Fraction Operations Quiz

Answer explanation

To add \(\frac{1}{4}\) and \(\frac{5}{16}\), convert \(\frac{1}{4}\) to sixteenths: \(\frac{1}{4} = \frac{4}{16}\). Now add: \(\frac{4}{16} + \frac{5}{16} = \frac{9}{16}\). Thus, the correct answer is \(\frac{9}{16}\).

Answer explanation

To add \(\frac{3}{8} + \frac{2}{5}\), find a common denominator, which is 40. Convert the fractions: \(\frac{3}{8} = \frac{15}{40}\) and \(\frac{2}{5} = \frac{16}{40}\). Now add: \(\frac{15}{40} + \frac{16}{40} = \frac{31}{40}\).

Answer explanation

To find the distance from the fountain to the playground, subtract the distance from the basketball court to the playground from the distance from the fountain to the basketball court: 76 3/8 - 33 1/4 = 43 1/8 feet.

Answer explanation

To add \(\frac{13}{27} + \frac{2}{9}\), convert \(\frac{2}{9}\) to a fraction with a denominator of 27: \(\frac{2}{9} = \frac{6}{27}\). Now add: \(\frac{13}{27} + \frac{6}{27} = \frac{19}{27}\). Thus, the answer is \(\frac{19}{27}\).

Answer explanation

To add \( \frac{3}{10} \) and \( \frac{3}{5} \), convert \( \frac{3}{5} \) to tenths: \( \frac{3}{5} = \frac{6}{10} \). Now add: \( \frac{3}{10} + \frac{6}{10} = \frac{9}{10} \). Thus, the correct answer is \( \frac{9}{10} \).

Answer explanation

To subtract the fractions, first convert \( \frac{3}{10} \) to have a common denominator of 30: \( \frac{3}{10} = \frac{9}{30} \). Now, subtract: \( \frac{16}{30} - \frac{9}{30} = \frac{7}{30} \). Simplifying \( \frac{7}{30} \) gives \( \frac{2}{15} \).

Answer explanation

To add the mixed numbers, convert them to improper fractions: \(3 \frac{1}{2} = \frac{7}{2}\) and \(4 \frac{2}{5} = \frac{22}{5}\). Finding a common denominator (10), we get \(\frac{35}{10} + \frac{44}{10} = \frac{79}{10} = 8 \frac{1}{10}\).

Answer explanation

To add 4 \frac{1}{2} and 5 \frac{6}{15}, convert to improper fractions: 4 \frac{1}{2} = \frac{9}{2} and 5 \frac{6}{15} = \frac{81}{15}. Finding a common denominator (30), we get \frac{135}{30} + \frac{162}{30} = \frac{297}{30} = 9 \frac{1}{3}.

Answer explanation

To add the mixed numbers, convert them to improper fractions: $7 \frac{13}{15} = \frac{118}{15}$ and $4 \frac{2}{3} = \frac{14}{3} = \frac{70}{15}$. Then, add: $\frac{118}{15} + \frac{70}{15} = \frac{188}{15} = 12 \frac{8}{15}$. Simplifying gives $12 \frac{4}{5}$.

Answer explanation

To add the mixed numbers, convert them to improper fractions: 4 11/15 = 71/15 and 4 6/9 = 42/9. Find a common denominator (45), then add: (71/15)*(3/3) + (42/9)*(5/5) = 213/45 + 210/45 = 423/45 = 8 1/3.