5/8 + 5/4 + 2/5
Understand the Problem
The question is asking for the sum of three fractions: 5/8, 5/4, and 2/5. We will need to find a common denominator in order to add them together correctly.
Answer
$ \frac{91}{40} $
Answer for screen readers
The sum of the fractions is $ \frac{91}{40} $ or $ 2 \frac{11}{40} $.
Steps to Solve
- Identify the fractions to add
We have the following fractions:
$$ \frac{5}{8}, \frac{5}{4}, \frac{2}{5} $$
- Find the least common denominator (LCD)
The denominators of the fractions are 8, 4, and 5. The least common multiple of these numbers is 40. This will be our common denominator.
- Convert each fraction to have the common denominator
Next, we need to convert each fraction so they all have the denominator of 40.
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For $\frac{5}{8}$: $$ \frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40} $$
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For $\frac{5}{4}$: $$ \frac{5}{4} = \frac{5 \times 10}{4 \times 10} = \frac{50}{40} $$
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For $\frac{2}{5}$: $$ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} $$
Now we have the fractions:
$$ \frac{25}{40}, \frac{50}{40}, \frac{16}{40} $$
- Add the fractions
Now that all fractions have the same denominator, we can add them:
$$ \frac{25}{40} + \frac{50}{40} + \frac{16}{40} = \frac{25 + 50 + 16}{40} = \frac{91}{40} $$
- Simplify if necessary
The fraction $\frac{91}{40}$ is already in its simplest form but can also be expressed as a mixed number:
$$ \frac{91}{40} = 2 \frac{11}{40} $$
The sum of the fractions is $ \frac{91}{40} $ or $ 2 \frac{11}{40} $.
More Information
The result $ \frac{91}{40} $ means that when you add these fractions together, you have taken a total of 91 parts out of 40 equal parts. The mixed number $ 2 \frac{11}{40} $ indicates that this is slightly more than 2.
Tips
- Not finding the least common denominator properly which may result in incorrect addition of the fractions.
- Forgetting to convert all fractions to the same denominator before adding.
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