Multiplying Fractions Word Problems Worksheet

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

1. The Pie Problem
* Step 1: Identify the starting amount and the fraction eaten. There is $\frac{4}{5}$ of a pie left. Sarah eats $\frac{1}{6}$ of that leftover part.
* Step 2: To find out how much she ate, multiply the two fractions:
$$\frac{4}{5} \times \frac{1}{6}$$
* Step 3: Multiply the top numbers (numerators) and the bottom numbers (denominators):
$$4 \times 1 = 4$$
$$5 \times 6 = 30$$
So, the fraction is $\frac{4}{30}$.
* Step 4: Simplify the answer. Both 4 and 30 can be divided by 2.
$$4 \div 2 = 2$$
$$30 \div 2 = 15$$
The simplified fraction is $\frac{2}{15}$.

2. The Cupcake Weight Problem
* Step 1: Identify the total number of cupcakes and the weight of one cupcake. There are 24 cupcakes. Each weighs $\frac{1}{10}$ pound.
* Step 2: Multiply the whole number by the fraction to find the total weight:
$$24 \times \frac{1}{10}$$
* Step 3: Think of 24 as $\frac{24}{1}$. Multiply across:
$$24 \times 1 = 24$$
$$1 \times 10 = 10$$
The result is $\frac{24}{10}$.
* Step 4: Simplify the fraction. Both numbers are even, so divide by 2:
$$24 \div 2 = 12$$
$$10 \div 2 = 5$$
The improper fraction is $\frac{12}{5}$.
* Step 5: Convert to a mixed number. 5 goes into 12 two times with a remainder of 2.
Answer: $2 \frac{2}{5}$ pounds.

3. The Salt Problem
* Step 1: Identify the total salt and the fraction used. There is $\frac{7}{8}$ kg of salt. Mrs. Jackson uses $\frac{2}{3}$ of it.
* Step 2: Multiply the fractions:
$$\frac{7}{8} \times \frac{2}{3}$$
* Step 3: Multiply straight across:
$$7 \times 2 = 14$$
$$8 \times 3 = 24$$
The fraction is $\frac{14}{24}$.
* Step 4: Simplify. Both numbers are divisible by 2:
$$14 \div 2 = 7$$
$$24 \div 2 = 12$$
The simplified fraction is $\frac{7}{12}$.

4. The Sugar Recipe Problem
* Step 1: Identify the sugar needed per batch and the number of batches. You need $\frac{9}{10}$ oz for one set of cookies. You are making 6 sets (cookies). *Note: The phrasing "make 6 cookies" in this context implies multiplying the ingredient amount by 6.*
* Step 2: Multiply the fraction by the whole number:
$$\frac{9}{10} \times 6$$
* Step 3: Treat 6 as $\frac{6}{1}$:
$$9 \times 6 = 54$$
$$10 \times 1 = 10$$
The fraction is $\frac{54}{10}$.
* Step 4: Simplify. Divide top and bottom by 2:
$$54 \div 2 = 27$$
$$10 \div 2 = 5$$
The fraction is $\frac{27}{5}$.
* Step 5: Convert to a mixed number. 5 goes into 27 five times ($5 \times 5 = 25$) with a remainder of 2.
Answer: $5 \frac{2}{5}$ oz.

Final Answer:
1. 2/15
2. 2 2/5 pounds
3. 7/12 kilograms
4. 5 2/5 oz