8/3 added to 30/2 in Fraction Form

The result of 8/3 added to 30/2 is: 17 2/3

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions \(\frac83\) and \(\frac302\).

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 3 and 2 is 6.

Step 3: Convert Fractions to Equivalent Fractions

Convert \(\frac83\) to \(\frac{16}6\)
Convert \(\frac302\) to \(\frac{90}6\)

Step 4: Add the Numerators

Add the numerators: 16 + 90 = 106

Step 5: Simplify the Fraction

We can simplify \(\frac1066\) to its lowest form.
The greatest common divisor (GCD) of 106 and 6 is 2.
Dividing both numerator and denominator by the GCD, we get \(\frac533\).

Step 6: Convert to Mixed Number

The fraction \(\frac533\) can be written as the mixed number \(17\frac23\).

Final Answer

The result of 8/3 added to 30/2 is:

\[ \frac{8}{3} + \frac{30}{2} = 17\frac23 \]

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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