PSAT Math Flashcards: Ratios And Proportions

What this deck covers

This deck focuses on Ratios And Proportions, giving you a quick way to review the definitions, rules, and examples that matter most for PSAT 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 definition of the ratio $a:b$ in fraction form (with $b \ne 0$)?

Answer: $\frac{a}{b}$. A ratio $a:b$ is expressed as a fraction with $a$ in the numerator and $b$ in the denominator.

Flashcard 2: Which equation represents inverse variation between $y$ and $x$ with constant $k$?

Answer: $y=\frac{k}{x}$. In inverse variation, $y$ equals a constant divided by $x$.

Flashcard 3: A map scale is $1$ inch $=5$ miles. What distance is $3.6$ inches?

Answer: $18$ miles. Multiply: $3.6 \times 5 = 18$ miles.

Flashcard 4: What is the unit rate for $\frac{a}{b}$ when $b$ represents the number of units?

Answer: $\frac{a}{b}$ per $1$ unit. Divide the total amount $a$ by the number of units $b$.

Flashcard 5: What is the cross-products test for $\frac{a}{b}=\frac{c}{d}$?

Answer: $ad=bc$. Cross-multiply to check if ratios are equal.

Flashcard 6: A map scale is $1$ inch:$50$ miles. What distance is shown by $3.5$ inches?

Answer: $175$ miles. Multiply map distance by scale: $3.5 \times 50 = 175$ miles.

Flashcard 7: Identify the unit rate for $\frac{x}{y}$ when $y$ is the number of units.

Answer: $\frac{x}{y}$ per $1$ unit. Divide the first quantity by the second to get rate per unit.

Flashcard 8: What is the definition of a ratio $a:b$ in fraction form?

Answer: $\frac{a}{b}$. A ratio compares two quantities as a fraction.

Flashcard 9: What is the definition of a constant of proportionality $k$ in $y=kx$?

Answer: $k=\frac{y}{x}$. The constant $k$ is the ratio of $y$ to $x$ in a proportional relationship.

Flashcard 10: Identify whether the relationship is proportional: points $(2,6)$ and $(5,15)$ in $y=kx$.

Answer: Proportional; $k=3$. Check if $\frac{y}{x}$ is constant: $\frac{6}{2}=\frac{15}{5}=3$.

Flashcard 11: What is the property of equivalent ratios when multiplying both terms by $c$?

Answer: $a:b=(ac):(bc)$. Multiplying both terms of a ratio by the same number preserves the ratio.

Flashcard 12: If $y$ is proportional to $x$ with $k=\frac{5}{2}$, what is $y$ when $x=8$?

Answer: $y=20$. Use $y = kx$ with $k = \frac{5}{2}$: $y = \frac{5}{2} \times 8 = 20$.

Flashcard 13: A map scale is $1$ inch:$20$ miles. How many miles does $3.5$ inches represent?

Answer: $70$ miles. Multiply map distance by scale factor: $3.5 \times 20 = 70$ miles.

Flashcard 14: Which option is proportional to $x$ if the table includes $(x,y)=(2,6)$ and $(5,15)$?

Answer: $y=3x$. Check if $\frac{y}{x}$ is constant: $\frac{6}{2} = \frac{15}{5} = 3$, so $y = 3x$.

Flashcard 15: What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y = kx$?

Answer: $k = \frac{y}{x}$. In $y = kx$, solve for $k$ by dividing both sides by $x$.

Flashcard 16: Identify the simplified form of the ratio $12:18$.

Answer: $2:3$. Divide both terms by their GCD of $6$.

Flashcard 17: Two quantities are in the ratio $4:7$ with total $55$. What is the larger quantity?

Answer: $35$. Total parts = $4+7=11$; larger quantity = $\frac{7}{11} \times 55 = 35$.

Flashcard 18: What is the direct variation form if $y$ varies directly with $x$ and $y=18$ when $x=6$?

Answer: $y=3x$. Find $k$: $18 = k(6)$, so $k = 3$ and $y = 3x$.

Flashcard 19: What is the part-to-whole fraction for a part-to-part ratio $a:b$ (total $a+b$)?

Answer: $\frac{a}{a+b}$. Part $a$ over total $(a+b)$ gives the part-to-whole fraction.

