5/42 subtracted by 13/3 in Fraction Form

The result of 5/42 subtracted by 13/3 is: -5 11/14

Step-by-Step Solution

Step 1: Understand the Problem

We need to subtract the fraction $\frac{1}{3} 3$ from $\frac{5}{4} 2$ .

Step 2: Find the Least Common Multiple (LCM)

To subtract fractions, we need a common denominator. The LCM of 42 and 3 is 42.

Step 3: Convert Fractions to Equivalent Fractions

Convert $\frac{5}{4} 2$ to $\frac{5}{4} 2$
Convert $\frac{1}{3} 3$ to $\frac{182}{4} 2$

Step 4: Subtract the Numerators

Subtract the numerators: 5 - 182 = -177

Step 5: Simplify the Fraction

We can simplify $\frac{-}{1} 7742$ to its lowest form.
The greatest common divisor (GCD) of -177 and 42 is 3.
Dividing both numerator and denominator by the GCD, we get $\frac{-}{5} 914$ .

Step 6: Convert to Mixed Number

The fraction $\frac{-}{5} 914$ can be written as the mixed number $- 5 \frac{1}{1} 14$ .

Final Answer

The result of 5/42 subtracted by 13/3 is:

\frac{5}{42} - \frac{13}{3} = - 5 \frac{1}{1} 14

Understanding Fraction Subtraction

How to Subtract Fractions

To subtract fractions, you need to ensure they have a common denominator. Then subtract 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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