Certainly! Let's simplify the given fraction step by step:
Given:
[tex]\[ \frac{5ab}{25bc} \][/tex]
Step 1: Factor out any common terms in the numerator and the denominator.
- The numerator is [tex]\(5ab\)[/tex].
- The denominator is [tex]\(25bc\)[/tex].
Step 2: Notice that both the numerator and denominator contain the variable [tex]\(b\)[/tex]. We can factor [tex]\(b\)[/tex] out from both.
[tex]\[ \frac{5ab}{25bc} = \frac{5a \cdot b}{25 \cdot b \cdot c} \][/tex]
Step 3: Cancel the common factor [tex]\(b\)[/tex] from the numerator and the denominator.
[tex]\[ \frac{5a \cdot b}{25 \cdot b \cdot c} = \frac{5a}{25c} \][/tex]
Step 4: Simplify the remaining expression by factoring out any common numerical coefficients. Here, [tex]\(5\)[/tex] is a common factor in both [tex]\(5a\)[/tex] and [tex]\(25c\)[/tex].
[tex]\[ \frac{5a}{25c} = \frac{5a}{5 \cdot 5c} = \frac{a}{5c} \][/tex]
So, the simplified form of the given fraction is:
[tex]\[ \frac{a}{5c} \][/tex]
Therefore:
[tex]\[ \frac{5ab}{25bc} = \frac{a}{5c} \][/tex]
