\%$ by weight. How many pounds of pure Arabica beans must be added to the mixture?

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5 pounds of pure Arabica beans must be added to the mixture.

To solve for the required added weight, first compute the original mass of Arabica beans:

45\%

of

20

pounds is

0.45 \times 20 = 9

pounds. Letting

x

represent the pounds of pure Arabica added, the updated mass of Arabica is

9 + x

pounds and the updated total mass of the coffee batch is

20 + x

pounds. Setting the ratio

\frac{9 + x}{20 + x} = 0.56

gives

9 + x = 0.56(20 + x)

. Expanding the right side results in

9 + x = 11.2 + 0.56x

. Subtracting

0.56x

and

9

from both sides gives

0.44x = 2.2

, which simplifies to

x = 5

pounds.

Adım Adım Çözüm

1

Determine the initial weight of Arabica beans.

Arabica weight =

0.45 \times 20 = 9

pounds.

The starting

20

-pound batch contains

45\%

Arabica beans.

2

Formulate the mixture fraction with the unknown added weight

x

.

\frac{9 + x}{20 + x} = 0.56

Adding

x

pounds of pure Arabica increases both the total Arabica weight (numerator) and the total mixture weight (denominator).

3

Solve the algebraic equation for

x

.

9 + x = 11.2 + 0.56x \implies 0.44x = 2.2 \implies x = 5

Isolating

x

yields the exact amount of pure Arabica required.

Anahtar Kavram

Solving percentage mixture problems using algebraic proportions

Tahmini Süre:1m 30s

Soru 45Soru →

A high school athletic department set a total fundraising goal of $\$2,400$ for new equipment. During the first week, the department raised $\frac{3}{8}$ of the total goal. During the second week, they raised $35\%$ of the total goal. During the third week, they raised $0.15$ of the total goal. How much money must the department raise in the fourth week to meet its total goal exactly?

\$288

\$300

\$480

\$615

\$2,100

Cevabı ve açıklamayı göster

Cevap: $\$300$

Cevap

The athletic department must raise

\$\text{300}

in the fourth week to meet its total goal.

Converting each portion into a dollar value relative to the total goal of

\$\text{2,400}

gives

\$\text{900}

for the first week,

\$\text{840}

for the second week, and

\$\text{360}

for the third week. Adding these amounts yields

\$\text{2,100}

raised in total. Subtracting

\$\text{2,100}

from

\$\text{2,400}

gives the remaining requirement of

\$\text{300}

.

Adım Adım Çözüm

1

Calculate the amount raised in Week 1 using the fraction

\frac{3}{8}

.

\frac{3}{8} \times \$2,400 = \$900

To find a fractional part of a total amount, multiply the total by the fraction.

2

Calculate the amount raised in Week 2 using the percentage

35\%

.

0.35 \times \$2,400 = \$840

Convert

35\%

to a decimal (

0.35

) and multiply by the total goal.

3

Calculate the amount raised in Week 3 using the decimal

0.15

.

0.15 \times \$2,400 = \$360

Multiply the decimal fraction directly by the total goal.

4

Sum the amounts raised during the first three weeks and subtract from the total goal.

Total raised =

\$900 + \$840 + \$360 = \$2,100

; Remaining needed =

\$2,400 - \$2,100 = \$300

Subtracting the total funds collected so far from the target yields the remaining requirement.

Anahtar Kavram

Fractions, Decimals, and Percentages

Soru 46Soru →

A technology firm allocated its annual equipment budget among three divisions. The engineering division received $\frac{3}{8}$ of the total budget, and the operations division received $30\%$ of the total budget. The remaining $\$52,000$ was allocated to the design division. What was the total equipment budget, in dollars, for the technology firm?

Cevabı ve açıklamayı göster

Cevap: 160000

Cevap

The total equipment budget for the technology firm was $160,000 dollars.

