How to Do Multiple Ways of Fractions Decomposition

A Step-by-step Guide to Do Multiple Ways of Fractions Decomposition

Here is a step-by-step guide to decomposing fractions in multiple ways:

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Step 1: Identify the fraction:

Determine the fraction you wish to decompose. For example, let’s choose the fraction (frac{5}{6}).

Step 2: Reduce the fraction, if possible:

Simplify the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, (frac{5}{6}) is already in its simplest form.

Step 3: Decompose using unit fractions:

a. Represent the fraction as the sum of unit fractions (fractions with a numerator of 1) with the same denominator.
Example: (frac{5}{6} = frac{1}{6}+ frac{1}{6} + frac{1}{6} + frac{1}{6} + frac{1}{6})

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Step 4: Decompose into smaller fractions with the same denominator:

a. Break the fraction into two or more fractions with the same denominator.
b. Simplify the resulting fractions, if possible.
Example: (frac{5}{6} = frac{4}{6} + frac{1}{6} → frac{2}{3} + frac{1}{6})

Step 5: Decompose using different denominators:

a. Find two or more fractions with different denominators that add up to the given fraction.
Example: ( frac{5}{6} = frac{1}{2} + frac{1}{3})

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Step 6: Decompose into a mixed number:

a. Represent the fraction as a mixed number by separating the whole number and the fractional part.
Example: ( frac{5}{6} = 0 + frac{5}{6} )

Step 7: Decompose using prime factorization (optional):

a. Find the prime factors of the numerator and denominator.
b. Represent the fraction using its prime factors.
Example: (frac{5}{6} = frac{5}{2*3} = frac{5}{2} * frac{1}{3})

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