ACT 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 ACT 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 $x$ if $\frac{2x}{5}=\frac{6}{15}$?

Answer: $x=1$. Cross multiply: $15 \cdot 2x=5 \cdot 6$, so $x=1$.

Flashcard 2: Convert the ratio 7:2 to a fraction.

Answer: $\frac{7}{2}$. Write as fraction with numerator and denominator.

Flashcard 3: What is the value of $x$ if $\frac{5}{x} = \frac{10}{15}$?

Answer: 7.5. Cross multiply: $10x = 5 \cdot 15$.

Flashcard 4: What is the simplest form of the ratio $\frac{3}{4}:\frac{9}{10}$?

Answer: $5:6$. Convert to common denominators, then simplify the ratio.

Flashcard 5: Convert the ratio 7:2 to a fraction.

Answer: $\frac{7}{2}$. Write as fraction with numerator and denominator.

Flashcard 6: What is the direct variation equation if $y$ varies directly with $x$ and $y=12$ when $x=3$?

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

Flashcard 7: What is the cross-products condition for $\frac{a}{b}=\frac{c}{d}$?

Answer: $ad=bc$. Cross multiply: multiply diagonally opposite terms to check equality.

Flashcard 8: What is the missing value $x$ if $2.5:10=3:x$?

Answer: $x=12$. Set up proportion: $\frac{2.5}{10}=\frac{3}{x}$, cross multiply.

Flashcard 9: What is the missing value $x$ if $7:5=21:x$?

Answer: $x=15$. Set up proportion: $\frac{7}{5}=\frac{21}{x}$, cross multiply.

Flashcard 10: What is the ratio of 8 to 32 in simplest form?

Answer: 1:4. Divide both numbers by their GCD of 8.

Flashcard 11: What is the cross product of $\frac{1}{4} = \frac{3}{x}$?

Answer: x = 12. Cross multiply: $1 \cdot x = 4 \cdot 3$.

Flashcard 12: What is the missing value $x$ if $4:9=x:36$?

Answer: $x=16$. Set up proportion: $\frac{4}{9}=\frac{x}{36}$, cross multiply.

Flashcard 13: Determine the simplest form of the ratio 8:20.

Answer: 2:5. Divide both terms by their GCD of 4.

Flashcard 14: What is $x$ if $\frac{x}{12}=\frac{5}{8}$?

Answer: $x=7.5$. Cross multiply: $8x=60$, so $x=7.5$.

Flashcard 15: Convert the ratio 9:3 to a fraction.

Answer: $\frac{3}{1}$. Write as improper fraction $\frac{9}{3} = \frac{3}{1}$.

Flashcard 16: State the definition of a proportion.

Answer: An equation that shows two ratios are equal. Two ratios set equal form a proportion.

Flashcard 17: What is the ratio of 10 to 50 in simplest form?

Answer: 1:5. Divide both numbers by their GCD of 10.

Flashcard 18: Find the missing value in $\frac{15}{x} = \frac{45}{75}$.

Answer: x = 25. Cross-multiply: $15 \times 75 = x \times 45$, so $x = 25$.

Flashcard 19: What is the ratio of 20 dollars to 5 dollars?

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

Flashcard 20: What is $x$ if $x$ is $30\%$ of $80$?

Answer: $x=24$. Calculate $30\%$ of $80$: $0.30 \times 80=24$.

Flashcard 21: State the definition of a proportion.

Answer: An equation that equates two ratios. A proportion states two ratios are equal.

Flashcard 22: What is the unit price for $12 for $8$ items?

Answer: $1.50 per item. Divide total cost by number of items: $\frac{12}{8}=1.50$.

Flashcard 23: What is the percent of $45$ out of $60$?

Answer: $75\%$. Convert to percentage: $\frac{45}{60}=0.75=75\%$.

Flashcard 24: What is the ratio of $1.5$ meters to $60$ centimeters in simplest form?

Answer: $5:2$. Convert to same units: $150$ cm to $60$ cm, then simplify.

Flashcard 25: What is the ratio of 10 to 50 in simplest form?

Answer: 1:5. Divide both numbers by their GCD of 10.

Flashcard 26: Express the ratio 9:12 as a fraction in simplest form.

Answer: $\frac{3}{4}$. Simplify by dividing numerator and denominator by 3.

Flashcard 27: How do you express the ratio of 15 to 5?

Answer: 3:1. Divide both terms by their GCD of 5.

Flashcard 28: What is the simplest form of the ratio $14:49$?

Answer: $2:7$. Divide both terms by their GCD of 7.

Flashcard 29: What is $x$ if $\frac{x}{9}=\frac{4}{6}$?

Answer: $x=6$. Cross multiply: $6x=36$, so $x=6$.

Flashcard 30: What is the unit rate for $7.5$ gallons used in $3$ hours?

Answer: $2.5$ gallons per hour. Divide gallons by hours: $\frac{7.5}{3}=2.5$.

Flashcard 31: What is the ratio of 15 minutes to 1 hour?

Answer: 1:4. Convert 1 hour to 60 minutes, then simplify $15:60$.

Flashcard 32: What is the missing value $x$ if $4:9=x:36$?

Answer: $x=16$. Set up proportion: $\frac{4}{9}=\frac{x}{36}$, cross multiply.

Flashcard 33: Simplify the ratio 36 to 48.

Answer: 3:4. Divide both numbers by their GCD of 12.

Flashcard 34: What is the ratio of 0.5 to 2.5 in simplest form?

Answer: 1:5. Convert to whole numbers: $5:25$, then divide by 5.

Flashcard 35: Find the value of $x$ if $\frac{4}{x} = \frac{12}{36}$.

Answer: $x = 12$. Cross-multiply: $4 \times 36 = x \times 12$, so $x = 12$.

Flashcard 36: What is $x$ if $\frac{x}{15}=\frac{2}{3}$?

Answer: $x=10$. Cross multiply: $3x=30$, so $x=10$.

Flashcard 37: What is the simplest form of the ratio $0.6:1.5$?

Answer: $2:5$. Convert to fractions: $\frac{3}{5}:\frac{3}{2}$, then simplify.

Flashcard 38: What is the inverse variation equation if $y$ varies inversely with $x$ and $y=6$ when $x=5$?

Answer: $y=\frac{30}{x}$. Find constant $k$: $k=6 \cdot 5=30$, so $y=\frac{30}{x}$.

Flashcard 39: What does the ratio $a:b$ mean when written as a fraction?

Answer: $\frac{a}{b}$. A ratio expressed as a fraction shows the first term divided by the second.

Flashcard 40: What is $x$ if $\frac{x}{12}=\frac{5}{8}$?

Answer: $x=7.5$. Cross multiply: $8x=60$, so $x=7.5$.

Flashcard 41: What is the missing value $x$ if $5:8=15:x$?

Answer: $x=24$. Set up proportion: $\frac{5}{8}=\frac{15}{x}$, cross multiply.

Flashcard 42: State the formula for a proportion.

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

Flashcard 43: What is the unit rate (per $1$) for $180$ miles in $3$ hours?

Answer: $60$ miles per hour. Divide distance by time: $\frac{180}{3}=60$.

Flashcard 44: Identify the cross-multiplication method for $\frac{a}{b} = \frac{c}{d}$.

Answer: $a \times d = b \times c$. Cross-products of a proportion are equal.

Flashcard 45: Identify the extremes in $\frac{5}{8} = \frac{10}{16}$.

Answer: 5 and 16. Extremes are the first and last terms.

Flashcard 46: What is the unit rate for $7.5$ gallons used in $3$ hours?

Answer: $2.5$ gallons per hour. Divide gallons by hours: $\frac{7.5}{3}=2.5$.

Flashcard 47: Convert the ratio 18:6 to simplest form.

Answer: 3:1. Divide both numbers by their GCD of 6.

Flashcard 48: What is the ratio of 15 minutes to 1 hour?

Answer: 1:4. Convert 1 hour to 60 minutes, then simplify $15:60$.

Flashcard 49: What is $y$ if $y$ varies directly with $x$ and $y=10$ when $x=4$, then $x=6$?

