Ratios & Proportions - SAT Math

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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