Ratios and Comparisons - ISEE Upper Level: Quantitative Reasoning
Card 1 of 23
If the ratio is $2:3$ and the first quantity is $14$, what is the second quantity?
If the ratio is $2:3$ and the first quantity is $14$, what is the second quantity?
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$21$. The first quantity 14 is 7 times 2, so multiply 3 by 7 to find the second.
$21$. The first quantity 14 is 7 times 2, so multiply 3 by 7 to find the second.
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Find and correct the ratio error: simplifying $18:24$ as $9:10$.
Find and correct the ratio error: simplifying $18:24$ as $9:10$.
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Correct: $18:24=3:4$. Simplify 18:24 by dividing both by 6, not incorrectly by 2 to get 9:12 or other errors.
Correct: $18:24=3:4$. Simplify 18:24 by dividing both by 6, not incorrectly by 2 to get 9:12 or other errors.
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Identify the equivalent ratio to $4:9$ among $8:18$, $6:16$, and $12:20$.
Identify the equivalent ratio to $4:9$ among $8:18$, $6:16$, and $12:20$.
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$8:18$. Check equivalents: 8:18 simplifies to 4:9 by dividing by 2, while others do not.
$8:18$. Check equivalents: 8:18 simplifies to 4:9 by dividing by 2, while others do not.
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What is the ratio of shaded to total if $9$ of $12$ squares are shaded, simplified?
What is the ratio of shaded to total if $9$ of $12$ squares are shaded, simplified?
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$3:4$. Shaded is 9 and total is 12, simplify by dividing both by 3.
$3:4$. Shaded is 9 and total is 12, simplify by dividing both by 3.
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A recipe uses flour to sugar in a $5:2$ ratio. If flour is $20$ cups, how much sugar is needed?
A recipe uses flour to sugar in a $5:2$ ratio. If flour is $20$ cups, how much sugar is needed?
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$8\ \text{cups}$. Flour is 5 parts equaling 20 cups, so 1 part is 4 cups, and sugar is 2 parts.
$8\ \text{cups}$. Flour is 5 parts equaling 20 cups, so 1 part is 4 cups, and sugar is 2 parts.
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If the ratio of cats to dogs is $3:5$ and there are $40$ dogs, how many cats are there?
If the ratio of cats to dogs is $3:5$ and there are $40$ dogs, how many cats are there?
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$24$. Dogs represent 5 parts equaling 40, so 1 part is 8, and cats are 3 parts.
$24$. Dogs represent 5 parts equaling 40, so 1 part is 8, and cats are 3 parts.
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If the ratio is $4:7$ and the total is $33$, what is the first quantity?
If the ratio is $4:7$ and the total is $33$, what is the first quantity?
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$12$. Total parts are 11, divide 33 by 11 to get 3 per part, then multiply by 4.
$12$. Total parts are 11, divide 33 by 11 to get 3 per part, then multiply by 4.
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What is the unit price (dollars per pound) for $\$9$ for $3$ lb?
What is the unit price (dollars per pound) for $\$9$ for $3$ lb?
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$\$3\ \text{per lb}$. Divide total cost by total pounds to find the price per pound.
$\$3\ \text{per lb}$. Divide total cost by total pounds to find the price per pound.
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What is the scale factor from $2:5$ to $6:15$?
What is the scale factor from $2:5$ to $6:15$?
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$3$. Each term in the first ratio is multiplied by 3 to obtain the second ratio.
$3$. Each term in the first ratio is multiplied by 3 to obtain the second ratio.
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What is the cross-multiplication condition for $\frac{a}{b}=\frac{c}{d}$?
What is the cross-multiplication condition for $\frac{a}{b}=\frac{c}{d}$?
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$ad=bc$. Cross-multiplication checks equality by verifying if the products of numerator and opposite denominator are equal.
$ad=bc$. Cross-multiplication checks equality by verifying if the products of numerator and opposite denominator are equal.
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What does the ratio $a:b$ mean in fraction form?
What does the ratio $a:b$ mean in fraction form?
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$\frac{a}{b}$. The ratio $a:b$ expresses the comparison of $a$ to $b$ as the fraction $\frac{a}{b}$.
$\frac{a}{b}$. The ratio $a:b$ expresses the comparison of $a$ to $b$ as the fraction $\frac{a}{b}$.
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What is the ratio of $12$ to $18$ in simplest form?
What is the ratio of $12$ to $18$ in simplest form?