Answer: $y=15$. Find constant: $k=\frac{10}{4}=2.5$, then $y=2.5(6)=15$.

Flashcard 50: What is $y$ if $y$ varies inversely with $x$ and $y=8$ when $x=3$, then $x=12$?

Answer: $y=2$. Find constant: $k=8 \cdot 3=24$, then $y=\frac{24}{12}=2$.

Flashcard 51: Express the ratio 30:120 as a fraction in simplest form.

Answer: $\frac{1}{4}$. Simplify by dividing numerator and denominator by 30.

Flashcard 52: Find the missing value in $\frac{15}{x} = \frac{45}{75}$.

Answer: x = 25. Cross-multiply: $15 \times 75 = x \times 45$, so $x = 25$.

Flashcard 53: If $\frac{a}{b} = \frac{c}{d}$, which are the means?

Answer: b and c. The means are the inner terms of the proportion.

Flashcard 54: What is the missing value $x$ if $7:5=21:x$?

Answer: $x=15$. Set up proportion: $\frac{7}{5}=\frac{21}{x}$, cross multiply.

Flashcard 55: What is the definition of an 'equivalent ratio'?

Answer: Ratios that express the same relationship. Different ratios that represent the same comparison.

Flashcard 56: What is the ratio of 20 to 30 in simplest form?

Answer: 2:3. Divide both terms by their GCD of 10.

Flashcard 57: What is $x$ if $\frac{x+4}{10}=\frac{3}{5}$?

Answer: $x=2$. Cross multiply: $5(x+4)=30$, so $x=2$.

Flashcard 58: Express the ratio of 14 to 42 in simplest form.

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

Flashcard 59: What is the inverse variation equation if $y$ varies inversely with $x$ and $y=6$ when $x=5$?

Answer: $y=\frac{30}{x}$. Find constant $k$: $k=6 \cdot 5=30$, so $y=\frac{30}{x}$.

Flashcard 60: What does the ratio $a:b$ mean when written as a fraction?

Answer: $\frac{a}{b}$. A ratio expressed as a fraction shows the first term divided by the second.

Flashcard 61: What is the missing value $x$ if $2.5:10=3:x$?

Answer: $x=12$. Set up proportion: $\frac{2.5}{10}=\frac{3}{x}$, cross multiply.

Flashcard 62: What is the decimal form of the ratio 2:5?

Answer: 0.4. Divide $2 \div 5 = 0.4$.

Flashcard 63: What is the scale factor from $\triangle A$ to $\triangle B$ if sides are $6$ and $15$?

Answer: $\frac{5}{2}$. Divide new length by original: $\frac{15}{6}=\frac{5}{2}$.

Flashcard 64: What is $x$ if $\frac{x+4}{10}=\frac{3}{5}$?

Answer: $x=2$. Cross multiply: $5(x+4)=30$, so $x=2$.

Flashcard 65: What is the ratio of $30$ minutes to $2$ hours in simplest form?

Answer: $1:4$. Convert to same units: $30$ min to $120$ min, then simplify.

Flashcard 66: What is the ratio of $250$ mL to $1.5$ L in simplest form?

Answer: $1:6$. Convert to same units: $250$ mL to $1500$ mL, then simplify.

Flashcard 67: Identify the cross-multiplication method for $\frac{a}{b} = \frac{c}{d}$.

Answer: $a \times d = b \times c$. Cross-products of a proportion are equal.

Flashcard 68: What is the ratio of $1.5$ meters to $60$ centimeters in simplest form?

Answer: $5:2$. Convert to same units: $150$ cm to $60$ cm, then simplify.

Flashcard 69: What is the equivalent ratio of 6:9?

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

Flashcard 70: What is the simplest form of the ratio $45:60$?

Answer: $3:4$. Divide both terms by their GCD of 15.

Flashcard 71: What is $x$ if $x$ is $30\%$ of $80$?

Answer: $x=24$. Calculate $30\%$ of $80$: $0.30 \times 80=24$.

Flashcard 72: Identify the extremes in the proportion $\frac{3}{5} = \frac{6}{10}$.

Answer: $3$ and $10$. Extremes are the outer terms in a proportion.

