If a recipe calls for $$\frac{2}{3}$$ cup of white sugar for every $$\frac{3}{4}$$ cup of brown sugar, how do you find the amount of brown sugar needed for 1 cup of white sugar?

Set up a proportion: if $$\frac{2}{3}$$ cup of white sugar corresponds to $$\frac{3}{4}$$ cup of brown sugar, then for 1 cup of white sugar, the amount of brown sugar is $$1 \times \frac{3}{4} \div \frac{2}{3} = 1 \frac{1}{8}$$ cups.

If Lauren bikes $$\frac{4}{3}$$ miles in $$\frac{1}{10}$$ hour, how do you calculate the time it takes to bike one mile?

Use the formula: Time = Distance ÷ Rate. Here, the rate is $$\frac{4}{3}$$ miles per $$\frac{1}{10}$$ hour, so the time for 1 mile is $$\frac{1}{\frac{4}{3} \div \frac{1}{10}} = \frac{3}{40}$$ hours.

How do you express a rate in terms of gallons per minute?

To express a rate in gallons per minute, divide the number of gallons by the number of minutes taken to fill that amount.

If Lora fills $$\frac{3}{5}$$ gallon of gas in $$\frac{1}{6}$$ minute, how many gallons can she fill in 1 minute?

Calculate the rate: $$\frac{3}{5} \div \frac{1}{6} = 3 \frac{3}{5}$$ gallons per minute.

What is the formula to find how many bags of food a dog can eat in a week?

If a dog eats $$\frac{1}{3}$$ of a bag in $$\frac{1}{2}$$ week, multiply the amount eaten in one week by the number of weeks: $$\frac{1}{3} \div \frac{1}{2} = \frac{2}{3}$$ bags in one week.

How do you solve a problem involving ratios and proportions?

Set up a proportion based on the given ratios, cross-multiply, and solve for the unknown variable.

What is the significance of the least common denominator (LCD) in complex fractions?

The least common denominator (LCD) helps to simplify complex fractions by providing a common base for the fractions involved.

How can you check if your answer to a unit rate problem is reasonable?

You can check if your answer is reasonable by estimating the values and comparing them to the calculated unit rate.

What is the difference between a proper fraction and an improper fraction?

A proper fraction has a numerator smaller than the denominator (e.g., $$\frac{1}{2}$$ ), while an improper fraction has a numerator larger than or equal to the denominator (e.g., $$\frac{5}{4}$$ ).

Unit Rate with Complex Fractions Flashcards

Student preview

14 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is expressed as a quantity per one unit of another quantity.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

2.

FLASHCARD QUESTION

Front

How do you find the unit rate from a complex fraction?

Back

To find the unit rate from a complex fraction, divide the numerator by the denominator to simplify the fraction, then express the result as a rate per one unit.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.7.RP.A.3

4.

FLASHCARD QUESTION

Front

How do you convert a complex fraction to a simple fraction?

Back

Multiply the numerator and the denominator by the least common denominator (LCD) of the fractions involved to eliminate the complex fraction.

5.

FLASHCARD QUESTION

Front

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

Back

The relationship is expressed by the formula: Distance = Rate × Time. This means that if you know any two of these values, you can find the third.

Tags

CCSS.6.RP.A.3B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.7.RP.A.1

7.

FLASHCARD QUESTION

Front

What is a mixed number?

Back

Tags

CCSS.3.NF.A.3C

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