Question

1. the penguin nursery is open two times a day: $\frac{2}{3}$ hour at noon and $\frac{5}{12}$ hour in the afternoon. how much time is the penguin nursery open every day? 5. two kinds of fish can be found in a small tank that is $5\frac{1}{7}$ feet long. the blue fish is $\frac{2}{15}$ feet long and the orange fish is $\frac{7}{10}$ feet long. how much longer is the orange fish? 6. an octopus weighed $\frac{5}{6}$ kilograms. after two weeks, its weight was increased by $\frac{3}{10}$ kilograms. but afterwards, it lost $\frac{1}{5}$ kilograms in weight as it was sick. what is its current weight?

Explanation:

4.

Step1: Find a common - denominator

The common denominator of 3 and 12 is 12. $\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}$.

Step2: Add the fractions

The time open at noon is $\frac{8}{12}$ hour and in the afternoon is $\frac{5}{12}$ hour. So the total time is $\frac{8}{12}+\frac{5}{12}=\frac{8 + 5}{12}=\frac{13}{12}=1\frac{1}{12}$ hours.

Step1: Find a common - denominator

The common denominator of 15 and 10 is 30. $\frac{2}{15}=\frac{2\times2}{15\times2}=\frac{4}{30}$ and $\frac{7}{10}=\frac{7\times3}{10\times3}=\frac{21}{30}$.

Step2: Subtract the fractions

To find how much longer the orange fish is, we subtract the length of the blue fish from the length of the orange fish. $\frac{21}{30}-\frac{4}{30}=\frac{21 - 4}{30}=\frac{17}{30}$ feet.

Step1: Add the weight increase

The initial weight of the octopus is $\frac{5}{6}$ kilograms and it increased by $\frac{3}{10}$ kilograms. First, find a common - denominator. The common denominator of 6 and 10 is 30. $\frac{5}{6}=\frac{5\times5}{6\times5}=\frac{25}{30}$ and $\frac{3}{10}=\frac{3\times3}{10\times3}=\frac{9}{30}$. So the weight after the increase is $\frac{25}{30}+\frac{9}{30}=\frac{25 + 9}{30}=\frac{34}{30}$ kilograms.

Step2: Subtract the weight loss

It then lost $\frac{1}{5}$ kilograms. Since $\frac{1}{5}=\frac{1\times6}{5\times6}=\frac{6}{30}$, the current weight is $\frac{34}{30}-\frac{6}{30}=\frac{34 - 6}{30}=\frac{28}{30}=\frac{14}{15}$ kilograms.

Answer:

$1\frac{1}{12}$ hours

5.