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$2:3$. Simplify by dividing both 12 and 18 by their greatest common divisor of 6.
$2:3$. Simplify by dividing both 12 and 18 by their greatest common divisor of 6.
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What is the ratio of $45$ minutes to $2$ hours in simplest form?
What is the ratio of $45$ minutes to $2$ hours in simplest form?
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$3:8$. Convert 2 hours to 120 minutes, then simplify 45:120 by dividing both by 15.
$3:8$. Convert 2 hours to 120 minutes, then simplify 45:120 by dividing both by 15.
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What is the ratio of $3$ feet to $18$ inches in simplest form?
What is the ratio of $3$ feet to $18$ inches in simplest form?
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$2:1$. Convert 3 feet to 36 inches, then simplify 36:18 by dividing both by 18.
$2:1$. Convert 3 feet to 36 inches, then simplify 36:18 by dividing both by 18.
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What is the ratio of $0.6$ to $0.15$ in simplest form?
What is the ratio of $0.6$ to $0.15$ in simplest form?
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$4:1$. Divide 0.6 by 0.15 to get 4, or multiply both by 100 and simplify 60:15 by dividing by 15.
$4:1$. Divide 0.6 by 0.15 to get 4, or multiply both by 100 and simplify 60:15 by dividing by 15.
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What is the ratio of $\frac{3}{4}$ to $\frac{5}{8}$ in simplest form?
What is the ratio of $\frac{3}{4}$ to $\frac{5}{8}$ in simplest form?
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$6:5$. Divide $\frac{3}{4}$ by $\frac{5}{8}$ to get $\frac{6}{5}$, or find a common denominator to compare.
$6:5$. Divide $\frac{3}{4}$ by $\frac{5}{8}$ to get $\frac{6}{5}$, or find a common denominator to compare.
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What is the ratio of boys to total students if there are $12$ boys and $8$ girls?
What is the ratio of boys to total students if there are $12$ boys and $8$ girls?
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$3:5$. Total students are 20, so simplify 12:20 by dividing both by 4.
$3:5$. Total students are 20, so simplify 12:20 by dividing both by 4.
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What is the ratio of girls to boys if there are $12$ boys and $8$ girls, simplified?
What is the ratio of girls to boys if there are $12$ boys and $8$ girls, simplified?
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$2:3$. Girls are 8 and boys are 12, so simplify 8:12 by dividing both by 4.
$2:3$. Girls are 8 and boys are 12, so simplify 8:12 by dividing both by 4.
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What is the unit rate (miles per hour) for $150$ miles in $3$ hours?
What is the unit rate (miles per hour) for $150$ miles in $3$ hours?
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$50\ \text{mph}$. Divide total miles by total hours to find the rate per hour.
$50\ \text{mph}$. Divide total miles by total hours to find the rate per hour.
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What is the missing number $x$ in $\frac{7}{x}=\frac{21}{30}$?
What is the missing number $x$ in $\frac{7}{x}=\frac{21}{30}$?
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$10$. Cross-multiply to get $7 \times 30 = 21x$, then solve for $x$.
$10$. Cross-multiply to get $7 \times 30 = 21x$, then solve for $x$.
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What is the missing number $x$ in the proportion $5:8=x:40$?
What is the missing number $x$ in the proportion $5:8=x:40$?
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$25$. Solve by cross-multiplying: $5 \times 40 = 8x$, so $x = \frac{200}{8}$.
$25$. Solve by cross-multiplying: $5 \times 40 = 8x$, so $x = \frac{200}{8}$.
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What is the missing number $x$ in the proportion $\frac{3}{4}=\frac{x}{20}$?
What is the missing number $x$ in the proportion $\frac{3}{4}=\frac{x}{20}$?
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$15$. Solve by cross-multiplying or multiplying both sides by 20 and then by $\frac{3}{4}$.
$15$. Solve by cross-multiplying or multiplying both sides by 20 and then by $\frac{3}{4}$.
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Which is larger: $\frac{3}{5}$ or $\frac{5}{9}$?
Which is larger: $\frac{3}{5}$ or $\frac{5}{9}$?
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$\frac{3}{5}$. Compare by cross-multiplying: $3 \times 9 = 27$ and $5 \times 5 = 25$, since 27 > 25.
$\frac{3}{5}$. Compare by cross-multiplying: $3 \times 9 = 27$ and $5 \times 5 = 25$, since 27 > 25.
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