SAT 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 SAT 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: Determine if $\frac{8}{12}$ and $\frac{2}{3}$ are equivalent.

Answer: Yes, they are equivalent. Both ratios simplify to $\frac{2}{3}$ when reduced.

Flashcard 2: State the formula for a proportion involving $a$, $b$, $c$, and $d$.

Answer: $\frac{a}{b} = \frac{c}{d}$. Two ratios set equal, forming an equation.

Flashcard 3: Express the ratio of 15 minutes to 1 hour as a fraction.

Answer: $\frac{1}{4}$. Convert 1 hour to 60 minutes, then simplify $\frac{15}{60}$.

Flashcard 4: Find the missing term: $\frac{6}{9} = \frac{x}{3}$.

Answer: $x = 2$. Cross multiply: $6 \times 3 = 9x$, so $x = 2$.

Flashcard 5: Solve the proportion: $\frac{3}{4} = \frac{x}{8}$.

Answer: $x = 6$. Cross-multiply: $3 \times 8 = 4 \times x$, so $24 = 4x$.

Flashcard 6: Solve for $x$: $\frac{x}{12} = \frac{3}{4}$.

Answer: $x = 9$. Cross multiply: $4x = 36$, so $x = 9$.

Flashcard 7: Express the ratio of 15 minutes to 1 hour as a fraction.

Answer: $\frac{1}{4}$. Convert 1 hour to 60 minutes, then simplify $\frac{15}{60}$.

Flashcard 8: Express 3 out of 8 as a ratio.

Answer: $3:8$. Direct conversion from part-to-whole relationship.

Flashcard 9: Convert the fraction $\frac{3}{4}$ to a ratio.

Answer: $3:4$. A fraction $\frac{a}{b}$ is equivalent to the ratio $a:b$.

Flashcard 10: What is the definition of a proportion?

Answer: A proportion is an equation stating two ratios are equal. Two ratios set equal to each other form an equation.

Flashcard 11: If $x : y = 5 : 2$, what is $\frac{y}{x}$?

Answer: $\frac{2}{5}$. For $x:y = 5:2$, we have $\frac{y}{x} = \frac{2}{5}$.

Flashcard 12: Express 25% as a ratio.

Answer: $1:4$. 25% means 25 out of 100, which simplifies to $1:4$.

Flashcard 13: Find the value of $x$ if $\frac{5}{x} = \frac{10}{15}$.

Answer: $x = 7.5$. Cross multiply: $5 \times 15 = 10x$, so $x = 7.5$.

Flashcard 14: Identify the extremes in the proportion $\frac{a}{b} = \frac{c}{d}$.

Answer: Extremes are $a$ and $d$. The outer terms in a proportion are the extremes.

Flashcard 15: Identify the missing term: $\frac{3}{4} = \frac{x}{8}$.

Answer: $x = 6$. Cross multiply: $3 \times 8 = 4 \times x$, so $24 = 4x$.

Flashcard 16: What is the definition of a proportion?

Answer: A proportion is an equation stating two ratios are equal. Two ratios set equal to each other form an equation.

Flashcard 17: If $a : b = 7 : 3$, what is $\frac{b}{a}$?

Answer: $\frac{3}{7}$. For $a:b = 7:3$, we have $\frac{b}{a} = \frac{3}{7}$.

Flashcard 18: Simplify the ratio 50:100.

Answer: $1:2$. Divide both terms by their GCD of 50.

Flashcard 19: Express 3 out of 8 as a ratio.

Answer: $3:8$. Direct conversion from part-to-whole relationship.

Flashcard 20: Convert the fraction $\frac{3}{4}$ to a ratio.

Answer: $3:4$. A fraction $\frac{a}{b}$ is equivalent to the ratio $a:b$.

Flashcard 21: If $\frac{a}{b} = \frac{3}{5}$, what is $\frac{b}{a}$?

Answer: $\frac{5}{3}$. Reciprocal of $\frac{3}{5}$ is $\frac{5}{3}$.

Flashcard 22: What is the ratio of 5 to 20 in simplest form?

Answer: $1:4$. Divide both terms by their GCD of 5.

Flashcard 23: What is the formula for converting a ratio to a percentage?

Answer: Multiply the ratio by 100. Convert the ratio to decimal form, then multiply by 100.

Flashcard 24: Express the proportion $\frac{1}{2} = \frac{n}{6}$ in words.

Answer: 1 is to 2 as $n$ is to 6. Standard verbal form of expressing proportional relationships.

