Unit Rates and Proportions

Front

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 quantity of one. For example, if you drive 60 miles in 2 hours, the unit rate is 30 miles per hour.

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How do you calculate a unit rate?

Back

To calculate a unit rate, divide the quantity of one item by the quantity of another item. For example, if you have 54 miles driven in 9 days, divide 54 by 9 to find the unit rate of 6 miles per day.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if 1/2 = 2/4, then these two ratios are in proportion.

Front

How do you determine if two ratios form a proportion?

Back

To determine if two ratios form a proportion, cross-multiply and see if the products are equal. If a/b = c/d, then check if a*d = b*c.

Front

What does it mean for a relationship to be proportional?

Back

A relationship is proportional if two quantities maintain a constant ratio. For example, if you double one quantity, the other quantity also doubles.

Front

What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both are also fractions. For example, (1/2)/(3/4) is a complex fraction.

Front

How do you simplify a complex fraction?

Back

To simplify a complex fraction, multiply the numerator and the denominator by the least common denominator (LCD) of the fractions involved.

Front

What is the unit rate of 18 miles in 6 hours?

Back

The unit rate is 3 miles per hour, calculated by dividing 18 by 6.

Front

What is the significance of unit rates in real life?

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Unit rates help compare different quantities in real life, such as speed, price per item, or efficiency, making it easier to make informed decisions.

Front

What is the difference between a proportional and a non-proportional relationship?

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A proportional relationship has a constant ratio, while a non-proportional relationship does not maintain a constant ratio.