177/21 added to 98/4 in Fraction Form

The result of 177/21 added to 98/4 is: 32 13/14

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{7} 721$ and $\frac{9}{8} 4$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 21 and 4 is 84.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{7} 721$ to $\frac{708}{8} 4$
Convert $\frac{9}{8} 4$ to $\frac{2058}{8} 4$

Step 4: Add the Numerators

Add the numerators: 708 + 2058 = 2766

Step 5: Simplify the Fraction

We can simplify $\frac{2}{7} 6684$ to its lowest form.
The greatest common divisor (GCD) of 2766 and 84 is 6.
Dividing both numerator and denominator by the GCD, we get $\frac{4}{6} 114$ .

Step 6: Convert to Mixed Number

The fraction $\frac{4}{6} 114$ can be written as the mixed number $32 \frac{1}{3} 14$ .

Final Answer

The result of 177/21 added to 98/4 is:

\frac{177}{21} + \frac{98}{4} = 32 \frac{1}{3} 14

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: