31/42 added to 146/4 in Fraction Form

The result of 31/42 added to 146/4 is: 37 5/21

Step-by-Step Solution

Step 1: Understand the Problem

We need to add the fractions $\frac{3}{1} 42$ and $\frac{1}{4} 64$ .

Step 2: Find the Least Common Multiple (LCM)

To add fractions, we need a common denominator. The LCM of 42 and 4 is 84.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{3}{1} 42$ to $\frac{62}{8} 4$
Convert $\frac{1}{4} 64$ to $\frac{3066}{8} 4$

Step 4: Add the Numerators

Add the numerators: 62 + 3066 = 3128

Step 5: Simplify the Fraction

We can simplify $\frac{3}{1} 2884$ to its lowest form.
The greatest common divisor (GCD) of 3128 and 84 is 4.
Dividing both numerator and denominator by the GCD, we get $\frac{7}{8} 221$ .

Step 6: Convert to Mixed Number

The fraction $\frac{7}{8} 221$ can be written as the mixed number $37 \frac{5}{2} 1$ .

Final Answer

The result of 31/42 added to 146/4 is:

\frac{31}{42} + \frac{146}{4} = 37 \frac{5}{2} 1

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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