Flashcard 25: What is the value of $x$ if $2:3 = 4:x$?

Answer: $x = 6$. Cross-multiply: $2x = 12$, so $x = 6$.

Flashcard 26: Solve for $x$: $\frac{4}{x} = \frac{8}{16}$.

Answer: $x = 8$. Cross multiply: $4 \times 16 = 8x$, so $x = 8$.

Flashcard 27: If $x : y = 5 : 2$, what is $\frac{y}{x}$?

Answer: $\frac{2}{5}$. For $x:y = 5:2$, we have $\frac{y}{x} = \frac{2}{5}$.

Flashcard 28: What is the value of $x$ if $5:x = 2:3$?

Answer: $x = 7.5$. Cross multiply: $5 \times 3 = x \times 2$, so $15 = 2x$.

Flashcard 29: What is the cross-multiplication step in $\frac{a}{b} = \frac{c}{d}$?

Answer: $ad = bc$. Multiply the outer terms and inner terms.

Flashcard 30: If $x$ is to $y$ as $3$ is to $4$, express this as a proportion.

Answer: $\frac{x}{y} = \frac{3}{4}$. Direct translation of the verbal proportion statement.

Flashcard 31: Express the ratio 20:5 in simplest form.

Answer: $4:1$. Divide both terms by their GCD of 5.

Flashcard 32: Solve for $x$: $\frac{4}{x} = \frac{8}{16}$.

Answer: $x = 8$. Cross multiply: $4 \times 16 = 8x$, so $x = 8$.

Flashcard 33: What is the definition of a ratio?

Answer: A comparison of two quantities by division. Shows how many times one quantity contains another.

Flashcard 34: What is the simplest form of the ratio 18:24?

Answer: $3:4$. Divide both terms by their GCD of 6.

Flashcard 35: What is the formula for finding the ratio of $a$ to $b$?

Answer: Ratio = $\frac{a}{b}$. Expresses the relationship between two quantities.

Flashcard 36: Find the missing value in the proportion $\frac{9}{x} = \frac{3}{5}$.

Answer: $x = 15$. Cross multiply: $9 \times 5 = 3 \times x$, so $45 = 3x$.

Flashcard 37: If $x : y = 3 : 4$, what is $\frac{x}{y}$?

Answer: $\frac{3}{4}$. Ratio notation directly converts to fraction form.

Flashcard 38: Identify the ratio form for $a:b = c:d$.

Answer: $\frac{a}{b} = \frac{c}{d}$. Colon notation converts to fraction form.

Flashcard 39: Identify the extremes in the proportion $\frac{a}{b} = \frac{c}{d}$.

Answer: Extremes are $a$ and $d$. The outer terms in a proportion are the extremes.

Flashcard 40: What is $x$ if $\frac{2}{x} = \frac{5}{10}$?

Answer: $x = 4$. Cross multiply: $2 \times 10 = 5x$, so $x = 4$.

Flashcard 41: Express 25% as a ratio.

Answer: $1:4$. 25% means 25 out of 100, which simplifies to $1:4$.

Flashcard 42: Convert the ratio 21:49 to simplest form.

Answer: $3:7$. Divide both terms by their GCD of 7.

Flashcard 43: State the formula for a proportion involving $a$, $b$, $c$, and $d$.

Answer: $\frac{a}{b} = \frac{c}{d}$. Two ratios set equal, forming an equation.

Flashcard 44: Which ratio is equivalent to $\frac{2}{3}$? $\frac{4}{6}$ or $\frac{3}{5}$?

Answer: $\frac{4}{6}$. Multiply numerator and denominator of $\frac{2}{3}$ by 2.

Flashcard 45: What is the reciprocal of a ratio $\frac{a}{b}$?

Answer: Reciprocal is $\frac{b}{a}$. Flip the numerator and denominator to find the reciprocal.

Flashcard 46: State the Cross-Multiplication Rule for proportions.

Answer: $a \times d = b \times c$ for $\frac{a}{b} = \frac{c}{d}$. Product of extremes equals product of means.

Flashcard 47: Identify the missing term: $\frac{3}{4} = \frac{x}{8}$.

Answer: $x = 6$. Cross multiply: $3 \times 8 = 4 \times x$, so $24 = 4x$.

Flashcard 48: Simplify the ratio 16:64.

Answer: $1:4$. Divide both terms by their GCD of 16.

Flashcard 49: Find the value of $x$ if $\frac{x}{6} = \frac{3}{2}$.

Answer: $x = 9$. Cross multiply: $2x = 18$, so $x = 9$.