Converting both allocated parts into decimals gives

\frac{3}{8} = 0.375

for engineering and

30\% = 0.30

for operations. Combined, these two divisions account for

0.375 + 0.30 = 0.675

(or

67.5\%

) of the total budget. The remaining fraction for the design division is

1 - 0.675 = 0.325

(or

32.5\%

). Dividing the design budget of

\$52,000

by

0.325

yields the total budget of

\$160,000

.

Adım Adım Çözüm

1

Convert the percentage and fraction to equivalent decimal values.

Engineering receives

\frac{3}{8} = 0.375

, and operations receives

30\% = 0.30

.

Expressing all portions in decimal form allows for straightforward addition and subtraction.

2

Sum the portions allocated to the engineering and operations divisions.

0.375 + 0.30 = 0.675

.

This finds the total proportion of the budget that has already been accounted for.

3

Determine the remaining decimal portion allocated to the design division.

1 - 0.675 = 0.325

.

The complete budget represents 1 whole (100%). Subtracting the allocated portions yields the design division's share.

4

Divide the dollar amount of the design division by its decimal portion to calculate the total budget.

\frac{52,000}{0.325} = 160,000

.

Since

\text{Design Portion} \times \text{Total Budget} = \text{Design Amount}

, dividing the amount by the decimal portion gives the total budget.

Anahtar Kavram

Solving multi-step applied word problems by converting between fractions, decimals, and percentages to determine an unknown total value.

Soru 47Soru →

A long-distance runner is training for an upcoming race. On Monday, she completed $\frac{2}{5}$ of her total weekly distance goal. On Tuesday, she completed $0.35$ of her total weekly distance goal. If she has $12$ miles left to complete her weekly goal, what is her total weekly goal distance, in miles?

16

21

30

48

60

Cevabı ve açıklamayı göster

Cevap: 48

Cevap

48 miles

Converting

\frac{2}{5}

to

0.40

gives a total completed portion of

0.40 + 0.35 = 0.75

of the goal. The remaining portion is

1 - 0.75 = 0.25

of the total goal. Setting

0.25 \times \text{total goal} = 12

miles gives a total weekly goal of

\frac{12}{0.25} = 48

miles.

Adım Adım Çözüm

1

Convert the fraction completed on Monday to a decimal

\frac{2}{5} = 0.40

Converting all completed portions to decimals allows for direct addition.

2

Calculate the total portion of the weekly goal completed on Monday and Tuesday

0.40 + 0.35 = 0.75

Summing Monday's and Tuesday's completed portions gives the total completed fraction of the goal.

3

Determine the remaining fraction of the weekly goal

1 - 0.75 = 0.25

Subtracting the completed portion from the total whole (1.00) yields the fraction remaining.

4

Set up an equation relating the remaining fraction to the remaining miles to find the total goal distance

x

0.25x = 12 \implies x = \frac{12}{0.25} = 48

Dividing the remaining distance by the remaining fraction yields the total weekly goal distance.

Anahtar Kavram

Combining fractions and decimals to determine a total quantity from a remaining part

Tahmini Süre:1m 15s

Soru 48Soru →

An artisan bakery prepared a total batch of dough weighing $60$ pounds. In the morning, the baker used $\frac{2}{5}$ of the total dough to make loaves of bread. In the afternoon, the baker used $35\%$ of the remaining dough to make pastries. How many pounds of dough from the initial batch were left unused at the end of the day?

12.6

15.0

23.4

36.6

47.4

Cevabı ve açıklamayı göster

Cevap: $23.4$

Cevap

The weight of the dough left unused at the end of the day is

23.4

pounds.

First, calculate the dough used in the morning:

\frac{2}{5}

of

60

pounds is

24

pounds. The remaining dough is

60 - 24 = 36

pounds. Next,

35\%

of

36

pounds is

0.35 \times 36 = 12.6

pounds used for pastries. Subtracting this from

36

pounds gives

36 - 12.6 = 23.4

pounds remaining unused.

