Graph Interpretation - ISEE Lower Level Quantitative Reasoning

1. What is the approximate fraction if a bar reaches about $8$ on a scale from $0$ to $10$?

   $\frac{4}{5}$. Divide the bar height by the maximum scale value and simplify: $8 \div 10 = \frac{4}{5}$.

2. What is the approximate fraction if a bar reaches about $6$ on a scale from $0$ to $12$?

   $\frac{1}{2}$. Divide the bar height by the maximum scale value and simplify: $6 \div 12 = \frac{1}{2}$.

3. What is the total if a bar is at $18$ and this is $\frac{3}{4}$ of the total?

   $24$. Divide the bar value by the given fraction to find the total: $18 \div \frac{3}{4} = 24$.

4. What fraction of a whole does a pie slice represent if its central angle is about $72^\circ$?

   $\frac{1}{5}$. A central angle of $72^\circ$ represents one-fifth of a full $360^\circ$ circle, as $72 \div 360 = \frac{1}{5}$.

5. What is the total if a bar is at $12$ and this is $\frac{3}{8}$ of the total?

   $32$. Divide the bar value by the given fraction to find the total: $12 \div \frac{3}{8} = 32$.

6. What is the total if a bar is at $24$ and this is $\frac{2}{3}$ of the total?

   $36$. Divide the bar value by the given fraction to find the total: $24 \div \frac{2}{3} = 36$.

7. What fraction of a whole does a pie slice represent if its central angle is about $60^\circ$?

   $\frac{1}{6}$. A central angle of $60^\circ$ represents one-sixth of a full $360^\circ$ circle, as $60 \div 360 = \frac{1}{6}$.

8. What percent of a whole does a pie slice represent if its central angle is about $144^\circ$?

   $40\%$. Convert the angle fraction to percent by calculating $(144 \div 360) \times 100 = 40\%$.

9. What is the category value if the total is $64$ and the pie slice is $\frac{3}{8}$?

   $24$. Multiply the total by the fraction to find the category value: $64 \times \frac{3}{8} = 24$.

10. What percent of a whole does a pie slice represent if its central angle is about $36^\circ$?

    $10\%$. Convert the angle fraction to percent by calculating $(36 \div 360) \times 100 = 10\%$.

11. What is the category value if the total is $50$ and the pie slice is $10\%$?

    $5$. Multiply the total by the percentage as a decimal to find the category value: $50 \times 0.1 = 5$.

12. What is the ratio of two bar heights $12$ to $36$ in simplest form?

    $1:3$. Divide both heights by their greatest common divisor to simplify the ratio: $12:36 \div 12 = 1:3$.

13. What fraction of a whole does a pie slice represent if its central angle is about $120^\circ$?

    $\frac{1}{3}$. A central angle of $120^\circ$ represents one-third of a full $360^\circ$ circle, as $120 \div 360 = \frac{1}{3}$.

14. What is the category value if the total is $90$ and the pie slice is $\frac{1}{3}$?

    $30$. Multiply the total by the fraction to find the category value: $90 \times \frac{1}{3} = 30$.

15. What is the total if a bar is at $30$ and this is $\frac{3}{5}$ of the total?

    $50$. Divide the bar value by the given fraction to find the total: $30 \div \frac{3}{5} = 50$.

16. What is the category value if the total is $80$ and the pie slice is $25\%$?

    $20$. Multiply the total by the percentage as a decimal to find the category value: $80 \times 0.25 = 20$.

17. What is the approximate fraction if a bar reaches about $15$ on a scale from $0$ to $20$?

    $\frac{3}{4}$. Divide the bar height by the maximum scale value and simplify: $15 \div 20 = \frac{3}{4}$.

18. What is the difference between two bar heights $35$ and $20$ as read from a bar graph?

    $15$. Subtract the smaller bar height from the larger one: $35 - 20 = 15$.

19. What fraction of a whole does a pie slice represent if its central angle is about $45^\circ$?

    $\frac{1}{8}$. A central angle of $45^\circ$ represents one-eighth of a full $360^\circ$ circle, as $45 \div 360 = \frac{1}{8}$.

20. What is the total of two bar heights $18$ and $27$ as read from a bar graph?

    $45$. Add the heights of the two bars directly from the graph: $18 + 27 = 45$.

21. What is the total if a bar is at $28$ and this is $70\%$ of the total?

    $40$. Divide the bar value by the given percentage as a decimal to find the total: $28 \div 0.7 = 40$.

22. What fraction of a whole does a pie slice represent if its central angle is about $180^\circ$?

    $\frac{1}{2}$. A central angle of $180^\circ$ represents half of a full $360^\circ$ circle, as $180 \div 360 = \frac{1}{2}$.

23. What is the approximate fraction if a bar reaches about $9$ on a scale from $0$ to $12$?

    $\frac{3}{4}$. Divide the bar height by the maximum scale value and simplify: $9 \div 12 = \frac{3}{4}$.

24. What is the total if a bar is at $45$ and this is $75\%$ of the total?

    $60$. Divide the bar value by the given percentage as a decimal to find the total: $45 \div 0.75 = 60$.

25. What fraction of a whole does a pie slice represent if its central angle is about $90^\circ$?

    $\frac{1}{4}$. A central angle of $90^\circ$ represents one-quarter of a full $360^\circ$ circle, as $90 \div 360 = \frac{1}{4}$.

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