Flashcard 50: Find the value of $x$ if $\frac{5}{x} = \frac{10}{15}$.

Answer: $x = 7.5$. Cross multiply: $5 \times 15 = 10x$, so $x = 7.5$.

Flashcard 51: What is the definition of a ratio?

Answer: A comparison of two quantities by division. Shows how many times one quantity contains another.

Flashcard 52: Solve for $x$: $\frac{3}{x} = \frac{5}{15}$.

Answer: $x = 9$. Cross multiply: $3 \times 15 = 5x$, so $x = 9$.

Flashcard 53: What is the formula for converting a ratio to a percentage?

Answer: Multiply the ratio by 100. Convert the ratio to decimal form, then multiply by 100.

Flashcard 54: Convert the ratio $5:10$ to its simplest form.

Answer: $1:2$. Divide both terms by their GCD of 5.

Flashcard 55: Express the ratio $\frac{2}{5}$ as a percentage.

Answer: 40%. Convert to decimal: $0.4 = 40\%$.

Flashcard 56: Determine if $\frac{8}{12}$ and $\frac{2}{3}$ are equivalent.

Answer: Yes, they are equivalent. Both ratios simplify to $\frac{2}{3}$ when reduced.

Flashcard 57: Which ratio is equivalent to $\frac{2}{3}$? $\frac{4}{6}$ or $\frac{3}{5}$?

Answer: $\frac{4}{6}$. Multiply numerator and denominator of $\frac{2}{3}$ by 2.

Flashcard 58: If $x$ is to $y$ as $3$ is to $4$, express this as a proportion.

Answer: $\frac{x}{y} = \frac{3}{4}$. Direct translation of the verbal proportion statement.

Flashcard 59: What is $x$ if $\frac{2}{x} = \frac{5}{10}$?

Answer: $x = 4$. Cross multiply: $2 \times 10 = 5x$, so $x = 4$.

Flashcard 60: State the Cross-Multiplication Rule for proportions.

Answer: $a \times d = b \times c$ for $\frac{a}{b} = \frac{c}{d}$. Product of extremes equals product of means.

Flashcard 61: Determine if $\frac{15}{25}$ and $\frac{3}{5}$ are equivalent.

Answer: Yes, they are equivalent. Both ratios reduce to $\frac{3}{5}$ in simplest form.

Flashcard 62: What is the definition of a ratio?

Answer: A comparison of two quantities by division. Expressed as a fraction or with a colon separator.

Flashcard 63: Find the missing term: $7:x = 14:28$.

Answer: $x = 14$. Cross-multiply: $7 \times 28 = 14x$, so $196 = 14x$.

Flashcard 64: Convert the ratio 7:28 to its simplest form.

Answer: $1:4$. Divide both terms by their GCD of 7.

Flashcard 65: What is the value of $x$ if $5:x = 2:3$?

Answer: $x = 7.5$. Cross multiply: $5 \times 3 = x \times 2$, so $15 = 2x$.

Flashcard 66: What is the value of $x$ if $2:3 = 4:x$?

Answer: $x = 6$. Cross-multiply: $2x = 12$, so $x = 6$.

Flashcard 67: State the formula for a proportion.

Answer: $\frac{a}{b} = \frac{c}{d}$, where $a, b, c, d$ are quantities. States that two ratios are equal to each other.

Flashcard 68: Identify the means in the proportion $\frac{a}{b} = \frac{c}{d}$.

Answer: Means are $b$ and $c$. The middle terms in a proportion are the means.

Flashcard 69: What is the simplest form of the ratio 10:25?

Answer: $2:5$. Divide both terms by their GCD of 5.

Flashcard 70: Simplify the ratio 16:64.

Answer: $1:4$. Divide both terms by their GCD of 16.

Flashcard 71: Find the missing value: $\frac{7}{x} = \frac{14}{28}$.

Answer: $x = 14$. Cross multiply: $7 \times 28 = 14x$, so $x = 14$.

Flashcard 72: What is the simplest form of the ratio 12:48?

Answer: $1:4$. Divide both terms by their GCD of 12.

Flashcard 73: If $a : b = 7 : 3$, what is $\frac{b}{a}$?

Answer: $\frac{3}{7}$. For $a:b = 7:3$, we have $\frac{b}{a} = \frac{3}{7}$.

Flashcard 74: What is the cross-multiplication step in $\frac{a}{b} = \frac{c}{d}$?

Answer: $ad = bc$. Multiply the outer terms and inner terms.

