Word Problems of fractions worksheets - Math Worksheets ... - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

1. Staff Fractions
* Goal: Find the fraction of staff that is female.
* Given: $\frac{5}{8}$ of the staff are male.
* Logic: The total staff represents one whole ($1$). To find the female portion, subtract the male portion from the whole. (Note: The information about part-time work is extra information not needed to solve for gender).
* Calculation:
$$1 - \frac{5}{8} = \frac{8}{8} - \frac{5}{8} = \frac{3}{8}$$
* Result: $\frac{3}{8}$ of the staff is female.

2. Shark Feeding
* Goal: Find how much fish is fed at night.
* Given:
* Morning feeding: $\frac{2}{15}$ ton.
* Afternoon feeding: $\frac{1}{15}$ ton *more* than morning.
* Total daily feeding: $\frac{1}{2}$ ton.
* Step 1: Find Afternoon amount.
$$\frac{2}{15} + \frac{1}{15} = \frac{3}{15} \text{ ton}$$
* Step 2: Find Morning + Afternoon total.
$$\frac{2}{15} + \frac{3}{15} = \frac{5}{15} \text{ ton}$$
*(Simplify $\frac{5}{15}$ to $\frac{1}{3}$)*.
* Step 3: Subtract from Daily Total to find Night amount.
$$\frac{1}{2} - \frac{1}{3}$$
*Common denominator is 6:*
$$\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$$
* Result: $\frac{1}{6}$ ton is fed at night.

3. Baby Otter Weight
* Goal: Find the average weight of a newborn otter.
* Given:
* Baby's weight: $\frac{7}{8}$ kg.
* This is $\frac{9}{10}$ kg *less* than the average.
* Logic: Since the baby is lighter, we must *add* the difference to the baby's weight to find the average.
* Calculation:
$$\frac{7}{8} + \frac{9}{10}$$
*Find common denominator for 8 and 10, which is 40.*
$$\frac{7 \times 5}{40} + \frac{9 \times 4}{40} = \frac{35}{40} + \frac{36}{40} = \frac{71}{40}$$
*Convert to mixed number:* $40$ goes into $71$ once with $31$ left over.
* Result: $1 \frac{31}{40}$ kilograms.

4. Penguin Nursery Time
* Goal: Find the total time the nursery is open.
* Given: Noon: $\frac{2}{3}$ hour. Afternoon: $\frac{5}{12}$ hour.
* Calculation:
$$\frac{2}{3} + \frac{5}{12}$$
*Convert $\frac{2}{3}$ to twelfths ($\times 4$ on top and bottom): $\frac{8}{12}$.*
$$\frac{8}{12} + \frac{5}{12} = \frac{13}{12}$$
*Convert to mixed number:*
* Result: $1 \frac{1}{12}$ hours.

5. Fish Length Comparison
* Goal: Find how much longer the orange fish is than the blue fish.
* Given: Orange: $\frac{7}{10}$ feet. Blue: $\frac{2}{15}$ feet. (The tank length is extra info).
* Calculation:
$$\frac{7}{10} - \frac{2}{15}$$
*Common denominator for 10 and 15 is 30.*
$$\frac{7 \times 3}{30} - \frac{2 \times 2}{30} = \frac{21}{30} - \frac{4}{30} = \frac{17}{30}$$
* Result: $\frac{17}{30}$ feet.

6. Octopus Weight
* Goal: Find the current weight.
* Given:
* Start: $\frac{5}{6}$ kg.
* Gain: $\frac{3}{10}$ kg.
* Loss: $\frac{1}{5}$ kg.
* Step 1: Add the gain.
$$\frac{5}{6} + \frac{3}{10}$$
*Common denominator is 30.*
$$\frac{25}{30} + \frac{9}{30} = \frac{34}{30} \text{ kg}$$
* Step 2: Subtract the loss.
$$\frac{34}{30} - \frac{1}{5}$$
*Convert $\frac{1}{5}$ to thirtieths ($\frac{6}{30}$).*
$$\frac{34}{30} - \frac{6}{30} = \frac{28}{30}$$
* Step 3: Simplify.
Divide top and bottom by 2: $\frac{14}{15}$.
* Result: $\frac{14}{15}$ kilograms.

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Final Answer:
1. 3/8
2. 1/6 ton
3. 1 31/40 kilograms
4. 1 1/12 hours
5. 17/30 feet
6. 14/15 kilograms