A grocery store has 10 kilograms of granola. One customer buys 1 2/5 kilograms of granola. Another customer buys 3 4/5 kilograms. How much granola is left in the store?
Understand the Problem
The question is asking how much granola is left in the store after two customers make purchases. The initial amount of granola is 10 kilograms, and one customer buys 1 2/5 kilograms while another buys 3 4/5 kilograms. We will subtract the total purchased amount from the initial amount to find the remaining granola.
Answer
The amount of granola left in the store is \( 4 \frac{4}{5} \) kilograms.
Answer for screen readers
The amount of granola left in the store is ( 4 \frac{4}{5} ) kilograms.
Steps to Solve
- Convert mixed numbers to improper fractions
The first customer buys ( 1 \frac{2}{5} ) kilograms, which can be converted to an improper fraction: $$ 1 \frac{2}{5} = \frac{5 \cdot 1 + 2}{5} = \frac{7}{5} $$ The second customer buys ( 3 \frac{4}{5} ) kilograms, which converts to: $$ 3 \frac{4}{5} = \frac{5 \cdot 3 + 4}{5} = \frac{19}{5} $$
- Add the fractions together
Next, we add the amounts bought by both customers: $$ \text{Total bought} = \frac{7}{5} + \frac{19}{5} = \frac{7 + 19}{5} = \frac{26}{5} $$
- Convert the initial amount to a fraction
The initial amount of granola is ( 10 ) kilograms, which we can express as a fraction: $$ 10 = \frac{10 \cdot 5}{5} = \frac{50}{5} $$
- Subtract the total purchased from the initial amount
Now we subtract the total purchased from the initial amount: $$ \text{Remaining granola} = \frac{50}{5} - \frac{26}{5} = \frac{50 - 26}{5} = \frac{24}{5} $$
- Convert back to a mixed number
To express ( \frac{24}{5} ) as a mixed number:
- ( 24 \div 5 = 4 ) remainder ( 4 ) Thus, $$ \frac{24}{5} = 4 \frac{4}{5} $$
The amount of granola left in the store is ( 4 \frac{4}{5} ) kilograms.
More Information
Finding how much granola is left involves basic operations with fractions, including converting mixed numbers to improper fractions, adding them, and performing subtraction. This problem helps illustrate how to manage fractions effectively in a real-world scenario.
Tips
- Incorrectly adding fractions: Ensure that the denominators are the same before adding, especially with mixed numbers.
- Forgetting to convert back: When finishing operations, remember to convert improper fractions back to mixed numbers if required by the context.
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