Flashcard 73: What is the decimal form of the ratio 3:20?

Answer: 0.15. Divide $3 \div 20 = 0.15$.

Flashcard 74: In the proportion $\frac{a}{b} = \frac{c}{d}$, identify the means.

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

Flashcard 75: Find the missing term: $\frac{5}{x} = \frac{15}{9}$.

Answer:

1. Cross multiply: $15x = 5 \cdot 9$.

Flashcard 76: Find the missing number in the proportion $\frac{2}{5} = \frac{8}{x}$.

Answer: x = 20. Cross-multiply: $2 \times x = 5 \times 8$, so $x = 20$.

Flashcard 77: What is the direct variation equation if $y$ varies directly with $x$ and $y=12$ when $x=3$?

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

Flashcard 78: Convert the ratio 9:3 to a fraction.

Answer: $\frac{3}{1}$. Write as improper fraction $\frac{9}{3} = \frac{3}{1}$.

Flashcard 79: Convert the ratio 16:4 to simplest form.

Answer: 4:1. Divide both numbers by their GCD of 4.

Flashcard 80: Find the value of $x$ if $\frac{4}{x} = \frac{12}{36}$.

Answer: x = 12. Cross-multiply: $4 \times 36 = x \times 12$, so $x = 12$.

Flashcard 81: What is the simplest form of the ratio $\frac{3}{4}:\frac{9}{10}$?

Answer: $5:6$. Convert to common denominators, then simplify the ratio.

Flashcard 82: What is $x$ if $\frac{x}{9}=\frac{4}{6}$?

Answer: $x=6$. Cross multiply: $6x=36$, so $x=6$.

Flashcard 83: Express the ratio 14:21 as a fraction in simplest form.

Answer: $\frac{2}{3}$. Simplify by dividing numerator and denominator by 7.

Flashcard 84: What is the simplest form of the ratio $14:49$?

Answer: $2:7$. Divide both terms by their GCD of 7.

Flashcard 85: If $\frac{7}{x} = \frac{21}{42}$, what is the value of $x$?

Answer:

1. Cross multiply: $21x = 7 \cdot 42$.

Flashcard 86: What is the ratio of $30$ minutes to $2$ hours in simplest form?

Answer: $1:4$. Convert to same units: $30$ min to $120$ min, then simplify.

Flashcard 87: Express the ratio 9:12 as a fraction in simplest form.

Answer: $\frac{3}{4}$. Simplify by dividing numerator and denominator by 3.

Flashcard 88: What is the simplified ratio of 75 to 100?

Answer: 3:4. Divide both terms by their GCD of 25.

Flashcard 89: Solve for $x$ if $\frac{x}{3} = \frac{5}{15}$.

Answer: $x = 1$. Cross-multiply: $x \times 15 = 3 \times 5$, so $x = 1$

Flashcard 90: What is the value of $x$ if $\frac{7}{x} = \frac{14}{28}$?

Answer:

1. Cross multiply: $14x = 7 \cdot 28$.

Flashcard 91: What is the ratio of 20 to 30 in simplest form?

Answer: 2:3. Divide both terms by their GCD of 10.

Flashcard 92: What is the equivalent ratio of 6:9?

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

Flashcard 93: If $a:b = 5:7$, what is the reciprocal ratio $b:a$?

Answer: 7:5. Reciprocal of $5:7$ is $7:5$.

Flashcard 94: Express the ratio 45:60 in simplest form.

Answer: 3:4. Divide both terms by their GCD of 15.

Flashcard 95: What is the ratio of 10 to 25 in simplest form?

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

Flashcard 96: If $a:b = 3:4$, what is $b:a$?

Answer: 4:3. Reciprocal of $3:4$ is $4:3$.

Flashcard 97: Find the missing term: $\frac{8}{x} = \frac{16}{24}$.

Answer:

1. Cross multiply: $16x = 8 \cdot 24$.

Flashcard 98: Express the ratio 45:60 in simplest form.

Answer: 3:4. Divide both terms by their GCD of 15.

Flashcard 99: What is the proportion if 3:4 = x:8?

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

Flashcard 100: Identify the simplest form of the ratio 9:12.

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