Proportional Relationships

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Presentation transcript:

Proportional Relationships Rate: a ratio that compares two quantities measured in different units Unit Rate: a rate in which the second quantity in the comparison is one unit Constant: a value that does not change Constant of Proportionality: a constant ratio of two variables related proportionally. Complex Fraction: a fraction that has a fraction in its numerator, denominator or both

Proportional Relationships Rate of Change: a rate that describes how one quantity changes in relation to another quantity Proportional Relationship: between two quantities is one in which the rate of change is constant, or one in which the ratio of one quantity to the other is constant. Proportion: a statement that two rates or ratios are equivalent, for example: 6mi/2hr = 3mi/1hr OR 2/4 = 1/2

Proportional Relationships If there is a proportional relationship between x and y, you can describe that relationship using the equation y=kx. The variable k is called the constant of proportionality, and it represents the constant rate of change or constant ratio between x and y. The value of k is represented by the equation k = y/x

RATES Common Rate Comparisons: mi/hr, ft/sec,…………..distance/time UNIT RATE: finding the rate for 1 unit of (time/denominator) measurement.

RATES – Exit Ticket The information for two pay-as-you-go cell phone companies is given. ON CALL: 3.5 hrs @ $10 TALK TIME: ½ hr @ $1.25 What is the unit rate in dollars per hour for each company Which company offers the best deal? Explain. Another company offers a rate of $0.05 per minute. How would you find the unit rate per hour? Is the rate in part c a better deal than On Call or Talk Time? Explain.

RATES – Exit Ticket (answers) The information for two pay-as-you-go cell phone companies is given. ON CALL: 3.5 hrs @ $10 (÷ by 3.5 == $2.8571/hr) TALK TIME: ½ hr @ $1.25 (x by 2 == $2.50/hr) What is the unit rate in dollars per hour for each company ON CALL: $2.86, TALK TIME: $2.50 Which company offers the best deal? Explain. TALK TIME – cost less per hour unit rate Another company offers a rate of $0.05 per minute. How would you find the unit rate per hour? multiply the rate by 60 (60 min = 1hr). This unit rate per hour will be $3.00/hr Is the rate in Part C a better deal than On Call or Talk Time? Explain. The rate in Part C is not a better deal than On Call or Talk Time because it costs more per unit rate/hour

Proportional Relationships Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.