Unit rate and constant rates of change

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What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a single unit. It is often used to describe how much of one quantity corresponds to one unit of another quantity.

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How do you calculate the unit rate from a given quantity over time?

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To calculate the unit rate, divide the total quantity by the total time. For example, if a store sees 120 customers in 8 hours, the unit rate is 120 customers ÷ 8 hours = 15 customers per hour.

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What is the constant rate of change?

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The constant rate of change is a rate that describes how a quantity changes in relation to another quantity consistently over time. It is often represented as a linear relationship.

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If a table shows the relationship between the number of tickets and total cost, how can you determine the cost per ticket?

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To determine the cost per ticket, divide the total cost by the number of tickets. For example, if the total cost is $54 for 2 tickets, the cost per ticket is $54 ÷ 2 = $27.

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How can you find the rate of change from a graph?

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The rate of change can be found by calculating the slope of the line on the graph, which is the change in the y-value divided by the change in the x-value (rise/run).

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What is the formula for calculating the unit rate in terms of money earned per hour?

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The formula is: Unit Rate = Total Earnings ÷ Total Hours Worked. For example, if Alycia earned $20.40 in 3 hours, her unit rate is $20.40 ÷ 3 = $6.80 per hour.

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What does it mean if a rate is described as 'constant'?

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A constant rate means that the rate does not change over time; it remains the same regardless of the quantity or time interval.

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How do you convert a rate into a unit rate?

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To convert a rate into a unit rate, divide both the numerator and the denominator by the denominator's value to express the rate per one unit of the denominator.

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What is the significance of understanding unit rates in real-life applications?

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Understanding unit rates helps individuals make informed decisions, such as comparing prices, understanding speed, and evaluating efficiency in various contexts.

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What is the relationship between distance, time, and speed?

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The relationship is defined by the formula: Speed = Distance ÷ Time. This shows how fast an object is moving based on the distance traveled over a specific time period.