To simplify the fraction [tex]\(\frac{7ab}{28bc}\)[/tex], follow these steps:
1. Identify and divide out common factors:
- Both the numerator and the denominator have a common variable [tex]\( b \)[/tex].
- In addition, the numerical coefficients (7 and 28) have a common factor.
2. Numerically simplify the fraction:
- [tex]\(7\)[/tex] and [tex]\(28\)[/tex] can both be divided by their greatest common divisor (GCD), which is [tex]\(7\)[/tex].
- Dividing the numerator by [tex]\(7\)[/tex]: [tex]\( \frac{7}{7} = 1 \)[/tex].
- Dividing the denominator by [tex]\(7\)[/tex]: [tex]\( \frac{28}{7} = 4 \)[/tex].
This results in the fraction: [tex]\(\frac{1ab}{4bc}\)[/tex].
3. Cancel out the common variable [tex]\( b \)[/tex]:
- Both the numerator and the denominator have the variable [tex]\( b \)[/tex].
- Since [tex]\( b \)[/tex] appears in both the numerator and the denominator, it can be canceled out.
This results in the fraction: [tex]\(\frac{1a}{4c}\)[/tex].
4. Final simplified form:
- After canceling the common factors and variables, the simplified form of the fraction is [tex]\(\frac{a}{4c}\)[/tex].
Therefore, [tex]\(\frac{7ab}{28bc}\)[/tex] simplifies to [tex]\(\frac{a}{4c}\)[/tex].
