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Difference between revisions of "Rate"

(Rate definition)
 
(Rewriting with strategy for rate problems as well as Alcumus problem links.)
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By definition, rate is a quantity which is typically measured by something that is being measured against something else or even a group of other things. It is used in different things including ratios and fractions, where the numerator and denominator are being measured against each other. These are used all the time in mathematics and science because in Physics people often measure things to one another, such as velocity of a fast particle to the speed of light. In math, we use them all the time whether it is a fraction, like <math>2/3</math>, or a constant ratio of 50 pineapples per potato. These are also used in slope intercept equations as both slope, <math>xy</math> values and the <math>y-</math>intercept can be fractions which are ratios.
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A '''rate''' is a type of [[ratio]] where something of one unit is compared with something else of another unit. Rates are applied in many real-world scenarios like unit conversions, speed/velocity, and per-item price.
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Example: <math>\frac{2}{3}</math> where <math>2</math> is being compared to <math>3.</math>
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Unit cancellation is a common strategy used in rate and conversion problems where if there are two instances of a unit written -- one on the numerator and the other on the denominator, then the instances are crossed out. For instance <math>\frac{60 \text{ kilometers}}{1 \text{ hour}} \cdot 2 \text{ hours} = 120 \text{ kilometers}</math>.
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==Problems==
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* Practice Problems on [https://artofproblemsolving.com/alcumus/ Alcumus]
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** Unit Conversions
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** Speed and Other Rates
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[[Category:Definition]]

Revision as of 20:37, 7 September 2020

A rate is a type of ratio where something of one unit is compared with something else of another unit. Rates are applied in many real-world scenarios like unit conversions, speed/velocity, and per-item price.


Unit cancellation is a common strategy used in rate and conversion problems where if there are two instances of a unit written -- one on the numerator and the other on the denominator, then the instances are crossed out. For instance $\frac{60 \text{ kilometers}}{1 \text{ hour}} \cdot 2 \text{ hours} = 120 \text{ kilometers}$.

Problems

  • Practice Problems on Alcumus
    • Unit Conversions
    • Speed and Other Rates
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