5th Grade Math Word Problems: Free Worksheets with Answers ... - Free Printable

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

1) Lucy's Running Distance
* Step 1: Identify the daily distance and the number of days. Lucy runs $\frac{5}{6}$ of a kilometer every day. A week has 7 days.
* Step 2: Multiply the daily distance by the number of days: $\frac{5}{6} \times 7$.
* Step 3: To multiply a fraction by a whole number, think of the whole number as a fraction over 1 ($\frac{7}{1}$). Multiply the numerators ($5 \times 7 = 35$) and the denominators ($6 \times 1 = 6$).
* Step 4: The result is $\frac{35}{6}$. This is an improper fraction. To make it a mixed number, see how many times 6 goes into 35. It goes in 5 times with 5 left over.
* Calculation: $5 \times 6 = 30$, and $35 - 30 = 5$. So, $5 \frac{5}{6}$.

2) Micah's Swimming Time
* Step 1: Find out how long it takes to swim 1 full kilometer. It takes 4 minutes to swim $\frac{1}{10}$ km. To get 1 whole km, you need ten $\frac{1}{10}$s. So, multiply the time by 10: $4 \text{ minutes} \times 10 = 40 \text{ minutes}$ per kilometer.
* Step 2: Calculate the time for 2 kilometers. Multiply the time for 1 km by 2: $40 \text{ minutes} \times 2 = 80 \text{ minutes}$.
* Alternative Method: You can also set up a proportion. If $\frac{1}{10}$ km takes 4 mins, then 2 km is 20 times larger than $\frac{1}{10}$ km (because $2 \div \frac{1}{10} = 20$). So, $4 \text{ minutes} \times 20 = 80 \text{ minutes}$.

3) Baseball Players
* Step 1: Find the number of left-handed players. There are 27 players total, and $\frac{1}{9}$ are left-handed. Calculate $\frac{1}{9}$ of 27: $27 \div 9 = 3$ left-handed players.
* Step 2: Find how many of those left-handed players are over 6 feet tall. We know there are 3 left-handed players, and $\frac{2}{3}$ of them are tall. Calculate $\frac{2}{3}$ of 3: $(3 \div 3) \times 2 = 1 \times 2 = 2$.

4) Pizzas with Mushrooms
* Step 1: Find the number of pizzas with toppings. Danny ordered 16 pizzas, and $\frac{3}{4}$ have toppings. Calculate $\frac{3}{4}$ of 16: $(16 \div 4) \times 3 = 4 \times 3 = 12$ pizzas with toppings.
* Step 2: Find how many of those have only mushrooms. Of the 12 pizzas with toppings, $\frac{1}{3}$ have olives, and the rest have mushrooms. This means $\frac{2}{3}$ have mushrooms (since $1 - \frac{1}{3} = \frac{2}{3}$).
* Step 3: Calculate $\frac{2}{3}$ of 12: $(12 \div 3) \times 2 = 4 \times 2 = 8$.

5) Birthday Cake
* Step 1: Identify the amount of leftover cake and the amount eaten. There was $\frac{5}{8}$ of a cake left. Mariah ate $\frac{1}{5}$ of that leftover amount.
* Step 2: Multiply the fractions to find the portion of the whole cake she ate: $\frac{1}{5} \times \frac{5}{8}$.
* Step 3: Multiply numerators ($1 \times 5 = 5$) and denominators ($5 \times 8 = 40$). The result is $\frac{5}{40}$.
* Step 4: Simplify the fraction. Both numbers can be divided by 5. $5 \div 5 = 1$ and $40 \div 5 = 8$. The simplified answer is $\frac{1}{8}$.

6) Cookie Boxes
* Step 1: Find the weight of one box of cookies. Each cookie weighs $\frac{2}{3}$ pounds, and there are 4 cookies in a box.
* Step 2: Multiply the weight of one cookie by the number of cookies in a box: $\frac{2}{3} \times 4$.
* Step 3: Think of 4 as $\frac{4}{1}$. Multiply numerators ($2 \times 4 = 8$) and denominators ($3 \times 1 = 3$). The result is $\frac{8}{3}$ pounds.
* Step 4: Convert to a mixed number. 3 goes into 8 two times with 2 left over. So, $2 \frac{2}{3}$ pounds.
*(Note: The total number of cookies, 36, is extra information not needed to find the weight of a single box).*

Final Answer:
1) $5 \frac{5}{6}$ kilometers
2) 80 minutes
3) 2 players
4) 8 pizzas
5) $\frac{1}{8}$ of the cake
6) $2 \frac{2}{3}$ pounds