45/213 added to 31/4 in Fraction Form
The result of 45/213 added to 31/4 is: 7 273/284
Step-by-Step Solution
Step 1: Understand the Problem
We need to add the fractions \(\frac45213\) and \(\frac314\).
Step 2: Find the Least Common Multiple (LCM)
To add fractions, we need a common denominator. The LCM of 213 and 4 is 852.
Step 3: Convert Fractions to Equivalent Fractions
Convert \(\frac45213\) to \(\frac{180}852\)
Convert \(\frac314\) to \(\frac{6603}852\)
Step 4: Add the Numerators
Add the numerators: 180 + 6603 = 6783
Step 5: Simplify the Fraction
We can simplify \(\frac6783852\) to its lowest form.
The greatest common divisor (GCD) of 6783 and 852 is 3.
Dividing both numerator and denominator by the GCD, we get \(\frac2261284\).
Step 6: Convert to Mixed Number
The fraction \(\frac2261284\) can be written as the mixed number \(7\frac273284\).
Final Answer
The result of 45/213 added to 31/4 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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