6th Grade Math Flashcards: Understand Unit Rate Concept

What this deck covers

This deck focuses on Understand Unit Rate Concept, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the unit rate (first per second) for the ratio $3:4$?

Answer: $\frac{3}{4}$ per $1$. Divide first quantity by second: $\frac{3}{4}$ gives amount of first per one second.

Flashcard 2: What is the unit rate for the ratio $3:4$ written as a fraction?

Answer: $\frac{3}{4}$. Divide first quantity by second: $\frac{3}{4}$.

Flashcard 3: Identify the unit rate (miles per hour) for $150$ miles in $3$ hours.

Answer: $50$ miles per hour. Divide total distance by time: $\frac{150}{3} = 50$.

Flashcard 4: Choose the correct unit rate for $8$ notebooks for $20: \\frac{5}{2}$or$$\frac{2}{5}$ per notebook?

Answer: \\frac{5}{2}$per notebook. Cost per item is$\frac{20}{8} = \frac{5}{2} = 2.50$ dollars each.

Flashcard 5: What is the unit rate (cost per pound) for $18 for $6$ lb of apples?

Answer: $3 per lb. Divide cost by pounds: $\frac{18}{6} = 3$.

Flashcard 6: What does the unit rate $\frac{a}{b}$ mean in words for a ratio $a:b$?

Answer: It means "$\frac{a}{b}$ units of the first quantity per $1$ unit of the second.". Unit rate shows the amount of first quantity for each single unit of second quantity.

Flashcard 7: What is the unit rate (cups of sugar per cup of flour) for a ratio $3:4$?

Answer: $\frac{4}{3}$ cups sugar per $1$ cup flour. Second quantity per first: $\frac{4}{3}$ sugar per flour.

Flashcard 8: Identify the error: "For ratio $5:0$, the unit rate is $\frac{5}{0}$." What is the correct statement?

Answer: No unit rate exists because $b=0$ and division by $0$ is undefined. Cannot divide by zero; unit rate requires $b \ne 0$.

Flashcard 9: What is the unit rate (dollars per item) for $12$ items costing $3 total?

Answer: \ \frac{1}{4} $per item. Divide total cost by number of items:$\frac{3}{12} = \frac{1}{4}$.

Flashcard 10: Identify the unit rate (words per minute) for $240$ words in $6$ minutes.

Answer: $40$ words per minute. Divide total words by time: $\frac{240}{6} = 40$.

Flashcard 11: Find the unit rate (minutes per mile) for $30$ minutes to run $5$ miles.

Answer: $6$ minutes per mile. Divide minutes by miles: $\frac{30}{5} = 6$.

Flashcard 12: Find the unit rate in $\text{notebooks per dollar}$ for $8$ notebooks that cost $20.

Answer: $\frac{2}{5}$ notebook per dollar. Divide quantity by cost: $\frac{8}{20} = \frac{2}{5}$ notebooks per dollar.

Flashcard 13: What is the unit rate (items per dollar) for $12$ items costing $3 total?

Answer: $4$ items per dollar. Divide number of items by cost: $\frac{12}{3} = 4$.

Flashcard 14: Which quantity must be $1$ in a unit rate: the numerator or the denominator?

Answer: The denominator must be $1$ (the "per $1$" amount). Unit rates always express "per one" of something.

Flashcard 15: Find the unit rate in $\text{minutes per page}$ for $45$ pages in $9$ minutes.

Answer: $\frac{1}{5}$ minute per page. Divide time by pages: $\frac{9}{45} = \frac{1}{5}$ minute to read one page.

Flashcard 16: Identify the unit rate (cost per ounce) for $6 for $8$ ounces.

Answer: \\frac{3}{4}$per ounce. Divide total cost by ounces:$\frac{6}{8} = \frac{3}{4}$.

Flashcard 17: Find the unit rate in $\text{pages per minute}$ for $45$ pages in $9$ minutes.

Answer: $5$ pages per minute. Divide total pages by time: $\frac{45}{9} = 5$ pages read in one minute.

Flashcard 18: Identify the unit rate for the ratio $2.5:0.5$ (first per second).

Answer: $5$ per $1$. Divide first by second: $\frac{2.5}{0.5} = 5$ units of first per one second.

Flashcard 19: Which quantity must be $1$ in a unit rate written as $\frac{a}{b}$?

