What is the total mass of the mixed nuts?
Understand the Problem
The question is asking for the total mass of three packets of mixed nuts, given their individual weights in kilograms. We need to sum the fractions of the weights to find the total mass.
Answer
The total mass of the mixed nuts is $\frac{7}{5}$ kg or $1 \frac{2}{5}$ kg.
Answer for screen readers
The total mass of the mixed nuts is $\frac{7}{5}$ kg or $1 \frac{2}{5}$ kg.
Steps to Solve
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Identify the weights of the packets The weights of the three packets are given as follows:
- Packet 1: $\frac{3}{10}$ kg
- Packet 2: $\frac{5}{10}$ kg
- Packet 3: $\frac{6}{10}$ kg
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Sum the fractions To find the total mass, we need to sum the three fractions. It's easier to ensure they have the same denominator, which they already do.
[ \text{Total mass} = \frac{3}{10} + \frac{5}{10} + \frac{6}{10} ]
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Add the numerators We add the numerators since the denominators are the same:
[ \frac{3 + 5 + 6}{10} = \frac{14}{10} ]
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Simplify the fraction We can simplify $\frac{14}{10}$:
[ \frac{14}{10} = \frac{7}{5} ]
This can also be expressed as a mixed number:
[ \frac{7}{5} = 1 \frac{2}{5} \text{ kg} ]
The total mass of the mixed nuts is $\frac{7}{5}$ kg or $1 \frac{2}{5}$ kg.
More Information
Kevin bought a total of 1.4 kg of mixed nuts (when expressed as a decimal). Each packet adds up to more than one kilogram, showing how combining smaller amounts can lead to a larger total.
Tips
- Forgetting to add fractions correctly: Ensure that when summing fractions, the denominators must remain the same throughout the process.
- Not simplifying the final fraction: Always check to see if the fraction can be simplified or expressed as a mixed number.
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