Q4 Simplify Flashcards
The three principles of simplification
- Make big numbers small
- Use familiar comparisons
- Prefer local comparisons
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.
17,000 divided by 1,800 = 9
About 9 typical houses can fit inside a Trader Joe’s
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.
47,000 divided by 90,000 = 5.3
The number of marchers was equal to about 5 home football games
Ratio formula
Whole divided by Portion
Each year, about 35 million Americans report flu symptoms, and 35,000 die. Find the ratio.
35,000,000 flu symptoms divided by 35,000 deaths times 100 = (1 in) 1,000
What is implied in a ratio formula?
Whole divided by Portion = (1 in) Ratio
“1 in” is implied
How is data about people easier to understand?
When the data is personalized
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.
17,047,725 divided by 326,644 = 52.2 = 52
1 in 52 vehicles sold in a year were electric
The total amount UF spent on instruction in a year was $770,500,000. There are 56,079 college students. Simplify instruction per student.
“Per” means divide
$770,500,000 divided by 56,079 = $13,740
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)
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
Why does reported crime have little meaning?
- Crime increases with population
- Factor in population as a form of normalization
8,174 reported crimes divided by 392,945 people = .0208 crimes per person a year
Why is this incorrect? What can be done instead?
- 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
How do you determine what time unit to simplify to?
The smallest unit that doesn’t have a result of less than 1
Best time unit to simplify Louvre Museum visits
Daily, because most people don’t just stay for a minute, they stay for most of the day
Best time unit to simplify a CEO’s annual salary
- Typical and familiar salary comparisons are month, week, and hour
- Hour is the smallest unit that still offers a fair comparison
Area
- Length times Width
- Two dimensional
- Square units
Volume
- Length times Width times Depth
- Three dimensional
- Cubic units
Ikea’s Miami location has an area of 416,000 square feet. A football field’s area is 57,600 square feet. Simplify.
416,000 divided by 57,600 = 7.2
Seven football fields could fit inside the Miami Ikea
A football field has a Length of 120 yards and a Width of 160 feet. Convert to feet.
1 yard = 3 feet
120 times 3 feet = 360 feet
How to convert feet to yards
1 yard = 3 feet
Divide the yards by 3 feet
What is a local comparison for a forest fire size?
A city’s geographical size
What is a local comparison for a site or location?
A lake
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?
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
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.
30,000 divided by 3,270 = 9.2 pools
The dirt excavated would fill 9 Olympic-sized swimming pools
The Kennedy Space Center brought in 85,000 cubic yards of sand. Epcot’s Spaceship Earth is 2,187,000 cubic feet. Compare.
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.
To convert cubic yards to cubic feet . . .
Multiply by 27
To convert cubic feet to cubic yards . . .
Divide by 27
Why are ratios often the best option to use?
They are more personal
12,759,000 US children live in poverty. There are 73,470,000 US children. Make this easier to grasp.
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
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?
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
How do you convert a percentage to a ratio?
Percent means “per 100”
100 divided by Percentage = (1 in) Ratio
When rounding for a ratio, it is better to . . .
Be conservative and understate than overstate
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?
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
Americans aged 20-29 who exceed obesity standards is 40%. Make this into a ratio.
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