Adım Adım Çözüm

1

Calculate the weight of dough used in the morning.

\frac{2}{5} \times 60 = 24

pounds

The bakery used

\frac{2}{5}

of the total

60

-pound batch.

2

Find the dough remaining after the morning baking.

60 - 24 = 36

pounds

Subtract the amount used in the morning from the initial batch weight.

3

Calculate the percentage of dough remaining after the afternoon baking.

100\% - 35\% = 65\%

of the remaining dough

Since

35\%

of the remaining dough was used for pastries,

65\%

remained unused.

4

Calculate the final unused weight of dough.

0.65 \times 36 = 23.4

pounds

Multiply the remaining weight (

36

pounds) by the percentage left unused (

65\%

).

Anahtar Kavram

Multistep calculation involving fractional parts of a whole followed by percentage parts of a remainder.

Tahmini Süre:1m 30s

Soru 49Soru →

A nutritionist analyzed the proportion of daily recommended fiber provided by four different snack bars. The proportions were recorded as follows: Fruit Bar ( $58\%$ ), Oat Bar ( $\frac{7}{12}$ ), Nut Bar ( $0.585$ ), and Seed Bar ( $\frac{3}{5}$ ). Arrange the four snack bars in order from the LEAST proportion of daily recommended fiber to the GREATEST proportion of daily recommended fiber.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

Fruit Bar (

58\%

), Oat Bar (

\frac{7}{12}

), Nut Bar (

0.585

), Seed Bar (

\frac{3}{5}

)

To order the values from least to greatest, convert each representation into a standard decimal form: Fruit Bar =

58\% = 0.580

, Oat Bar =

\frac{7}{12} \approx 0.5833

, Nut Bar =

0.5850

, and Seed Bar =

\frac{3}{5} = 0.6000

. Arranging these decimals in increasing order yields

0.5800 < 0.5833 < 0.5850 < 0.6000

, which corresponds to Fruit Bar, Oat Bar, Nut Bar, and Seed Bar.

Adım Adım Çözüm

1

Convert each numerical value into a common format (decimal representation) to allow direct comparison.

Fruit Bar:

58\% = \frac{58}{100} = 0.580

; Oat Bar:

\frac{7}{12} = 7 \div 12 \approx 0.5833

; Nut Bar:

0.585

; Seed Bar:

\frac{3}{5} = \frac{6}{10} = 0.600

.

Converting all numbers to decimals makes it straightforward to compare place values from left to right.

2

Compare the resulting decimal values up to the thousandths place:

0.5800

,

0.5833

,

0.5850

, and

0.6000

.

In order from smallest to largest decimal value:

0.5800 < 0.5833 < 0.5850 < 0.6000

.

Comparing the hundredths and thousandths digits shows that

0.580

is smallest, followed by

0.5833

, then

0.585

, and finally

0.600

.

3

Map the ordered decimals back to their original snack bar representations.

Fruit Bar (

58\%

) < Oat Bar (

\frac{7}{12}

) < Nut Bar (

0.585

) < Seed Bar (

\frac{3}{5}

).

This establishes the exact required sequence from least to greatest fiber proportion.

Anahtar Kavram

Converting and Comparing Mixed Numerical Representations (Fractions, Decimals, and Percentages)

Tahmini Süre:1m 15s

Soru 50Soru →

At an agricultural orchard, a seasonal harvest consisted of apples, pears, and peaches. Of the total harvest, $\frac{3}{8}$ were apples and $42.5\%$ were pears. If the remaining harvest consisted of $96$ bushels of peaches, what was the total number of bushels of fruit harvested by the orchard?

120

256

384

480

640

Cevabı ve açıklamayı göster

Cevap: $480$

Cevap

The total harvest was 480 bushels of fruit.

