83/43 added to 164/4 in Fraction Form

The result of 83/43 added to 164/4 is: 42 40/43

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{8}{3} 43$ and $\frac{1}{6} 44$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 43 and 4 is 172.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{8}{3} 43$ to $\frac{332}{1} 72$
Convert $\frac{1}{6} 44$ to $\frac{7052}{1} 72$

Step 4: Add the Numerators

Add the numerators: 332 + 7052 = 7384

Step 5: Simplify the Fraction

We can simplify $\frac{7}{3} 84172$ to its lowest form.
The greatest common divisor (GCD) of 7384 and 172 is 4.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{8} 4643$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{8} 4643$ can be written as the mixed number $42 \frac{4}{0} 43$ .

Final Answer

The result of 83/43 added to 164/4 is:

\frac{83}{43} + \frac{164}{4} = 42 \frac{4}{0} 43

Understanding Fraction Addition

How to Add Fractions

To add fractions, you need to ensure they have a common denominator. Then add the numerators:

$\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}$ (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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