Ratios and Unit Rates

Front

What is a ratio?

Back

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

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something (e.g., miles per hour, dollars per item).

Front

How do you determine if two ratios are equivalent?

Back

Two ratios are equivalent if they simplify to the same fraction or if their cross products are equal.

Front

What is the formula to find the unit rate?

Back

The unit rate can be found by dividing the total quantity by the number of units (e.g., total cost divided by total weight).

Front

If a teacher grades 25 assignments in 20 minutes, how do you find the rate of grading per assignment?

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To find the rate per assignment, divide the total number of assignments by the total time taken (25 assignments / 20 minutes = 1.25 assignments per minute).

Front

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

Back

Understanding ratios helps in making comparisons, analyzing relationships between quantities, and solving problems in various contexts such as finance, cooking, and scaling.

Front

How can you convert a ratio into a fraction?

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To convert a ratio into a fraction, write the first quantity as the numerator and the second quantity as the denominator (e.g., the ratio 4:1 becomes the fraction 4/1).

Front

What is the relationship between ratios and proportions?

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A proportion is an equation that states that two ratios are equal, often used to solve for unknown values.

Front

How do you calculate the unit price of an item?

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To calculate the unit price, divide the total price by the quantity of items purchased (e.g., $40 for 5 pounds of concrete = $8 per pound).

Front

What is the importance of unit rates in budgeting?

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Unit rates help in comparing costs and making informed decisions about spending, allowing for better budgeting and financial planning.