Converting the fraction of apples

\frac{3}{8}

gives

37.5\%

. Combining this with the

42.5\%

of pears yields

80\%

of the total harvest. The remaining

20\%

of the harvest represents the

96

bushels of peaches. Dividing

96

by

0.20

gives the total harvest of

480

bushels.

Adım Adım Çözüm

1

Convert the fraction of apples to a percentage.

\frac{3}{8} = 0.375 = 37.5\%

Converting all quantities to percentages allows for direct addition and comparison.

2

Find the combined percentage of apples and pears.

37.5\% + 42.5\% = 80\%

Adding the percentage of apples and pears determines the portion of the harvest that is not peaches.

3

Calculate the percentage representing peaches.

100\% - 80\% = 20\%

The remaining percentage of the total harvest corresponds to the peaches.

4

Solve for the total number of bushels harvested.

96 \div 0.20 = 480

bushels

Dividing the number of peach bushels by its corresponding decimal fraction (

0.20

) yields the total harvest.

Anahtar Kavram

Solving word problems involving mixed fractions, decimals, percentages, and unknown total quantities.

Tahmini Süre:1m 15s

Soru 51Soru →

A municipal solar power facility distributes its total generating capacity among three sectors: residential, commercial, and municipal. The residential sector is allocated $\frac{7}{15}$ of the total capacity, and the commercial sector is allocated $36\%$ of the total capacity. The remaining $26$ megawatts (MW) of capacity is allocated to municipal buildings. What is the total generating capacity, in megawatts, of the facility?

Cevabı ve açıklamayı göster

Cevap: 150

Cevap

The total generating capacity of the facility is 150 megawatts.

The residential portion (

\frac{7}{15}

) and commercial portion (

36\% = \frac{9}{25}

) combine to equal

\frac{62}{75}

of the total capacity. The municipal portion makes up the remaining

\frac{13}{75}

of the total, which is given as

26

MW. Setting

\frac{13}{75} T = 26

and solving yields

T = 150

MW.

Adım Adım Çözüm

1

Convert the commercial percentage into a simplified fraction.

36\% = \frac{36}{100} = \frac{9}{25}

Converting all proportions to fractions allows for direct operations.

2

Find the combined fraction of capacity allocated to residential and commercial sectors.

\frac{7}{15} + \frac{9}{25} = \frac{35}{75} + \frac{27}{75} = \frac{62}{75}

Finding a common denominator (

75

) allows adding the two fractional parts.

3

Find the fraction corresponding to the remaining municipal portion.

1 - \frac{62}{75} = \frac{13}{75}

Subtracting the allocated fraction from

1

yields the unallocated fractional portion.

4

Calculate the total capacity by setting up a linear equation.

\frac{13}{75} \times \text{Total} = 26 \implies \text{Total} = 26 \times \frac{75}{13} = 150

Multiplying the known remaining value by the reciprocal of its fraction gives the whole total.

Anahtar Kavram

Combining fractions and percentages to find an unknown total amount.

Tahmini Süre:1m 30s

Soru 52Soru →

A marine biology research team collected a water sample from an estuary to analyze its composition. In the sample, $\frac{3}{10}$ of the total volume is saltwater, $45\%$ of the total volume is brackish water, and $0.05$ of the total volume is mineral sediment. The remaining portion of the sample is freshwater. What fraction of the total sample volume is freshwater?

\frac{1}{10}

\frac{1}{4}

\frac{1}{5}

\frac{7}{20}

\frac{2}{5}

Cevabı ve açıklamayı göster

Cevap: $\frac{1}{5}$

Cevap

The fraction of the total sample volume that is freshwater is

\frac{1}{5}

.

Converting all three non-freshwater portions to decimals yields

0.30

(saltwater),

0.45

(brackish water), and

0.05

(sediment). Adding these together gives

0.80

. Subtracting

0.80

from the total sample volume of

1.00

leaves

0.20

, which converts to the simplified fraction

\frac{1}{5}

.

