Q4 Simplify

Question 1

The three principles of simplification

Answer 1

1. Make big numbers small
2. Use familiar comparisons
3. Prefer local comparisons

Question 2

Trader Joe’s has about 17,000 square feet of floor space. How big is that? Compare it to the median Florida house size of 1,800 square feet.

Answer 2

17,000 divided by 1,800 = 9
About 9 typical houses can fit inside a Trader Joe’s

Question 3

The Women’s March in Washington had about 470,000 marchers in just Washington DC. How big is that?
Compare it to the Swamp Stadium’s capacity of 90,000 people.

Answer 3

47,000 divided by 90,000 = 5.3
The number of marchers was equal to about 5 home football games

Question 4

Ratio formula

Answer 4

Whole divided by Portion

Question 5

Each year, about 35 million Americans report flu symptoms, and 35,000 die. Find the ratio.

Answer 5

35,000,000 flu symptoms divided by 35,000 deaths times 100 = (1 in) 1,000

Question 6

What is implied in a ratio formula?

Answer 6

Whole divided by Portion = (1 in) Ratio
“1 in” is implied

Question 7

How is data about people easier to understand?

Answer 7

When the data is personalized

Question 8

326,644 electric vehicles are sold in a year, and there are 17,047,725 sales of all vehicles in a year. Find the ratio.

Answer 8

17,047,725 divided by 326,644 = 52.2 = 52
1 in 52 vehicles sold in a year were electric

Question 9

The total amount UF spent on instruction in a year was $770,500,000. There are 56,079 college students. Simplify instruction per student.

Answer 9

“Per” means divide
$770,500,000 divided by 56,079 = $13,740

Question 10

Americans generate about 367,790,000 tons of trash in a year. 139,590,000 tons end up in the landfill. There are 326,971,407 Americans. Simplify trash per person. (There are 2,000 pounds in a ton)

Answer 10

139,590,000 divided by 326,971,407 = .43 tons per person per year
.43 is a partial unit, so convert to pounds

139,590,000 times 2,000 = 279,180,000,000 pounds
279,180,000,000 divided by 329,971,407 = 854 pounds per year
This is a big number, so make it small by changing it to per day.

854 divided by 265 = 2.3 pounds per person per day

Question 11

Why does reported crime have little meaning?

Answer 11

• Crime increases with population
• Factor in population as a form of normalization

Question 12

8,174 reported crimes divided by 392,945 people = .0208 crimes per person a year
Why is this incorrect? What can be done instead?

Answer 12

• Need a number of 1 or larger
• 1 person could commit several crimes at once or over a year
• Number of crimes is not the same as number of criminals
• Not all crime is reported
• Instead, calculate number of crimes per 1,000 people

Question 13

How do you determine what time unit to simplify to?

Answer 13

The smallest unit that doesn’t have a result of less than 1

Question 14

Best time unit to simplify Louvre Museum visits

Answer 14

Daily, because most people don’t just stay for a minute, they stay for most of the day

Question 15

Best time unit to simplify a CEO’s annual salary

Answer 15

• Typical and familiar salary comparisons are month, week, and hour
• Hour is the smallest unit that still offers a fair comparison

Question 16

Area

Answer 16

• Length times Width
• Two dimensional
• Square units

Question 17

Volume

Answer 17

• Length times Width times Depth
• Three dimensional
• Cubic units

Question 18

Ikea’s Miami location has an area of 416,000 square feet. A football field’s area is 57,600 square feet. Simplify.

Answer 18

416,000 divided by 57,600 = 7.2
Seven football fields could fit inside the Miami Ikea

Question 19

A football field has a Length of 120 yards and a Width of 160 feet. Convert to feet.

Answer 19

1 yard = 3 feet
120 times 3 feet = 360 feet

Question 20

How to convert feet to yards

Answer 20

1 yard = 3 feet
Divide the yards by 3 feet

Question 21

What is a local comparison for a forest fire size?

Answer 21

A city’s geographical size

Question 22

What is a local comparison for a site or location?

Answer 22

A lake

Question 23

Presume we have an area of 80 yards by 20 yards. In a packed crowd, each person takes up about 5 square feet. How much space does each person take?

Answer 23

Convert the yards to square feet
80 x 3 = 240 feet
20 x 3 = 60 feet
240 x 60 = 14,400 square feet
14,400 divided by 5 = 2,880

About 2,900 people are present

Question 24

An Olympic-sized swimming pool is 3,270 cubic yards. 30,000 cubic yards of soil were excavated to construct a parking garage nearby. Compare.

Answer 24

30,000 divided by 3,270 = 9.2 pools
The dirt excavated would fill 9 Olympic-sized swimming pools

Question 26

The Kennedy Space Center brought in 85,000 cubic yards of sand. Epcot’s Spaceship Earth is 2,187,000 cubic feet. Compare.

Answer 26

Convert cubic feet to cubic yards
1 cubic yard = 27 cubic feet
2,187,000 cubic feet divided by 27 = 81,000 cubic yards
The Kennedy Space Center brought in enough sand to fill Epcot’s Spaceship Earth.

Question 26

To convert cubic yards to cubic feet . . .

Answer 26

Multiply by 27

Question 26

To convert cubic feet to cubic yards . . .

Answer 26

Divide by 27

Question 27

Why are ratios often the best option to use?

Answer 27

They are more personal

Question 28

12,759,000 US children live in poverty. There are 73,470,000 US children. Make this easier to grasp.

Answer 28

Convert it to a ratio
73,470,000 divided by 12,759,000 = (1 in) 5.75 children

1 in 6 US children live in poverty

Question 29

12,759,000 US children live in poverty. There are 73,470,000 US children. If you only had the percentage, how do you make it a ratio?

Answer 29

12,759,000 divided by 73,470,000 times 100 = 17.4%
Percent means “per 100”
100 divided by 17.4 = (1 in) 5.75

Question 30

How do you convert a percentage to a ratio?

Answer 30

Percent means “per 100”
100 divided by Percentage = (1 in) Ratio

Question 31

When rounding for a ratio, it is better to . . .

Answer 31

Be conservative and understate than overstate

Question 32

Americans who are homeowners is 66.3%. The ratio is 100 divided by 66.3 = (1 in) 1.5 people. Rounding up to 2 people makes it 1 in 2 people, or 50%. This is far off from the original 66.3%. How do you make it more precise while still be simplified?

Answer 32

Multiply both sides of the ratio by 2 to get 2 in 3 people
2 divided by 3 = 66.7%

66 out of 100 people would be precise, but that’s not simplification
6 out of 10 would be simplification, but not precise

Question 33

Americans aged 20-29 who exceed obesity standards is 40%. Make this into a ratio.

Answer 33

100 divided by 40 = (1 in) 2.5 people
Could round up to 1 in 3, but it would be far off because 1 divided by 3 = 33.3% and that’s way less than 40%
Multiply each side of the ratio by 2
100 divided by 40 = (2 in) 5 people