How do I decompose the fractions \(\frac{4}{5}\) and \(\frac{4}{7}\)?
Answer (3)
4 divided by 5= 0.80 4 divided by 7= 0.57142857142
The fractions 4/5 and 4/7 are in their simplest form and cannot be further decomposed as their numerators and denominators are prime to each other.
To decompose the fractions 4/5 and 4/7, we're looking for a way to break each fraction down into a sum or product of simpler fractions. In mathematics, this can sometimes involve breaking them down into a series of fractions whose numerators are a factor of the original numerator and whose denominators are both a factor of the original denominator and a factor of other denominators we would like to compare our fraction to. Let's start with the first fraction, 4/5.
Step 1: Prime factorize each numerator and denominator For 4/5, the numerator and denominator are already prime numbers, so this step doesn't apply here. The fraction cannot be simplified any further because 4 and 5 have no common factors except 1.
For 4/7, similarly, both the numerator and the denominator are prime numbers with no common factors other than 1, so the fraction is already in its simplest form and cannot be decomposed further.
Step 2: Find the Least Common Denominator (LCD) if you are working with multiple fractions If you were to compare or combine 4/5 and 4/7, you would find the LCD to multiply each fraction by a factor that would give them the same denominator.
Step 3: Decompose by creating a series of equivalent fractions For the purpose of this question, if we do not need to compare these fractions, there is no further decomposition to be done as both fractions are already in their simplest forms.
The fractions 5 4 and 7 4 cannot be decomposed further as they are already in simplified form. To work with them together, a common denominator of 35 can be found, allowing for operations like addition. Equivalent fractions would be 35 28 and 35 20 .
;
