Skills Beta

Fractions, Decimals and Percents

A part of a whole is the part divided by the whole, a decimal from 0 to 1, and a percent is that decimal times 100.

Practice 3: Analyze Data

Part 1 · Hook

Why this matters

Most statistics in Unit 1 start the same way: count how many individuals are in a group, then divide by how many there are in all. 18 of 24 students, 132 of 400 adults, 9 of 24 sport players. If you can turn a part of a whole into a decimal and a percent, and pick the right whole, you are ready for the first summaries of data.

Part 2 · Prerequisite check

Quick check before you start

1. A class records each student’s number of siblings. What kind of variable is that?

  1. Quantitative and discrete
  2. Categorical
  3. Quantitative and continuous
  4. A parameter
Show the answer

A count of siblings takes whole-number values, so it is quantitative and discrete.

  • Correct: Quantitative and discrete:
  • Categorical:
  • Quantitative and continuous:
  • A parameter:

2. A school asks 50 of its 900 students about lunch. What is the population?

  1. The 900 students
  2. The 50 students
  3. The lunch menu
  4. The students who answered yes
Show the answer

The population is the whole group the question is about.

  • Correct: The 900 students:
  • The 50 students:
  • The lunch menu:
  • The students who answered yes:

Part 3 · See it

See it first

Twenty-four boxes in a row, 18 shaded in plum, above a scale from 0 to 1 marked every 0.25. A dashed line at 0.75 marks where the shaded part ends. The caption reads: part over whole, 18 over 24, equals 0.75, equals 75%.
18 of 24 is a part over its whole: 0.75 of the bar, or 75%. LevlPrep original diagram.

Part 4 · Step by step

How it works, step by step

  1. Find the whole the question names ("of the sport players")that number goes on the bottom of the fraction
  2. Count the part inside that wholethat number goes on top
  3. Divide the top by the bottomthe decimal is between 0 and 1; times 100 gives the percent

Part 5 · Key ideas

Key ideas

  • A part of a whole is the part divided by the whole: partwhole\frac{\text{part}}{\text{whole}}. The result is a decimal from 0 to 1.
  • A percent is a decimal times 100: 0.375=37.5%0.375 = 37.5\%. To go back, divide by 100.
  • The whole is the group the question says "of": "what part of the sport players" tells you to divide by the number of sport players.
  • Compare groups of different sizes with decimals or percents, not counts.

Part 6 · Misconception

A common mistake

The wrong idea: School B has more walkers, 25 against 18, so a larger part of school B walks.

What actually happens: School B is also bigger. As parts of their own wholes, 1830=0.60\frac{18}{30} = 0.60 and 2550=0.50\frac{25}{50} = 0.50, so a larger part of school A walks.

Part 7 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

1. In a reading group, 18 of the 24 students finished the book. What part of the group finished, as a decimal?

Type a number. A table answer and a calculator answer are both accepted.

Show the answer

Part over whole: 1824=0.75\frac{18}{24} = 0.75, which is 75% of the group.

  • Answer: 0.75

2. Which decimal and percent equal 38\frac{3}{8}?

  1. 0.38 and 3.8%, rounding the decimal first
  2. 0.375 and 37.5%
  3. 2.667 and 266.7%, from dividing 8 by 3
  4. 0.38 and 38%, the same as 38 out of 100
Show the answer

38\frac{3}{8}=3÷8= 3 \div 8=0.375= 0.375=37.5%= 37.5\%.

  • 0.38 and 3.8%, rounding the decimal first: The decimal 0.375 is 37.5%, not 3.8%: a percent is the decimal times 100.
  • Correct: 0.375 and 37.5%: Right: 3 divided by 8 is 0.375, and moving the decimal point two places gives 37.5%.
  • 2.667 and 266.7%, from dividing 8 by 3: That divides 8 by 3. A fraction is the top divided by the bottom: 3 ÷ 8.
  • 0.38 and 38%, the same as 38 out of 100: Close after rounding, but the exact values are 0.375 and 37.5%.

3. What is 45% of 300?

  1. 13,500
  2. 6.67
  3. 165
  4. 135
Show the answer

Change the percent to a decimal and multiply: 0.45×300=1350.45 \times 300 = 135.

  • 13,500: Multiplying by 45 instead of 0.45 makes the answer 100 times too big.
  • 6.67: A percent of a number is a multiplication: 0.45 × 300.
  • 165: That is the other 55% of 300. The question asks for 45%.
  • Correct: 135: Right: 45% is 0.45, and 0.45×300=1350.45 \times 300 = 135.

4. Of 60 seniors, 24 play a school sport, and 9 of those 24 play two sports. What part of the sport players play two sports?

  1. 0.375
  2. 0.15
  3. 0.40
  4. 2.667
Show the answer

First find the whole the question names ("of the sport players"): 24. Then part over whole: 924=0.375\frac{9}{24} = 0.375.

  • Correct: 0.375: Right: the whole is the 24 sport players, so the part is 924=0.375\frac{9}{24} = 0.375.
  • 0.15: That uses the wrong whole. The question is about the sport players, so divide by 24.
  • 0.40: That is the part of all seniors who play a sport, not the part of players who play two.
  • 2.667: That is the whole over the part. Put the part, 9, on top.

5. At school A, 18 of 30 students walk to school. At school B, 25 of 50 walk. Which statement is correct?

  1. More of school B walks, because 25 is larger than 18
  2. The schools are the same, since both have some walkers
  3. A larger part of school A walks: 0.60 against 0.50
  4. School B, because 50 students is larger than 30 students
Show the answer

Counts from groups of different sizes cannot be compared directly. Divide each part by its own whole and compare the decimals.

  • More of school B walks, because 25 is larger than 18: School B has more walkers, but it also has more students. Compare each part with its own whole.
  • The schools are the same, since both have some walkers: The decimals 0.60 and 0.50 differ, so the schools differ.
  • Correct: A larger part of school A walks: 0.60 against 0.50: Right: comparing parts of different wholes needs the decimals, 1830=0.60\frac{18}{30} = 0.60 and 2550=0.50\frac{25}{50} = 0.50.
  • School B, because 50 students is larger than 30 students: The size of the school alone says nothing about the part that walks.

6. Of 120 people at a concert, 42 bought a T-shirt. Type an expression for the percent who bought a T-shirt (for example, a fraction times 100).

Type the expression as on the exam, with the values substituted.

Show the answer

42120×100=35\frac{42}{120} \times 100 = 35, so 35% bought a T-shirt.

  • Answer: 42120⋅100\frac{42}{120} \cdot 100

Part 8 · Summary

Summary

A part of a whole is the part divided by the whole, a decimal from 0 to 1, and a percent is that decimal times 100. Pick the whole from the words of the question, and compare groups of different sizes with decimals or percents, never raw counts.

Part 9 · Up next

What comes next

Part 10 · Connections

Connections

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