82/157 added to 2/2 in Fraction Form
The result of 82/157 added to 2/2 is: 1 82/157
Step-by-Step Solution
Step 1: Understand the Problem
We need to add the fractions \(\frac82157\) and \(\frac22\).
Step 2: Find the Least Common Multiple (LCM)
To add fractions, we need a common denominator. The LCM of 157 and 2 is 314.
Step 3: Convert Fractions to Equivalent Fractions
Convert \(\frac82157\) to \(\frac{164}314\)
Convert \(\frac22\) to \(\frac{314}314\)
Step 4: Add the Numerators
Add the numerators: 164 + 314 = 478
Step 5: Simplify the Fraction
We can simplify \(\frac478314\) to its lowest form.
The greatest common divisor (GCD) of 478 and 314 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac239157\).
Step 6: Convert to Mixed Number
The fraction \(\frac239157\) can be written as the mixed number \(1\frac82157\).
Final Answer
The result of 82/157 added to 2/2 is:
Understanding Fraction Addition
How to Add Fractions
To add fractions, you need to ensure they have a common denominator. Then add the numerators:
\( \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \) (when denominators are different)
Or simply \( \frac{a}{b} + \frac{c}{b} = \frac{a + c}{b} \) (when denominators are the same)
Why Simplify Fractions?
Simplifying fractions makes them easier to work with and understand. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
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