Flashcard 20: If a scale factor is $\frac{3}{2}$ and the original length is $8$, what is the new length?

Answer: $12$. New length = original × scale factor = $8 \times \frac{3}{2} = 12$.

Flashcard 21: A mixture has ratio water:juice $=4:1$. What fraction of the mixture is juice?

Answer: $\frac{1}{5}$. Juice is $1$ part out of $4+1=5$ total parts.

Flashcard 22: Identify $x$ if $\frac{x}{12}=\frac{5}{3}$.

Answer: $x=20$. Cross-multiply: $3x = 60$, so $x = 20$.

Flashcard 23: What is the scale factor from a length $8$ to a length $12$?

Answer: $\frac{3}{2}$. Scale factor is $\frac{\text{new}}{\text{old}}=\frac{12}{8}=\frac{3}{2}$.

Flashcard 24: If $y$ is proportional to $x$ and $y=18$ when $x=6$, what is $y$ when $x=10$?

Answer: $y=30$. Find $k = 3$, then $y = 3(10) = 30$.

Flashcard 25: Find the unit rate for $12 for $8$ pounds.

Answer: $1.50 per pound. Divide total cost by quantity: \frac{\12}{8}=$1.50$ per pound.

Flashcard 26: Find the percent $p$ if the part is $18$ and the whole is $60$.

Answer: $p=30\%$. Use $p = \frac{\text{part}}{\text{whole}} \times 100\% = \frac{18}{60} \times 100\% = 30\%$.

Flashcard 27: What is the constant of proportionality $k$ if $y$ is proportional to $x$?

Answer: $k=\frac{y}{x}$. The constant $k$ is the ratio of $y$ to $x$ in direct variation.

Flashcard 28: What is the percent equivalent of the ratio $\frac{p}{100}$?

Answer: $p\%$. Percent means "per hundred," so $\frac{p}{100} = p\%$.

Flashcard 29: What is the equation of proportionality if $y$ is proportional to $x$ with $k=7$?

Answer: $y=7x$. Direct proportionality means $y = kx$ where $k$ is the constant.

Flashcard 30: Find $k$ if $y$ is proportional to $x$ and $(x,y)=(6,15)$.

Answer: $k=\frac{5}{2}$. Calculate $k = \frac{y}{x} = \frac{15}{6} = \frac{5}{2}$.

Flashcard 31: Identify whether the relationship is proportional: points $(1,2)$ and $(3,6)$.

Answer: Yes, $\frac{y}{x}=2$ for both points. Both points have the same ratio $\frac{y}{x}=2$.

Flashcard 32: What is the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$?

Answer: $ad=bc$. Cross-multiply by multiplying the numerator of each fraction by the denominator of the other.

Flashcard 33: What is the formula for a part-to-whole fraction for the other part $b$ out of $a+b$?

Answer: $\frac{b}{a+b}$. Part $b$ over the total $(a+b)$ gives its part-to-whole fraction.

Flashcard 34: Identify whether the table shows proportionality: $(x,y)=(2,6),(3,9),(5,15)$.

Answer: Yes, $\frac{y}{x}=3$ for all pairs. Check: $\frac{6}{2}=\frac{9}{3}=\frac{15}{5}=3$, constant ratio confirms proportionality.

Flashcard 35: Identify the simplified form of the ratio $18:24$.

Answer: $3:4$. Divide both terms by their GCD of $6$: $18÷6:24÷6 = 3:4$.

Flashcard 36: If lengths scale by $\frac{3}{2}$, what factor scales the area?

Answer: $\left(\frac{3}{2}\right)^2=\frac{9}{4}$. Area scales by the square of the linear scale factor.

Flashcard 37: Identify $k$ if $y$ varies directly with $x$ and $y=14$ when $x=7$.

Answer: $k=2$. Direct variation: $k=\frac{y}{x}=\frac{14}{7}=2$.

Flashcard 38: Find $x$ if $\frac{x}{9}=\frac{14}{21}$.

Answer: $x=6$. Simplify $\frac{14}{21} = \frac{2}{3}$, then $\frac{x}{9} = \frac{2}{3}$ gives $x = 6$.

Flashcard 39: What is the ratio of boys to girls if there are $12$ boys and $18$ girls, simplified?

Answer: $2:3$. Simplify $12:18$ by dividing by GCD $6$.

Flashcard 40: Find $y$ if $y$ varies inversely with $x$, $k=24$, and $x=6$.

Answer: $y=4$. Use $y = \frac{k}{x}$: $y = \frac{24}{6} = 4$.

Flashcard 41: State the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$.

Answer: $ad=bc$ (with $b,d\ne 0$). Cross-multiply to get the product of extremes equals the product of means.

Flashcard 42: A map scale is $1:50{,}000$. What distance on the map represents $100{,}000$ cm in reality?

Answer: $2$ cm. Map distance = real distance ÷ scale = $\frac{100{,}000}{50{,}000} = 2$ cm.

Flashcard 43: What is the definition of the ratio $a:b$ in fraction form?

Answer: $\frac{a}{b}$. A ratio $a:b$ is expressed as a fraction with $a$ in the numerator and $b$ in the denominator.

Flashcard 44: What is the ratio $0.6:1$ written as a simplified whole-number ratio?

Answer: $3:5$. Multiply both parts by $5$ to eliminate decimals: $0.6×5:1×5=3:5$.

Flashcard 45: What is the percent equivalent of the ratio $\frac{p}{100}$?

Answer: $p\%$. Percent means per hundred, so $\frac{p}{100} = p\%$.

Flashcard 46: What is the scale factor from an original length $L$ to a new length $L'$?

Answer: $\frac{L'}{L}$. Scale factor is the ratio of new length to original length.

Flashcard 47: Find the unit rate: What is $84$ miles in $3$ hours in miles per hour?

Answer: $28$ miles per hour. Divide total miles by hours: $\frac{84}{3} = 28$ miles per hour.

Flashcard 48: What is the missing value $x$ in the proportion $\frac{x}{14}=\frac{3}{7}$?

Answer: $x=6$. Cross-multiply: $7x=42$, so $x=6$.

Flashcard 49: Find the unit rate: $18$ miles in $3$ hours.

Answer: $6$ miles per hour. Divide total miles by total hours: $\frac{18}{3} = 6$ miles per hour.

Flashcard 50: What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?

Answer: $\frac{a}{b}=\frac{c}{d}$. A proportion states that two ratios are equal.

Flashcard 51: What is the percent form of the ratio $3:20$?

Answer: $15\%$. Convert ratio to fraction: $\frac{3}{20}=0.15=15\%$.

Flashcard 52: Find $x$ if $\frac{3}{5}=\frac{x}{20}$.

Answer: $x=12$. Cross-multiply: $3 \cdot 20 = 5x$, so $60 = 5x$.

Flashcard 53: Identify the constant of proportionality in the table: $x=2,4,6$ and $y=10,20,30$.

Answer: $k=5$. Each $y$-value equals $5$ times its $x$-value.

Flashcard 54: Find $x$ if $\frac{x}{9}=\frac{4}{3}$.

Answer: $x=12$. Cross-multiply: $3x = 36$, so $x = 12$.

Flashcard 55: What is the unit rate for $\frac{a}{b}$ units per 1 unit of $b$?

Answer: $\frac{a}{b}$ per $1$ (with $b\ne 0$). Unit rate expresses how many units of $a$ per one unit of $b$.

Flashcard 56: What is $x$ if $\frac{7}{x}=\frac{21}{30}$?

Answer: $x=10$. Cross-multiply: $21x=210$, so $x=10$.

Flashcard 57: A shirt is discounted $20\%$ from $35. What is the sale price?

Answer: $28. Sale price = 35 - 0.20(35) = 35 - 7 = \28$.

Flashcard 58: What is the scale factor from a drawing length $6$ to an actual length $15$?

Answer: $\frac{5}{2}$. Scale factor = $\frac{\text{actual}}{\text{drawing}}=\frac{15}{6}=\frac{5}{2}$.

Flashcard 59: A class has boys:girls $=2:3$. What fraction of the class is girls?

Answer: $\frac{3}{5}$. Girls are $3$ parts out of $2+3=5$ total parts.

Flashcard 60: A recipe uses flour:sugar $=2:3$. If flour is $8$ cups, what is sugar?

Answer: $12$ cups. Set up proportion: $\frac{2}{3} = \frac{8}{s}$, so $s = 12$.

Flashcard 61: A recipe uses flour:sugar $=2:3$. If flour is $8$ cups, how many cups of sugar are needed?

Answer: $12$ cups. Set up proportion: $\frac{2}{3} = \frac{8}{x}$, cross-multiply to get $x = 12$.

Flashcard 62: Identify the constant of proportionality $k$ if $y$ is proportional to $x$.

Answer: $k=\frac{y}{x}$. The constant $k$ is the ratio of $y$ to $x$.

Flashcard 63: A class has boys:girls $=3:5$ and $24$ students total. How many boys are in the class?

Answer: $9$. Total parts = $3+5=8$, boys = $\frac{3}{8} × 24 = 9$.

Flashcard 64: State the formula for converting a part-to-whole ratio $p:w$ to a fraction.

Answer: $\frac{p}{w}$ (with $w\ne 0$). Part-to-whole ratio becomes a fraction with part as numerator, whole as denominator.

Flashcard 65: If a recipe uses flour:sugar $=4:1$, how much sugar is needed for $12$ cups of flour?

Answer: $3$ cups. Set up proportion: $\frac{4}{1} = \frac{12}{x}$, so $x = 3$.

Flashcard 66: What is the cross-multiplication result of $\frac{a}{b}=\frac{c}{d}$ (with $b,d\ne 0$)?

Answer: $ad=bc$. Cross-multiply by multiplying the numerator of each fraction by the other's denominator.

Flashcard 67: What is the proportion equation that states $\frac{a}{b}$ equals $\frac{c}{d}$?

Answer: $\frac{a}{b}=\frac{c}{d}$. A proportion states that two ratios are equal.

Flashcard 68: Identify the equivalent ratio to $3:5$ with second term $20$.

Answer: $12:20$. Multiply both terms by $4$ since $5 \times 4 = 20$.

Flashcard 69: If a scale drawing uses $1$ inch for $5$ feet, what actual length corresponds to $7$ inches?

Answer: $35$ feet. Multiply: $7$ inches × $5$ feet/inch = $35$ feet.

Flashcard 70: Identify the means in the proportion $\frac{a}{b}=\frac{c}{d}$.

Answer: $b$ and $c$. The means are the inner terms when written as $a:b::c:d$.

Flashcard 71: A recipe uses flour:sugar $=3:2$. If flour is $12$ cups, what is sugar in cups?

Answer: $8$ cups. Set up proportion: $\frac{3}{2} = \frac{12}{s}$, so $s = 8$ cups.

Flashcard 72: What is the percent equivalent of the ratio $3:20$?

Answer: $15\%$. Convert ratio to percent: $\frac{3}{20} = 0.15 = 15\%$.

Flashcard 73: If $y$ is proportional to $x$ and $y=18$ when $x=6$, what is $k$ in $y=kx$?

Answer: $3$. Substitute values: $18 = k(6)$, so $k = \frac{18}{6} = 3$.

Flashcard 74: Identify whether the table shows proportionality: $(x,y)=(2,5),(4,10),(6,16)$.

Answer: No, ratios $\frac{y}{x}$ are not constant. Check: $\frac{5}{2}=2.5$, $\frac{10}{4}=2.5$, but $\frac{16}{6}=2.67$, not constant.

Flashcard 75: Find $x$ if $7:21=x:12$.

Answer: $x=4$. Set up proportion $\frac{7}{21} = \frac{x}{12}$; simplify to get $x = 4$.

Flashcard 76: What is the unit rate for $150$ miles in $3$ hours?

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

Flashcard 77: What is the scale factor from an original length $L$ to a new length $L'$?

Answer: $\frac{L'}{L}$. Scale factor is the ratio of new to original length.

Flashcard 78: If $y$ is proportional to $x$ with $k=\frac{5}{2}$, what is $y$ when $x=8$?

Answer: $20$. Substitute: $y = \frac{5}{2}(8) = \frac{40}{2} = 20$.

Flashcard 79: Find $x$ if $\frac{x}{9}=\frac{4}{3}$.

Answer: $x=12$. Cross-multiply: $3x = 36$, so $x = 12$.

Flashcard 80: What is the inverse variation form if $y$ varies inversely with $x$ and $y=4$ when $x=3$?

