Ratios & Proportions - PSAT Math
Card 1 of 30
What is the new length if an $18$ cm segment is scaled by factor $\frac{5}{3}$?
What is the new length if an $18$ cm segment is scaled by factor $\frac{5}{3}$?
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$30$ cm. Multiply: $18 \times \frac{5}{3}=30$.
$30$ cm. Multiply: $18 \times \frac{5}{3}=30$.
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Identify whether the relationship is proportional: points $(1,2)$ and $(3,6)$.
Identify whether the relationship is proportional: points $(1,2)$ and $(3,6)$.
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Yes, $\frac{y}{x}=2$ for both points. Both points have the same ratio $\frac{y}{x}=2$.
Yes, $\frac{y}{x}=2$ for both points. Both points have the same ratio $\frac{y}{x}=2$.
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What is $x$ if $\frac{x+2}{10}=\frac{3}{5}$?
What is $x$ if $\frac{x+2}{10}=\frac{3}{5}$?
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$x=4$. Cross-multiply: $5(x+2)=30$, so $x+2=6$ and $x=4$.
$x=4$. Cross-multiply: $5(x+2)=30$, so $x+2=6$ and $x=4$.
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What is $x$ if $\frac{x}{12}=\frac{5}{8}$?
What is $x$ if $\frac{x}{12}=\frac{5}{8}$?
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$x=\frac{15}{2}$. Cross-multiply: $8x=60$, so $x=\frac{60}{8}=\frac{15}{2}$.
$x=\frac{15}{2}$. Cross-multiply: $8x=60$, so $x=\frac{60}{8}=\frac{15}{2}$.
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Which expression gives the constant of proportionality when $y$ is proportional to $x$?
Which expression gives the constant of proportionality when $y$ is proportional to $x$?
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$k=\frac{y}{x}$. The constant ratio between proportional quantities.
$k=\frac{y}{x}$. The constant ratio between proportional quantities.
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Identify the constant of proportionality in the table: $x=2,4,6$ and $y=10,20,30$.
Identify the constant of proportionality in the table: $x=2,4,6$ and $y=10,20,30$.
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$k=5$. Each $y$-value equals $5$ times its $x$-value.
$k=5$. Each $y$-value equals $5$ times its $x$-value.
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What is the equation for direct variation if $y$ varies directly with $x$ with constant $k$?
What is the equation for direct variation if $y$ varies directly with $x$ with constant $k$?
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$y=kx$. Direct variation means $y$ is a constant multiple of $x$.
$y=kx$. Direct variation means $y$ is a constant multiple of $x$.
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What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=18$ when $x=6$?
What is the constant of proportionality $k$ if $y$ is proportional to $x$ and $y=18$ when $x=6$?
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$k=3$. Find $k$ using $y=kx$: $18=k(6)$, so $k=3$.
$k=3$. Find $k$ using $y=kx$: $18=k(6)$, so $k=3$.
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What is the unit rate for $150$ miles in $3$ hours?
What is the unit rate for $150$ miles in $3$ hours?
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$50$ miles per hour. Divide total distance by total time: $\frac{150}{3}=50$.
$50$ miles per hour. Divide total distance by total time: $\frac{150}{3}=50$.
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What is the simplest form of the ratio $18:24$?
What is the simplest form of the ratio $18:24$?
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$3:4$. Divide both terms by their GCD of 6.
$3:4$. Divide both terms by their GCD of 6.
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What is the cross-products condition for $\frac{a}{b}=\frac{c}{d}$?
What is the cross-products condition for $\frac{a}{b}=\frac{c}{d}$?
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$ad=bc$. Cross-multiply to check if two ratios are equal.
$ad=bc$. Cross-multiply to check if two ratios are equal.
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What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?
What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?
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$\frac{a}{b}=\frac{c}{d}$ (with $b,d\ne 0$). Two ratios are equal when their cross-products are equal.
$\frac{a}{b}=\frac{c}{d}$ (with $b,d\ne 0$). Two ratios are equal when their cross-products are equal.
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What is the equation of a proportional relationship on a coordinate plane?
What is the equation of a proportional relationship on a coordinate plane?
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A line through the origin: $y=kx$. Proportional relationships pass through $(0,0)$ with slope $k$.
A line through the origin: $y=kx$. Proportional relationships pass through $(0,0)$ with slope $k$.
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What is $y$ if $y$ varies directly with $x$ and $y=14$ when $x=7$, then $x=10$?
What is $y$ if $y$ varies directly with $x$ and $y=14$ when $x=7$, then $x=10$?
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$y=20$. Find $k=2$ from first pair, then $y=2(10)=20$.
$y=20$. Find $k=2$ from first pair, then $y=2(10)=20$.
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What is the ratio of $x$ to $y$ if $x=27$ and $y=36$, in simplest form?
What is the ratio of $x$ to $y$ if $x=27$ and $y=36$, in simplest form?
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$3:4$. Simplify $\frac{27}{36}$ by dividing by GCD of 9.
$3:4$. Simplify $\frac{27}{36}$ by dividing by GCD of 9.
