Interpreting Ratios - SSAT Middle Level Quantitative

1. Find the missing term: $4:7=x:21$. What is $x$?

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

2. What is the simplest form of the ratio $0.6:0.9$?

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

3. What is the ratio $1.5$ meters to $50$ centimeters in simplest form?

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

4. What is the ratio of $9$ cats to $12$ dogs in simplest form?

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

5. What does the ratio $a:b$ represent in words?

   $a$ 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.

6. What is the ratio of $18$ students who passed to $24$ students total in simplest form?

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

7. What is the ratio of $8$ red marbles to $24$ total marbles in simplest form?

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

8. If the ratio of cats to dogs is $1:4$, what fraction of the animals are dogs?

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

9. What does the ratio $a:b$ mean as a fraction of the first quantity to the second?

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

10. What is the ratio $5$ minutes to $2$ minutes written in simplest form?

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

11. What is the simplest form of the ratio $150:2{,}000$?

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

12. Which number should you divide both terms by to simplify $24:36$ in one step?

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

13. Identify the simplified ratio equivalent to $7:21$.

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

14. What is the simplest form of the ratio $45:60$?

    $3:4$. Divide both terms of $45:60$ by their greatest common divisor of $15$ to obtain the simplified form with coprime integers.

15. What is the simplest form of the ratio $12:18$?

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

16. If the ratio of apples to oranges is $2:3$, what fraction of the fruit are apples?

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

17. What is the simplest form of the ratio $16:24$?

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

18. What is the simplest form of the ratio $81:27$?

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

19. What is the ratio $3$ feet to $18$ inches in simplest form?

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

20. What is the simplest form of the ratio $\frac{3}{4}:\frac{9}{16}$?

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

21. What is the ratio of $15$ girls to $10$ boys written in simplest form?

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

22. What is the simplest form of the ratio $28:35$?

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

23. Find the missing term: $\frac{6}{x}=\frac{3}{5}$. What is $x$?

    $10$. Cross-multiply the proportions $\frac{6}{x}=\frac{3}{5}$ to solve for $x= \frac{6 \times 5}{3}$.

24. Which ratio is equivalent to $3:5$ when both terms are multiplied by $4$?

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

25. What is the ratio $2$ hours to $30$ minutes in simplest form?

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

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