30/35 added to 21/4 in Fraction Form

The result of 30/35 added to 21/4 is: 6 3/28

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{0} 35$ and $\frac{2}{1} 4$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 35 and 4 is 140.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{0} 35$ to $\frac{120}{1} 40$
Convert $\frac{2}{1} 4$ to $\frac{735}{1} 40$

Step 4: Add the Numerators

Add the numerators: 120 + 735 = 855

Step 5: Simplify the Fraction

We can simplify $\frac{8}{5} 5140$ to its lowest form.
The greatest common divisor (GCD) of 855 and 140 is 5.
Dividing both numerator and denominator by the GCD, we get $\frac{1}{7} 128$ .

Step 6: Convert to Mixed Number

The fraction $\frac{1}{7} 128$ can be written as the mixed number $6 \frac{3}{2} 8$ .

Final Answer

The result of 30/35 added to 21/4 is:

\frac{30}{35} + \frac{21}{4} = 6 \frac{3}{2} 8

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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