Interpreting Ratios - SSAT Middle Level: Quantitative

$1:3$. Divide both $8$ and $24$ by their greatest common divisor of $8$ to simplify the red-to-total marbles ratio.

$3:4$. Divide both $9$ and $12$ by their greatest common divisor of $3$ to simplify the cats-to-dogs ratio.

$1:3$. Divide both terms of $7:21$ by their greatest common divisor of $7$ to obtain the simplified equivalent ratio.

$5:2$. The terms $5$ and $2$ are coprime, so the ratio $5:2$ is already in its simplest form.

$4:1$. Convert $2$ hours to $120$ minutes, then divide $120:30$ by $30$ to simplify the ratio in consistent units.

$2:1$. Convert $3$ feet to $36$ inches, then divide $36:18$ by $18$ to simplify using consistent units.

$3:1$. Convert $1.5$ meters to $150$ centimeters, then divide $150:50$ by $50$ to simplify in matching units.

$3:40$. Divide both $150$ and $2,000$ by their greatest common divisor of $50$ to reach the simplest form.

$12:20$. Multiplying both terms of $3:5$ by $4$ produces an equivalent ratio with scaled values while maintaining the proportion.

$rac{2}{5}$. The fraction of apples is the apple parts divided by total parts, where total is $2+3=5$.

$rac{4}{5}$. The fraction of dogs is the dog parts divided by total animal parts, where total is $1+4=5$.

$3:4$. Divide both $18$ and $24$ by their greatest common divisor of $6$ to simplify the passed-to-total students ratio.

$a$ to $b$. The colon in the ratio $a:b$ is verbally expressed as '$a$ to $b$' to indicate the comparative relationship between the two quantities.

$rac{a}{b}$. The ratio $a:b$ expresses the relationship between $a$ and $b$ as the fraction $rac{a}{b}$, representing $a$ per unit of $b$.

$2:3$. Divide both terms of $12:18$ by their greatest common divisor of $6$ to simplify to the equivalent ratio with smallest integers.

$3:2$. Divide both $15$ and $10$ by their greatest common divisor of $5$ to express the girls-to-boys ratio in simplest terms.

$4:5$. Divide both terms of $28:35$ by their greatest common divisor of $7$ to reach the simplest equivalent ratio.

$2:3$. Divide both terms of $16:24$ by their greatest common divisor of $8$ to simplify to the lowest terms.

$3:1$. Divide both terms of $81:27$ by their greatest common divisor of $27$ to obtain the simplified ratio.

$4:3$. To simplify $rac{3}{4}:rac{9}{16}$, multiply both by $16$ to clear denominators, yielding $12:9$, then divide by $3$.

$2:3$. Multiply both decimals in $0.6:0.9$ by $10$ to get $6:9$, then divide by $3$ to simplify.

$12$. The greatest common divisor of $24$ and $36$ is $12$, which simplifies the ratio to $2:3$ in a single division step.

$12$. Set up the proportion $rac{4}{7}=rac{x}{21}$ and solve for $x$ by multiplying $4$ by $3$, since $7 imes 3=21$.

$10$. Cross-multiply the proportions $rac{6}{x}=rac{3}{5}$ to solve for $x= rac{6 imes 5}{3}$.