Adım Adım Çözüm

1

Convert all given volume proportions into decimals.

Saltwater =

\frac{3}{10} = 0.30

, Brackish water =

45\% = 0.45

, Mineral sediment =

0.05

.

Converting all components to a common decimal format allows direct addition.

2

Sum the proportions of saltwater, brackish water, and mineral sediment.

0.30 + 0.45 + 0.05 = 0.80

.

This calculates the combined proportion of the sample that is not freshwater.

3

Subtract the combined non-freshwater proportion from the whole sample (

1.00

).

1.00 - 0.80 = 0.20

.

The remainder of the sample represents the freshwater component.

4

Convert the decimal portion to a simplified fraction.

0.20 = \frac{20}{100} = \frac{1}{5}

.

The question asks for the proportion formatted as a simplified fraction.

Anahtar Kavram

Converting between fractions, decimals, and percentages to solve multi-step word problems.

Soru 53Soru →

A sports analyst tracks four basketball players' shooting efficiencies over a season, expressed in different numerical formats:

- Player P: $\frac{9}{16}$
- Player Q: $0.58$
- Player R: $54.5\%$
- Player S: $\frac{11}{20}$

Place the players in order of their shooting efficiency from least to greatest.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

Player R (

54.5\%

), Player S (

\frac{11}{20}

), Player P (

\frac{9}{16}

), Player Q (

0.58

)

To order the shooting efficiencies from least to greatest, convert each representation into a decimal: Player R is

54.5\% = 0.545

, Player S is

\frac{11}{20} = 0.55

, Player P is

\frac{9}{16} = 0.5625

, and Player Q is

0.58

. Comparing these decimals gives

0.545 < 0.55 < 0.5625 < 0.58

, corresponding to the sequence: Player R, Player S, Player P, Player Q.

Adım Adım Çözüm

1

Convert all given values into a common format, such as decimals.

Player P:

\frac{9}{16} = 0.5625

; Player Q:

0.58

; Player R:

54.5\% = 0.545

; Player S:

\frac{11}{20} = 0.55

Converting fractions and percentages into decimals allows for direct numerical comparison.

2

Compare the resulting decimal values.

0.545 < 0.55 < 0.5625 < 0.58

Aligning decimals by place value confirms the ascending sequence.

3

Match the ordered decimals back to the original player designations.

Player R (

0.545

) < Player S (

0.55

) < Player P (

0.5625

) < Player Q (

0.58

)

This establishes the correct order from least to greatest efficiency.

Anahtar Kavram

Comparing and ordering numbers by converting fractions, decimals, and percentages into a unified numerical representation.

Soru 54Soru →

A chemistry lab technician measures the concentration of sugar by weight in four distinct liquid samples:

• Sample P: $\frac{7}{16}$
• Sample Q: $0.425$
• Sample R: $44\%$
• Sample S: $\frac{4}{9}$

Which of the following lists the four samples in order from least sugar concentration to greatest sugar concentration?

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from least to greatest concentration is Sample Q, Sample P, Sample R, and Sample S.

To arrange the values from least to greatest, convert all numbers to decimals: Sample Q is

0.425

; Sample P is

\frac{7}{16} = 0.4375

; Sample R is

44\% = 0.44

; and Sample S is

\frac{4}{9} = 0.4444\dots

. Comparing these decimals gives

0.4250 < 0.4375 < 0.4400 < 0.4444\dots

, which corresponds to the sequence Sample Q, Sample P, Sample R, Sample S.

Adım Adım Çözüm

1

Convert each fraction, decimal, and percentage to a common decimal representation.

Sample P = 7/16 = 0.4375; Sample Q = 0.425; Sample R = 44% = 0.44; Sample S = 4/9 ≈ 0.4444...

Converting all numbers to decimals allows for direct place-value comparison.

2

Compare the converted decimal values from left to right.

0.4250 < 0.4375 < 0.4400 < 0.4444...

