17/2 added to 12/3 in Fraction Form
The result of 17/2 added to 12/3 is: 12 1/2
Step-by-Step Solution
Step 1: Understand the Problem
We need to add the fractions \(\frac172\) and \(\frac123\).
Step 2: Find the Least Common Multiple (LCM)
To add fractions, we need a common denominator. The LCM of 2 and 3 is 6.
Step 3: Convert Fractions to Equivalent Fractions
Convert \(\frac172\) to \(\frac{51}6\)
Convert \(\frac123\) to \(\frac{24}6\)
Step 4: Add the Numerators
Add the numerators: 51 + 24 = 75
Step 5: Simplify the Fraction
We can simplify \(\frac756\) to its lowest form.
The greatest common divisor (GCD) of 75 and 6 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac252\).
Step 6: Convert to Mixed Number
The fraction \(\frac252\) can be written as the mixed number \(12\frac12\).
Final Answer
The result of 17/2 added to 12/3 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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