Answer: The second quantity (the denominator) is $1$ unit. Unit rates always have a denominator of 1.

Flashcard 20: What is the unit rate in hamburgers per dollar if $15$ hamburgers cost $75?

Answer: $\frac{1}{5}$ hamburger per dollar. Divide hamburgers by dollars: $\frac{15}{75} = \frac{1}{5}$.

Flashcard 21: Identify the unit rate (dollars per pound) for $18 for $6$ lb of apples.

Answer: $3 per pound. Divide price by weight: $\frac{18}{6} = 3$.

Flashcard 22: Find and correct the unit rate error: "Ratio $10:2$ gives unit rate $\frac{2}{10}$ per $1$."

Answer: Correct unit rate is $\frac{10}{2}=5$ per $1$. Unit rate divides first by second, not second by first.

Flashcard 23: What is the unit rate (kilometers per liter) for $150$ km on $10$ L of gas?

Answer: $15$ km per liter. Divide distance by fuel: $\frac{150}{10} = 15$.

Flashcard 24: What is the unit rate (second per first) for the ratio $3:4$?

Answer: $\frac{4}{3}$ per $1$. Flip the ratio to get second per first: $\frac{4}{3}$ units of second per one first.

Flashcard 25: What is the unit rate (pounds per dollar) if $6$ lb of apples cost $18?

Answer: $\frac{1}{3}$ lb per dollar. Divide pounds by dollars: $\frac{6}{18} = \frac{1}{3}$.

Flashcard 26: Identify the unit rate for the ratio $\frac{3}{4}:\frac{1}{2}$ (first per second).

Answer: $\frac{3}{2}$ per $1$. Divide fractions: $\frac{3/4}{1/2} = \frac{3}{4} \times \frac{2}{1} = \frac{3}{2}$.

Flashcard 27: What is the unit rate (items per dollar) for $15$ hamburgers for $75?

Answer: $\frac{1}{5}$ hamburger per dollar. Divide items by dollars: $\frac{15}{75} = \frac{1}{5}$.

Flashcard 28: What unit rate corresponds to the ratio $3:4$ (first quantity per $1$ of second)?

Answer: $\frac{3}{4}$ per $1$. Divide the first quantity by the second: $\frac{3}{4}$.

Flashcard 29: What is the unit rate (dollars per item) for $75 for $15$ hamburgers?

Answer: $5 per hamburger. Divide total cost by number of items: $\frac{75}{15} = 5$.

Flashcard 30: Which option is the unit rate for $8$ notebooks for $12: $\frac{12}{8}$ or $\frac{8}{12}$ dollars per notebook?

Answer: $\frac{12}{8}=\frac{3}{2}$ dollars per notebook. Price per item means dollars divided by notebooks.

Flashcard 31: What is the unit rate (dollars per ticket) for $54 for $6$ tickets?

Answer: $9 per ticket. Divide cost by tickets: $\frac{54}{6} = 9$.

Flashcard 32: Identify the error: A student says the unit rate for $8:2$ is $\frac{2}{8}$. What is correct?

Answer: Correct unit rate is $\frac{8}{2} = 4$. For $8:2$, divide first by second: $\frac{8}{2} = 4$.

Flashcard 33: What is the unit rate (pages per minute) for $45$ pages in $9$ minutes?

Answer: $5$ pages per minute. Divide pages by minutes: $\frac{45}{9} = 5$.

Flashcard 34: What is the definition of a unit rate for a ratio $a:b$ with $b\ne 0$?

Answer: The unit rate is $\frac{a}{b}$, meaning "$a$ per $1$ of $b$.". Expresses how many units of $a$ for each single unit of $b$.

Flashcard 35: Find and correct the unit rate statement: "Ratio $6:2$ means $\frac{2}{6}$ per $1$."

Answer: Correct unit rate is $\frac{6}{2}=3$ per $1$. The error shows reciprocal; correct is $\frac{6}{2} = 3$ per $1$.

Flashcard 36: Find the unit rate (teachers per student) for a ratio of $24$ students to $3$ teachers.

Answer: $\frac{1}{8}$ teacher per student. Divide teachers by students: $\frac{3}{24} = \frac{1}{8}$.

Flashcard 37: Choose the correct rate language for the unit rate of the ratio $9:12$.

Answer: $\frac{3}{4}$ of the first quantity for each $1$ of the second. Simplify $\frac{9}{12} = \frac{3}{4}$ for the unit rate.