Comparing digits at the hundredths and thousandths places establishes the relative sizes.

3

Map the ordered decimal values back to their original sample names.

Sample Q < Sample P < Sample R < Sample S

Ordering matches the decimal values calculated: 0.425 < 0.4375 < 0.44 < 0.4444...

Anahtar Kavram

Converting mixed numerical forms (fractions, decimals, percentages) to a single decimal format for ordering.

Soru 55Soru →

A community garden allocates space among three categories: vegetable beds, herb gardens, and flower borders. Vegetable beds take up $\frac{3}{8}$ of the total area, herb gardens take up $0.25$ of the total area, and flower borders occupy the remaining 1,800 square feet. What is the total area, in square feet, of the community garden?

2,700

2,880

4,800

675

7,200

Cevabı ve açıklamayı göster

Cevap: 4,800

Cevap

4,800 square feet

To find the total area, first convert

0.25

to

\frac{2}{8}

. Summing the vegetable portion (

\frac{3}{8}

) and the herb portion (

\frac{2}{8}

) gives

\frac{5}{8}

of the garden. The flower section takes up the remaining

1 - \frac{5}{8} = \frac{3}{8}

of the area. Setting

\frac{3}{8}

of the total area equal to 1,800 square feet and dividing 1,800 by

\frac{3}{8}

gives

1,800 \times \frac{8}{3} = 4,800

square feet.

Adım Adım Çözüm

1

Convert the decimal portion to a fraction with a common denominator.

0.25 = \frac{1}{4} = \frac{2}{8}

Converting all given portions into fractions with a common denominator allows direct addition.

2

Calculate the combined fraction for vegetable beds and herb gardens.

\frac{3}{8} + \frac{2}{8} = \frac{5}{8}

Adding the two known fractions identifies the combined portion of the garden accounted for by vegetables and herbs.

3

Find the fraction representing the flower borders.

1 - \frac{5}{8} = \frac{3}{8}

Subtracting the combined fraction from the whole (1) yields the fractional part representing the remaining 1,800 square feet.

4

Solve for the total garden area.

\text{Total Area} = 1,800 \div \frac{3}{8} = 1,800 \times \frac{8}{3} = 4,800\text{ sq ft}

Dividing the part by its corresponding fractional portion calculates the whole quantity.

Anahtar Kavram

Combining fractions and decimals to solve part-to-whole problems

Tahmini Süre:1m 30s

Soru 56Soru →

A coffee roasting company creates a custom espresso blend using three types of coffee beans: Arabica, Robusta, and Liberica. In the blend, $\frac{3}{8}$ of the total weight is Arabica beans and $40\%$ of the total weight is Robusta beans. The remaining weight of the blend consists of Liberica beans. If a batch of this custom blend contains $18$ ounces of Liberica beans, what is the total weight, in ounces, of the coffee bean batch?

30

48

62

72

80

Cevabı ve açıklamayı göster

Cevap: 80

Cevap

The total weight of the coffee bean batch is 80 ounces.

To find the total weight of the batch, first express each given portion as a decimal or percentage of the total weight. The Arabica beans make up

\frac{3}{8} = 0.375

or

37.5\%

of the total weight, and Robusta beans make up

40\%

of the total weight. Together, Arabica and Robusta represent

37.5\% + 40\% = 77.5\%

of the total weight. Consequently, Liberica beans represent the remaining

100\% - 77.5\% = 22.5\%

(or

0.225

) of the batch. Since

18

ounces equals

22.5\%

of the total weight

W

, we set up the equation

0.225 W = 18

and solve for

W

:

W = \frac{18}{0.225} = 80

ounces.

Adım Adım Çözüm

1

Convert the fractional share of Arabica beans into a decimal or percentage.

\frac{3}{8} = 0.375 = 37.5\%

Converting all components to a common format (percentages or decimals) allows easy addition of the component shares.

