To simplify the expression [tex]\(\frac{64 a b}{72 a b}\)[/tex], follow these steps:
1. Identify and factor out the common terms:
Both the numerator and the denominator have the common variable factors [tex]\(a\)[/tex] and [tex]\(b\)[/tex]. So, the expression can be rewritten as:
[tex]\[
\frac{64 \cdot a \cdot b}{72 \cdot a \cdot b}
\][/tex]
2. Cancel out the common variable factors:
Since [tex]\(a\)[/tex] and [tex]\(b\)[/tex] appear in both the numerator and the denominator, they can be canceled out:
[tex]\[
\frac{64 \cdot a \cdot b}{72 \cdot a \cdot b} = \frac{64}{72}
\][/tex]
3. Simplify the numerical fraction:
To simplify the fraction [tex]\(\frac{64}{72}\)[/tex], we need to find the greatest common divisor (GCD) of 64 and 72. The GCD of 64 and 72 is 8.
4. Divide the numerator and the denominator by the GCD:
Simplify the fraction by dividing both the numerator and the denominator by their GCD:
[tex]\[
\frac{64 \div 8}{72 \div 8} = \frac{8}{9}
\][/tex]
5. Write the final simplified expression:
Since we had canceled [tex]\(a\)[/tex] and [tex]\(b\)[/tex] earlier, the final simplified form of the original expression [tex]\(\frac{64 a b}{72 a b}\)[/tex] is:
[tex]\[
\frac{8}{9}
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\frac{8 a b}{9 a b} = \frac{8}{9}
\][/tex]