Flashcard 38: Find the unit rate (days per page) for reading $45$ pages in $9$ days.

Answer: $\frac{1}{5}$ day per page. Divide days by pages: $\frac{9}{45} = \frac{1}{5}$.

Flashcard 39: Find the unit rate (miles per minute) for $5$ miles in $30$ minutes.

Answer: $\frac{1}{6}$ mile per minute. Divide miles by minutes: $\frac{5}{30} = \frac{1}{6}$.

Flashcard 40: What is the unit rate (liters per kilometer) for $150$ km on $10$ L of gas?

Answer: $\frac{1}{15}$ L per km. Divide fuel by distance: $\frac{10}{150} = \frac{1}{15}$.

Flashcard 41: What is the unit rate (cups flour per cup sugar) for the ratio $3$ cups flour to $4$ cups sugar?

Answer: $\frac{3}{4}$ cup flour per $1$ cup sugar. Divide flour by sugar: $\frac{3}{4}$ per $1$ cup sugar.

Flashcard 42: Choose the correct unit rate for $8$ gallons in $4$ hours: $2$, $12$, or $\frac{1}{2}$ gal/hr?

Answer: $2$ gallons per hour. Divide total gallons by hours: $\frac{8}{4} = 2$.

Flashcard 43: Identify the unit rate (dollars per hamburger) for $75 for $15$ hamburgers.

Answer: $5 per hamburger. Divide total cost by number of items: $\frac{75}{15} = 5$.

Flashcard 44: What is the unit rate (cups sugar per cup flour) for the ratio $3$ cups flour to $4$ cups sugar?

Answer: $\frac{4}{3}$ cup sugar per $1$ cup flour. Divide sugar by flour: $\frac{4}{3}$ per 1 cup flour.

Flashcard 45: What is the unit rate in $\text{hamburgers per dollar}$ for $15$ hamburgers for $75?

Answer: $\frac{1}{5}$ hamburger per dollar. Divide items by cost: $\frac{15}{75} = \frac{1}{5}$ hamburger per dollar spent.

Flashcard 46: Find the unit rate in $\text{cost per notebook}$ for $8$ notebooks that cost $20.

Answer: \\frac{5}{2}$per notebook. Divide total cost by quantity:$\frac{20}{8} = \frac{5}{2}$ dollars per notebook.

Flashcard 47: What is the unit rate (minutes per page) for $45$ pages in $9$ minutes?

Answer: $\frac{1}{5}$ minute per page. Divide minutes by pages: $\frac{9}{45} = \frac{1}{5}$.

Flashcard 48: Find the unit rate in $\text{miles per hour}$ for $120$ miles in $3$ hours.

Answer: $40$ miles per hour. Divide distance by time: $\frac{120}{3} = 40$ miles in one hour.

Flashcard 49: What is the unit rate (miles per minute) for $30$ minutes to run $5$ miles?

Answer: $\frac{1}{6}$ mile per minute. Divide distance by time: $\frac{5}{30} = \frac{1}{6}$.

Flashcard 50: What condition must be true to define the unit rate $\frac{a}{b}$ for a ratio $a:b$?

Answer: $b \ne 0$. Can't divide by zero; ensures unit rate is defined.

Flashcard 51: What is the unit rate (cups of sugar per cup of flour) for flour:sugar = $3:4$?

Answer: $\frac{4}{3}$ cups sugar per $1$ cup flour. Divide cups of sugar by cups of flour: $\frac{4}{3}$.

Flashcard 52: What is the unit rate in $\text{dollars per hamburger}$ for $75 for $15$ hamburgers?

Answer: $5 per hamburger. Divide total cost by number of items: $\frac{75}{15} = 5$.

Flashcard 53: Which value must be nonzero in a ratio $a:b$ to form the unit rate $\frac{a}{b}$?

Answer: $b \ne 0$. Division by zero is undefined, so the denominator cannot be zero.

Flashcard 54: What is the unit rate (miles per hour) for $120$ miles in $3$ hours?

Answer: $40$ miles per hour. Divide total miles by hours: $\frac{120}{3} = 40$.

Flashcard 55: Find the unit rate (pages per day) for reading $45$ pages in $9$ days.

Answer: $5$ pages per day. Divide total pages by days: $\frac{45}{9} = 5$.

Flashcard 56: Identify the unit rate (miles per hour) for $120$ miles in $3$ hours.

