189/99 added to 21/4 in Fraction Form

The result of 189/99 added to 21/4 is: 7 7/44

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{1}{8} 999$ and $\frac{2}{1} 4$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 99 and 4 is 396.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{1}{8} 999$ to $\frac{756}{3} 96$
Convert $\frac{2}{1} 4$ to $\frac{2079}{3} 96$

Step 4: Add the Numerators

Add the numerators: 756 + 2079 = 2835

Step 5: Simplify the Fraction

We can simplify $\frac{2}{8} 35396$ to its lowest form.
The greatest common divisor (GCD) of 2835 and 396 is 9.
Dividing both numerator and denominator by the GCD, we get $\frac{3}{1} 544$ .

Step 6: Convert to Mixed Number

The fraction $\frac{3}{1} 544$ can be written as the mixed number $7 \frac{7}{4} 4$ .

Final Answer

The result of 189/99 added to 21/4 is:

\frac{189}{99} + \frac{21}{4} = 7 \frac{7}{4} 4

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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