177/23 added to 16/6 in Fraction Form

The result of 177/23 added to 16/6 is: 10 25/69

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{7} 723$ and $\frac{1}{6} 6$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 23 and 6 is 138.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{7} 723$ to $\frac{1062}{1} 38$
Convert $\frac{1}{6} 6$ to $\frac{368}{1} 38$

Step 4: Add the Numerators

Add the numerators: 1062 + 368 = 1430

Step 5: Simplify the Fraction

We can simplify $\frac{1}{4} 30138$ to its lowest form.
The greatest common divisor (GCD) of 1430 and 138 is 2.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{1} 569$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{1} 569$ can be written as the mixed number $10 \frac{2}{5} 69$ .

Final Answer

The result of 177/23 added to 16/6 is:

\frac{177}{23} + \frac{16}{6} = 10 \frac{2}{5} 69

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).

Fraction Calculator

Calculate operations between any two fractions: