14/8 added to 284/2 in Fraction Form

The result of 14/8 added to 284/2 is: 143 3/4

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions \(\frac148\) and \(\frac2842\).

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 8 and 2 is 8.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac148\) to \(\frac{14}8\)
Convert \(\frac2842\) to \(\frac{1136}8\)

Step 4: Add the Numerators

Add the numerators: 14 + 1136 = 1150

Step 5: Simplify the Fraction

We can simplify \(\frac11508\) to its lowest form.
The greatest common divisor (GCD) of 1150 and 8 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac5754\).

Step 6: Convert to Mixed Number

The fraction \(\frac5754\) can be written as the mixed number \(143\frac34\).

Final Answer

The result of 14/8 added to 284/2 is:

\[ \frac{14}{8} + \frac{284}{2} = 143\frac34 \]

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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