Flashcard 75: What is the simplest form of the ratio 10:25?

Answer: $2:5$. Divide both terms by their GCD of 5.

Flashcard 76: Find the missing term: $\frac{6}{9} = \frac{x}{3}$.

Answer: $x = 2$. Cross multiply: $6 \times 3 = 9x$, so $x = 2$.

Flashcard 77: Determine if $\frac{15}{25}$ and $\frac{3}{5}$ are equivalent.

Answer: Yes, they are equivalent. Both ratios reduce to $\frac{3}{5}$ in simplest form.

Flashcard 78: If $x : y = 3 : 4$, what is $\frac{x}{y}$?

Answer: $\frac{3}{4}$. Ratio notation directly converts to fraction form.

Flashcard 79: Convert the ratio 9:36 to simplest form.

Answer: $1:4$. Divide both terms by their GCD of 9.

Flashcard 80: What is the formula for finding the ratio of $a$ to $b$?

Answer: Ratio = $\frac{a}{b}$. Expresses the relationship between two quantities.

Flashcard 81: What is the ratio of 8 to 12 in simplest form?

Answer: $\frac{2}{3}$. Divide both numbers by their GCD of 4.

Flashcard 82: Convert the ratio 9:36 to simplest form.

Answer: $1:4$. Divide both terms by their GCD of 9.

Flashcard 83: Find the missing value: $\frac{7}{x} = \frac{14}{28}$.

Answer: $x = 14$. Cross multiply: $7 \times 28 = 14x$, so $x = 14$.

Flashcard 84: Find the missing term: $7:x = 14:28$.

Answer: $x = 14$. Cross-multiply: $7 \times 28 = 14x$, so $196 = 14x$.

Flashcard 85: State the formula for a proportion.

Answer: $\frac{a}{b} = \frac{c}{d}$, where $a, b, c, d$ are quantities. States that two ratios are equal to each other.

Flashcard 86: Identify the ratio form for $a:b = c:d$.

Answer: $\frac{a}{b} = \frac{c}{d}$. Colon notation converts to fraction form.

Flashcard 87: Express the ratio 20:5 in simplest form.

Answer: $4:1$. Divide both terms by their GCD of 5.

Flashcard 88: Find the missing value in the proportion $\frac{9}{x} = \frac{3}{5}$.

Answer: $x = 15$. Cross multiply: $9 \times 5 = 3 \times x$, so $45 = 3x$.

Flashcard 89: Solve for $x$: $\frac{x}{12} = \frac{3}{4}$.

Answer: $x = 9$. Cross multiply: $4x = 36$, so $x = 9$.

Flashcard 90: Express the proportion $\frac{1}{2} = \frac{n}{6}$ in words.

Answer: 1 is to 2 as $n$ is to 6. Standard verbal form of expressing proportional relationships.

Flashcard 91: Solve for $x$: $\frac{3}{x} = \frac{5}{15}$.

Answer: $x = 9$. Cross multiply: $3 \times 15 = 5x$, so $x = 9$.

Flashcard 92: Solve the proportion: $\frac{3}{4} = \frac{x}{8}$.

Answer: $x = 6$. Cross-multiply: $3 \times 8 = 4 \times x$, so $24 = 4x$.

Flashcard 93: Simplify the ratio 50:100.

Answer: $1:2$. Divide both terms by their GCD of 50.

Flashcard 94: What is the ratio of 8 to 12 in simplest form?

Answer: $\frac{2}{3}$. Divide both numbers by their GCD of 4.

Flashcard 95: If $\frac{a}{b} = \frac{3}{5}$, what is $\frac{b}{a}$?

Answer: $\frac{5}{3}$. Reciprocal of $\frac{3}{5}$ is $\frac{5}{3}$.

Flashcard 96: If $a : b = 4 : 5$, what is the value of $\frac{a}{b}$?

Answer: $\frac{4}{5}$. Ratio notation $a:b$ equals the fraction $\frac{a}{b}$.

Flashcard 97: Express the ratio 14:42 in simplest form.

Answer: $1:3$. Divide both terms by their GCD of 14.

Flashcard 98: Convert the ratio 7:28 to its simplest form.

Answer: $1:4$. Divide both terms by their GCD of 7.

Flashcard 99: Identify the means in the proportion $\frac{a}{b} = \frac{c}{d}$.

Answer: Means are $b$ and $c$. The middle terms in a proportion are the means.

Flashcard 100: Express the ratio 14:42 in simplest form.

Answer: $1:3$. Divide both terms by their GCD of 14.