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### Unit Rates

By Skanda Sudhir

Vocabulary and symbols

- : -This symbol is a shorter way to say, is to
- :: - This symbol is a shorter way to say, as is to.
- Unit – A math measurement used to find length, width, height,

weight, capacity, etc.

- Sample- A part of a whole quantity to figure out how many of that unit is in the quantity.
- Ratio- The proportional relation; rate
- Quantity- An amount out of a whole amount of different units.

What are unit rates and how do they help us?

Unitratesdescribe how many units of the first quantity can correspond to the type of units of the second quantity. A common unitrate is miles or kilometer per hour. Basically, you write unitrates like this: (exp.) minute : hour :: 60 : 1.

Unitrates help us by seeing how many of a unit is in a whole quantity. How? You sample and multiply! But the answer isn’t always right same or not in the real world because you can’t tell if all the quantities are the same amount ornot.

Examples and real world examples

Here are examples of unit rates

- People : mile :: 400 : 1
- Kids : school :: 1000 : 1
- Feet : yards :: 3 : 1
- The hunger : millionaires :: 10 : 15

Here are some real world examples:

- Usually used in finding ratios.
- Scientists, people who find population of people in a city, state, country, etc., etc. use unit rates to find different populations.

Problems

Sample problem 1: If there is 5 orphanages in 1 city, than how many orphanages are in 1,150 cities?

- The art museum has a painting that is 3ft wide. If the original painting was 6ft long and 2ft wide, how long was the painting in the museum?
- Scientists counted 1,785 cardinals living in an acre of land. How many cardinals would live in 15 acres of land?
- The ratio of my height to my baby brother’s height is 6 in. to 15 in. What is my baby brother’s height if I’m 60 in?

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