Answer: $y=\frac{12}{x}$. Find $k$: $4 = \frac{k}{3}$, so $k = 12$ and $y = \frac{12}{x}$.

Flashcard 81: What is the ratio of areas of similar figures with linear scale factor $k$?

Answer: $k^2:1$. Area scales with the square of the linear scale factor.

Flashcard 82: A class has boys:girls $=4:5$ and $27$ students total. How many boys are there?

Answer: $12$. Boys are $\frac{4}{9}$ of total: $\frac{4}{9} \times 27 = 12$.

Flashcard 83: What is the constant of proportionality $k$ if $y= kx$ and $(x,y)=(4,10)$?

Answer: $k=\frac{5}{2}$. Substitute and solve: $10 = k(4)$, so $k = \frac{10}{4} = \frac{5}{2}$.

Flashcard 84: What is the new length if an $18$ cm segment is scaled by factor $\frac{5}{3}$?

Answer: $30$ cm. Multiply: $18 \times \frac{5}{3}=30$.

Flashcard 85: What is the unit rate for $\frac{a}{b}$ (with $b>0$) interpreted as $a$ per $b$ units?

Answer: $\frac{a}{b}$ per $1$ unit. Divide the ratio by the denominator to find the rate per one unit.

Flashcard 86: What must be true about the graph of a proportional relationship?

Answer: It is a line through $(0,0)$. Proportional relationships always pass through the origin.

Flashcard 87: What is a proportion in terms of two ratios?

Answer: An equation stating two ratios are equal. A proportion sets two ratios equal, like $\frac{a}{b}=\frac{c}{d}$.

Flashcard 88: Find $y$ if $y$ is proportional to $x$ with $y=18$ when $x=6$, and $x=10$.

Answer: $y=30$. Find $k=3$ from first values, then $y=3(10)=30$.

Flashcard 89: What is $y$ if $y$ varies directly with $x$ and $y=14$ when $x=7$, then $x=10$?

Answer: $y=20$. Find $k=2$ from first pair, then $y=2(10)=20$.

Flashcard 90: What is the cross-products condition for $\frac{a}{b}=\frac{c}{d}$ with $b\neq 0$ and $d\neq 0$?

Answer: $ad=bc$. Cross-multiply the proportion to get this equality.

Flashcard 91: What is the percent equivalent of the ratio $1:4$ expressed as $\frac{1}{4}$?

Answer: $25\%$. Convert fraction to percent: $\frac{1}{4} = 0.25 = 25\%$.

Flashcard 92: Find the missing value: $\frac{7}{x}=\frac{21}{30}$.

Answer: $x=10$. Cross-multiply: $21x = 7 \cdot 30 = 210$, so $x = 10$.

Flashcard 93: What is the constant of proportionality $k$ in the equation $y=kx$ (with $x\neq 0$)?

Answer: $k=\frac{y}{x}$. Solve for $k$ by dividing both sides by $x$.

Flashcard 94: What is the definition of a ratio comparing quantity $a$ to quantity $b$?

Answer: $\frac{a}{b}$, read as $a:b$ or $a$ to $b$. A ratio compares two quantities by division.

Flashcard 95: Find $k$ if $y$ varies directly with $x$ and $(x,y)=(6,15)$.

Answer: $k=\frac{5}{2}$. From $y = kx$: $15 = k \cdot 6$, so $k = \frac{15}{6} = \frac{5}{2}$.

Flashcard 96: What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?

Answer: $\frac{a}{b}=\frac{c}{d}$. Two ratios form a proportion when they are equal.

Flashcard 97: What does it mean for two ratios to be proportional?

Answer: They are equal: $\frac{a}{b}=\frac{c}{d}$ with $b,d\ne 0$. Two ratios are proportional when their cross-products are equal.

Flashcard 98: What is the simplest form of the ratio $18:24$?

Answer: $3:4$. Divide both parts by their GCD: $18÷6=3$, $24÷6=4$.

Flashcard 99: Find $x$ if $\frac{7}{x}=\frac{14}{20}$.

Answer: $x=10$. Cross-multiply: $14x = 140$, so $x = 10$.

Flashcard 100: What is the missing value $x$ in the proportion $\frac{9}{12}=\frac{x}{20}$?

Answer: $x=15$. Cross-multiply: $9×20=12x$, so $x=\frac{180}{12}=15$.