2

Find the combined percentage share of Arabica and Robusta beans.

37.5\% + 40\% = 77.5\%

Adding the individual percentages determines the total fraction of the batch occupied by Arabica and Robusta.

3

Calculate the percentage share representing Liberica beans.

100\% - 77.5\% = 22.5\%

(or

0.225

in decimal form)

The remaining percentage of the batch must equal the Liberica portion.

4

Set up and solve the equation to find the total batch weight

W

.

0.225 \times W = 18 \implies W = \frac{18}{0.225} = 80

ounces

Dividing the given weight of Liberica beans by its fractional representation yields the total weight of the entire coffee blend.

Anahtar Kavram

Combining fractions and percentages to solve part-to-whole word problems

Tahmini Süre:1m 30s

Soru 57Soru →

In July, a company's IT department logged a set of service tickets. Of these tickets, $\frac{3}{10}$ were categorized as hardware issues, $45\%$ were categorized as software issues, and the remaining 60 tickets were categorized as network issues. What was the total number of service tickets logged by the IT department in July?

Cevabı ve açıklamayı göster

Cevap: 240

Cevap

The total number of service tickets logged in July was 240.

Converting

\frac{3}{10}

gives

30\%

. Combining hardware (

30\%

) and software (

45\%

) issues yields

75\%

of the total tickets. The network tickets make up the remaining

25\%

(

100\% - 75\%

). Setting

25\%

of the total equal to 60 tickets gives a total of

\frac{60}{0.25} = 240

service tickets.

Adım Adım Çözüm

1

Convert the fraction of hardware tickets to a percentage

\frac{3}{10} = 0.30 = 30\%

Expressing all portions as percentages enables direct combination.

2

Sum the percentages for hardware and software tickets

30\% + 45\% = 75\%

This determines the combined percentage of the non-network tickets.

3

Determine the remaining percentage corresponding to network tickets

100\% - 75\% = 25\%

The total of all categories must sum to 100%.

4

Calculate the total number of service tickets

\frac{60}{0.25} = 240

Dividing the quantity of network tickets by their decimal equivalent of 0.25 gives the total count.

Anahtar Kavram

Combining fractions and percentages to solve for an unknown whole amount

Tahmini Süre:1m 30s

Soru 58Soru →

A fitness center surveyed its members regarding their primary exercise routine. Of the members surveyed, $\frac{1}{4}$ chose strength training, $0.35$ chose cardio workouts, and $15\%$ chose group fitness classes. The remaining $75$ members chose swimming. What is the total number of members surveyed by the fitness center?

100

200

250

300

500

Cevabı ve açıklamayı göster

Cevap: 300

Cevap

300

Converting

\frac{1}{4}

to

25\%

and

0.35

to

35\%

, the three specified groups represent

25\% + 35\% + 15\% = 75\%

of the total members. Consequently, the remaining

25\%

of members choose swimming. Since

25\%

(or

\frac{1}{4}

) of the total surveyed group equals 75 members, multiplying 75 by 4 gives a total of 300 members.

Adım Adım Çözüm

1

Convert all given proportions to a common format (percentages or decimals)

Strength training =

\frac{1}{4} = 25\%

; Cardio workouts =

0.35 = 35\%

; Group fitness =

15\%

Converting all amounts to percentages allows for direct addition.

2

Calculate the total percentage accounted for by the first three categories

25\% + 35\% + 15\% = 75\%

Combining these parts determines what fraction of the total surveyed group is already accounted for.

3

Determine the percentage corresponding to the remaining members who chose swimming

100\% - 75\% = 25\%

The remaining members represent the remaining portion of the whole.

4

Set up an equation to find the total number of members (

T

)

0.25 T = 75 \implies T = \frac{75}{0.25} = 300

Dividing the part by its corresponding decimal percentage yields the total population.