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What is the scale factor from a length $8$ to a length $12$?
What is the scale factor from a length $8$ to a length $12$?
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$\frac{3}{2}$. Scale factor is $\frac{\text{new}}{\text{old}}=\frac{12}{8}=\frac{3}{2}$.
$\frac{3}{2}$. Scale factor is $\frac{\text{new}}{\text{old}}=\frac{12}{8}=\frac{3}{2}$.
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What is $x$ if $\frac{7}{x}=\frac{21}{30}$?
What is $x$ if $\frac{7}{x}=\frac{21}{30}$?
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$x=10$. Cross-multiply: $21x=210$, so $x=10$.
$x=10$. Cross-multiply: $21x=210$, so $x=10$.
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Find $y$ if $y$ is proportional to $x$, $k=4$, and $x=7$.
Find $y$ if $y$ is proportional to $x$, $k=4$, and $x=7$.
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$y=28$. Use $y = kx$: $y = 4 \cdot 7 = 28$.
$y=28$. Use $y = kx$: $y = 4 \cdot 7 = 28$.
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What is the definition of a constant of proportionality $k$ in $y=kx$?
What is the definition of a constant of proportionality $k$ in $y=kx$?
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$k=\frac{y}{x}$. The constant $k$ is the ratio of $y$ to $x$ in a proportional relationship.
$k=\frac{y}{x}$. The constant $k$ is the ratio of $y$ to $x$ in a proportional relationship.
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What is the unit rate for $\frac{a}{b}$ (with $b\ne 0$) expressed “per $1$”?
What is the unit rate for $\frac{a}{b}$ (with $b\ne 0$) expressed “per $1$”?
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$\frac{a}{b}$ per $1$. Unit rate divides the numerator by the denominator to get the rate per one unit.
$\frac{a}{b}$ per $1$. Unit rate divides the numerator by the denominator to get the rate per one unit.
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What is the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$?
What is the cross-multiplication rule for $\frac{a}{b}=\frac{c}{d}$?
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$ad=bc$. Cross-multiply by multiplying the numerator of each fraction by the denominator of the other.
$ad=bc$. Cross-multiply by multiplying the numerator of each fraction by the denominator of the other.
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What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?
What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?
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$\frac{a}{b}=\frac{c}{d}$. A proportion states that two ratios are equal.
$\frac{a}{b}=\frac{c}{d}$. A proportion states that two ratios are equal.
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Find $x$ if $5:8=x:40$.
Find $x$ if $5:8=x:40$.
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$x=25$. Cross-multiply: $8x=200$, so $x=25$.
$x=25$. Cross-multiply: $8x=200$, so $x=25$.
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What value of $x$ makes the proportion $\frac{3}{4} = \frac{x}{20}$ true?
What value of $x$ makes the proportion $\frac{3}{4} = \frac{x}{20}$ true?
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$15$. Cross-multiply: $3 × 20 = 4x$, so $60 = 4x$ and $x = 15$.
$15$. Cross-multiply: $3 × 20 = 4x$, so $60 = 4x$ and $x = 15$.
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What is the constant of proportionality $k$ in the equation $y=kx$ (with $x\neq 0$)?
What is the constant of proportionality $k$ in the equation $y=kx$ (with $x\neq 0$)?
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$k=\frac{y}{x}$. Solve for $k$ by dividing both sides by $x$.
$k=\frac{y}{x}$. Solve for $k$ by dividing both sides by $x$.
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What is the decimal form of $r%$?
What is the decimal form of $r%$?
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$\frac{r}{100}$. To convert percent to decimal, divide by 100.
$\frac{r}{100}$. To convert percent to decimal, divide by 100.
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What is the percent equivalent of the ratio $\frac{p}{100}$?
What is the percent equivalent of the ratio $\frac{p}{100}$?
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$p%$. Percent means "per hundred," so $\frac{p}{100} = p%$.
$p%$. Percent means "per hundred," so $\frac{p}{100} = p%$.
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What is the cross-products condition for $\frac{a}{b}=\frac{c}{d}$ with $b\neq 0$ and $d\neq 0$?
What is the cross-products condition for $\frac{a}{b}=\frac{c}{d}$ with $b\neq 0$ and $d\neq 0$?
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$ad=bc$. Cross-multiply to get the products equal.
$ad=bc$. Cross-multiply to get the products equal.
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What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?
What is the definition of a proportion using ratios $\frac{a}{b}$ and $\frac{c}{d}$?
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$\frac{a}{b}=\frac{c}{d}$. Two ratios form a proportion when they are equal.
$\frac{a}{b}=\frac{c}{d}$. Two ratios form a proportion when they are equal.
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What is the definition of the ratio $a:b$ written as a fraction?
What is the definition of the ratio $a:b$ written as a fraction?
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$\frac{a}{b}$. A ratio $a:b$ is expressed as the fraction $\frac{a}{b}$.
$\frac{a}{b}$. A ratio $a:b$ is expressed as the fraction $\frac{a}{b}$.
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