First, find the number of pages Liam has read. Multiply the total number of pages by the fraction he has read: \(\frac{2}{5} \times 120 = \frac{240}{5} = 48\) pages. The question asks for the number of pages left to read, so subtract the pages read from the total: \(120 - 48 = 72\) pages. Alternatively, find the fraction of the book left to read: \(1 - \frac{2}{5} = \frac{3}{5}\). Then, calculate this fraction of the total pages: \(\frac{3}{5} \times 120 = 72\) pages.

First, calculate the number of chickens: \(\frac{3}{8} \times 80 = 3 \times 10 = 30\) chickens. Next, calculate the number of cows: \(\frac{1}{5} \times 80 = 16\) cows. The question asks for how many more chickens there are than cows, so find the difference: \(30 - 16 = 14\).

First, find the number of quarters: \(\frac{3}{8} \times 40 = 15\) quarters. The value of the quarters is \(15 \times $0.25 = $3.75\). Next, find the number of dimes. The rest of the coins are dimes, so \(40 - 15 = 25\) dimes. The value of the dimes is \(25 \times $0.10 = $2.50\). Finally, add the values together to find the total value of the collection: \($3.75 + $2.50 = $6.25\).

Let T be the total number of people. The difference in the fraction of children and teenagers is \(\frac{1}{2} - \frac{1}{5} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}\). This difference represents 12 people, so \(\frac{3}{10}T = 12\). To find the total T, first find what \(\frac{1}{10}T\) is: \(12 \div 3 = 4\). Then the total T is \(4 \times 10 = 40\) people. The fraction of adults is \(1 - (\frac{1}{2} + \frac{1}{5}) = 1 - \frac{7}{10} = \frac{3}{10}\). The number of adults is \(\frac{3}{10}\) of the total: \(\frac{3}{10} \times 40 = 12\).

First, find the total fraction of the ribbon that was cut off. Since both fractions are of the original length, add them together: \(\frac{1}{5} + \frac{1}{2} = \frac{2}{10} + \frac{5}{10} = \frac{7}{10}\). The fraction of the ribbon that is left is \(1 - \frac{7}{10} = \frac{3}{10}\). This remaining \(\frac{3}{10}\) is equal to 18 inches. If \(\frac{3}{10}\) of the length is 18 inches, then \(\frac{1}{10}\) of the length is \(18 \div 3 = 6\) inches. The original length (\(\frac{10}{10}\)) is \(6 \times 10 = 60\) inches.

Calculate the amount of grape juice: \(\frac{4}{9} \times 36 = 16\) ounces. Calculate the amount of apple juice: \(\frac{1}{3} \times 36 = 12\) ounces. The total amount of juice is \(16 + 12 = 28\) ounces. To find the amount of sparkling water, subtract the juice amount from the total: \(36 - 28 = 8\) ounces. Alternatively, add the fractions \(\frac{4}{9} + \frac{1}{3} = \frac{7}{9}\). The remaining fraction for water is \(1 - \frac{7}{9} = \frac{2}{9}\). Then \(\frac{2}{9} \times 36 = 8\) ounces.

First, find the number of tulips: \(\frac{1}{3} \times 72 = 24\). Then, find the number of daffodils: \(\frac{1}{6} \times 72 = 12\). The total number of tulips and daffodils is \(24 + 12 = 36\). To find the number of roses, subtract this sum from the total number of flowers: \(72 - 36 = 36\). So, there are 36 roses.

This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In this scenario, 8 pencils out of 24 total are given away, and we need to identify what fraction 8 represents. The correct choice is B because 8 is 1/3 of 24 (since 24 ÷ 3 = 8, or 8 × 3 = 24). Choice A (1/2) would be 12 pencils, while choice C (1/4) would be 6 pencils. To help students: Emphasize checking fractions by multiplying - if 8 is 1/3 of the total, then 8 × 3 should equal 24. Practice identifying fractions from given parts and wholes to strengthen understanding of the relationship.

This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In this scenario, 16 party favors are shared equally among 4 friends, so each gets 16 ÷ 4 = 4 favors. The correct choice is B because each friend's share of 4 favors represents 4/16 = 1/4 of the total. Choice A (1/2) would mean each friend gets 8 favors, while choice C (1/3) would work if there were only 3 friends. To help students: Connect division problems to fractions by showing that equal sharing creates fractional parts. Practice converting between "each person gets X items" and "each person gets 1/Y of the total."

This question tests ISEE Lower Level students on finding a fraction of a set or group. The concept involves understanding fractions as parts of a set and applying simple division to find the part. In this scenario, we need to determine what fraction each friend gets when 16 party favors are shared equally among 4 friends. The correct choice is C because each friend gets 16 ÷ 4 = 4 favors, which is 4/16 = 1/4 of the total. Choice A (1/2) would mean each friend gets 8 favors, while choice B (1/3) would require 3 friends. To help students: Emphasize that equal sharing creates fractions, where the number of people becomes the denominator. Practice problems where students identify both the number of items per person and the fraction of the whole.