Question

Decompose the fraction in two different ways ​

Answer 1

To decompose
`\( (7)/(12) \)` into unit fractions, express it as
`\( (1)/(2) + (1)/(2) + (1)/(3) \)` . This representation involves summing fractions with denominators matching the prime factors of 12, verifying the decomposition's accuracy.

the fraction
`\( (7)/(12) \)` as an example.

Steps to Decompose
`\( (7)/(12) \)` into Unit Fractions:

Factorize the Denominator:

Find the prime factorization of the denominator ( 12 ).

-
`\( 12 = 2^2 * 3 \)`

Express the Numerator as a Sum of Unit Fractions:

Express the numerator ( 7 ) as a sum of fractions using the prime factors found in step 1.

`\( (7)/(12) = (1)/(2) + (1)/(2) + (1)/(3) \)`

This expression is based on the factorization of 12:
`\( 2^2 * 3 \),` where 2 is repeated twice and 3 appears once.

Verify the Result:

Sum up the unit fractions to confirm they equal the original fraction
`\( (7)/(12) \).`

`\( (1)/(2) + (1)/(2) + (1)/(3) = (7)/(12) \)`

Final Result:

`\( (7)/(12) \)` can be decomposed into unit fractions as
`\( (1)/(2) + (1)/(2)` +
`(1)/(3) \)`. The sum of these unit fractions equals the original fraction.

complete the question

"How to Decompose Fractions into Unit Fractions?"

Decomposing fractions into unit fractions involves expressing a given fraction as a sum of fractions, where each fraction in the sum has a numerator of 1. To decompose a fraction like
`\( (a)/(b) \)` into unit fractions:

1. Find factors of the denominator
`\( b \)`.

2. Express the numerator
`\( a \)` as a sum of these unit fractions.

3. Ensure that the sum of these unit fractions equals the original fraction
`\( (a)/(b) \).`