Rates, Ratios, 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 pay $1.95 for 5 bananas, the unit rate is the cost of one banana.

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How do you find the unit rate from a total cost?

Back

To find the unit rate from a total cost, divide the total cost by the number of items. For example, if you pay $31.20 for 15 gallons of gas, divide $31.20 by 15 to find the cost per gallon.

Front

What is the formula for solving proportions?

Back

The formula for solving proportions is cross-multiplication. If you have a proportion like a/b = c/d, you can solve for the unknown by cross-multiplying: a*d = b*c.

Front

How do you determine if two ratios are proportional?

Back

Two ratios are proportional if their cross products are equal. For example, for the ratios 10/12 and 20/32, you would check if 10*32 = 12*20.

Front

What is the average rate of speed?

Back

The average rate of speed is calculated by dividing the total distance traveled by the total time taken. For example, if Melissa drives 238 miles in 5 hours, her average speed is 238 miles / 5 hours = 48 MPH.

Front

What is a ratio?

Back

A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How can you convert a fraction to a decimal?

Back

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 2/5 = 0.4.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, and vice versa. For example, the ratio 2:3 can be written as the fraction 2/3.

Front

What does it mean for two ratios to be equivalent?

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Two ratios are equivalent if they represent the same relationship between quantities, meaning they simplify to the same fraction.