To write the ratio of [tex]\( 25c \)[/tex] to [tex]\( 80d \)[/tex] in simplest form, follow these steps:
1. Identify the given ratio:
We are given the ratio [tex]\( 25c \)[/tex] to [tex]\( 80d \)[/tex].
2. Express this ratio as a fraction:
[tex]\[
\frac{25c}{80d}
\][/tex]
3. Find the greatest common divisor (GCD) of 25 and 80:
The GCD of 25 and 80 is 5.
4. Simplify the numerator and the denominator by dividing both by their GCD:
[tex]\[
\frac{25 \div 5}{80 \div 5} = \frac{5}{16}
\][/tex]
5. Write down the simplified fraction that represents the ratio:
[tex]\[
\frac{5c}{16d}
\][/tex]
Therefore, the ratio of [tex]\( 25c \)[/tex] to [tex]\( 80d \)[/tex] in simplest form is [tex]\( \frac{5c}{16d} \)[/tex].
So, the ratio in simplest form is:
[tex]\[ \boxed{\frac{5c}{16d}} \][/tex]