Answer: $40$ miles per hour. Divide miles by hours: $\frac{120}{3} = 40$.

Flashcard 57: Identify the unit rate (pages per minute) for $45$ pages in $9$ minutes.

Answer: $5$ pages per minute. Divide pages by minutes: $\frac{45}{9} = 5$.

Flashcard 58: What does the unit rate $\frac{a}{b}$ mean in words for the ratio $a:b$?

Answer: $\frac{a}{b}$ units of the first quantity for each $1$ unit of the second. This expresses the ratio with the second quantity normalized to 1.

Flashcard 59: Find the unit rate in $\text{hours per mile}$ for $120$ miles in $3$ hours.

Answer: $\frac{1}{40}$ hour per mile. Divide time by distance: $\frac{3}{120} = \frac{1}{40}$ hour to travel one mile.

Flashcard 60: What is the unit rate in dollars per hamburger if $75 buys $15$ hamburgers?

Answer: $5 per hamburger. Divide total cost by number: $\frac{75}{15} = 5$.

Flashcard 61: What is the unit rate (cups of flour per cup of sugar) for a ratio $3:4$?

Answer: $\frac{3}{4}$ cup flour per $1$ cup sugar. First quantity per second: $\frac{3}{4}$ flour per sugar.

Flashcard 62: What is the unit rate (minutes per mile) for $30$ minutes to run $5$ miles?

Answer: $6$ minutes per mile. Divide total time by distance: $\frac{30}{5} = 6$.

Flashcard 63: Which unit rate matches the ratio $7$ notebooks for $21$ dollars: dollars per notebook?

Answer: $3$ dollars per notebook. Divide dollars by notebooks: $\frac{21}{7} = 3$.

Flashcard 64: What is the unit rate in $\text{cups of sugar per cup of flour}$ for a ratio $3:4$?

Answer: $\frac{4}{3}$ cups of sugar per cup of flour. For every $1$ cup of flour, there are $\frac{4}{3}$ cups of sugar.

Flashcard 65: Identify the restriction on $b$ in the ratio $a:b$ when forming $\frac{a}{b}$.

Answer: $b\ne 0$. Division by zero is undefined, so denominator cannot be zero.

Flashcard 66: What unit rate corresponds to the ratio $5:2$ (first quantity per $1$ of second)?

Answer: $\frac{5}{2}$ per $1$. Divide the first quantity by the second: $\frac{5}{2}$.

Flashcard 67: What is the unit rate in $\text{cups of flour per cup of sugar}$ for a ratio $3:4$?

Answer: $\frac{3}{4}$ cup of flour per cup of sugar. For every $1$ cup of sugar, there are $\frac{3}{4}$ cups of flour.

Flashcard 68: What is the definition of a unit rate for a ratio $a:b$ with $b \ne 0$?

Answer: Unit rate is $\frac{a}{b}$, meaning "$a$ per $1$ of $b$.". Expresses how much of the first quantity corresponds to one unit of the second.

Flashcard 69: What is the unit rate (cups of flour per cup of sugar) for flour:sugar $= 3:4$?

Answer: $\frac{3}{4}$ cup flour per $1$ cup sugar. Divide cups of flour by cups of sugar: $\frac{3}{4}$.

Flashcard 70: Identify the unit rate (ounces per dollar) for $6 for $8$ ounces.

Answer: $\frac{4}{3}$ ounces per dollar. Divide ounces by cost: $\frac{8}{6} = \frac{4}{3}$.

Flashcard 71: Which unit rate matches the ratio $7$ notebooks for $21$ dollars: notebooks per dollar?

Answer: $\frac{1}{3}$ notebook per dollar. Divide notebooks by dollars: $\frac{7}{21} = \frac{1}{3}$.

Flashcard 72: Which quantity must be $1$ when you express a ratio as a unit rate?

Answer: The second quantity (the denominator) must be $1$. Unit rates compare to exactly one unit, making the denominator $1$.

Flashcard 73: What is the unit rate (pounds per dollar) for $6$ lb for $18?

Answer: $\frac{1}{3}$ pound per dollar. Divide weight by price: $\frac{6}{18} = \frac{1}{3}$.

Flashcard 74: Find the unit rate (students per teacher) for a ratio of $24$ students to $3$ teachers.

Answer: $8$ students per teacher. Divide students by teachers: $\frac{24}{3} = 8$.