Anahtar Kavram

Converting between fractions, decimals, and percentages to calculate an unknown total quantity

Tahmini Süre:1m 15s

Soru 59Soru →

A quality control laboratory tested four battery models to measure the proportion of initial charge retained after 24 hours of continuous operation. The recorded results for each model are listed below:

- Model Alpha: $\frac{13}{20}$
- Model Beta: $64.5\%$
- Model Gamma: $\frac{5}{8}$
- Model Delta: $0.638$

Which of the following represents the battery models arranged in order from least to greatest proportion of remaining charge?

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct order from least to greatest proportion of remaining charge is Model Gamma (

\frac{5}{8}

), Model Delta (

0.638

), Model Beta (

64.5\%

), and Model Alpha (

\frac{13}{20}

).

Converting each model's retained charge to decimal form gives Model Gamma

= \frac{5}{8} = 0.625

, Model Delta

= 0.638

, Model Beta

= 64.5\% = 0.645

, and Model Alpha

= \frac{13}{20} = 0.650

. Comparing these values yields

0.625 < 0.638 < 0.645 < 0.650

, which matches the order Model Gamma, Model Delta, Model Beta, Model Alpha.

Adım Adım Çözüm

1

Convert each given fraction, percentage, and decimal into equivalent decimal values for direct comparison.

Model Alpha

= \frac{13}{20} = 0.650

; Model Beta

= 64.5\% = 0.645

; Model Gamma

= \frac{5}{8} = 0.625

; Model Delta

= 0.638

.

Converting all values to decimals standardizes the quantities so they can be compared easily by place value.

2

Compare the resulting decimal numbers from least to greatest.

0.625 < 0.638 < 0.645 < 0.650

Comparing digits from left to right: all have

0.6

in the tenths place; comparing the hundredths place shows

2 < 3 < 4 < 5

.

3

Map the sorted decimal values back to their original model designations.

Model Gamma (

\frac{5}{8}

), Model Delta (

0.638

), Model Beta (

64.5\%

), Model Alpha (

\frac{13}{20}

).

This establishes the required sequence from least to greatest.

Anahtar Kavram

Converting fractions, decimals, and percentages to a common format (decimals) to order rational numbers.

Soru 60Soru →

At an auto dealership, $\frac{2}{5}$ of the vehicles in the inventory are sedans, $35\%$ are SUVs, and the remaining 45 vehicles are trucks. What is the total number of vehicles in the dealership's inventory?

Cevabı ve açıklamayı göster

Cevap: 180

Cevap

The total number of vehicles in the dealership's inventory is 180.

Converting

\frac{2}{5}

to a percentage yields

40\%

. Adding the

40\%

sedans and

35\%

SUVs shows that

75\%

of the inventory consists of sedans and SUVs. Consequently, the remaining

25\%

of the inventory consists of trucks. Since there are 45 trucks,

25\%

of the total inventory equals 45. Dividing 45 by

0.25

yields the total inventory of 180 vehicles.

Adım Adım Çözüm

1

Convert fraction of sedans to a percentage

Sedans represent

40\%

of the total inventory.

To combine the amounts easily, convert

\frac{2}{5}

to percentage form:

\frac{2}{5} = 0.40 = 40\%

.

2

Calculate the combined percentage of sedans and SUVs

Sedans and SUVs together make up

75\%

of the inventory.

Add the two percentages:

40\% + 35\% = 75\%

.

3

Determine the remaining percentage representing trucks

Trucks make up

25\%

of the inventory.

The entire inventory equals

100\%

, so

100\% - 75\% = 25\%

.

4

Solve for the total number of vehicles

The total inventory is 180 vehicles.

Set up the equation

25\% \text{ of Total} = 45

, which gives

0.25 \times \text{Total} = 45

, so

\text{Total} = \frac{45}{0.25} = 180

.

Anahtar Kavram

Converting fractions to percentages to find an unknown total quantity from a remaining part

Fractions, Decimals, and Percentages

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