To write the ratio of 13.5 to 15.75 in fractional notation in its lowest terms, follow these steps:
1. Express the ratio as a fraction:
Initially, we can write the ratio of 13.5 to 15.75 as the fraction [tex]\(\frac{13.5}{15.75}\)[/tex].
2. Convert decimal numbers to integers:
To eliminate the decimals, multiply both the numerator and the denominator by 100 (since both numbers have two decimal places):
[tex]\[
\frac{13.5 \times 100}{15.75 \times 100} = \frac{1350}{1575}
\][/tex]
3. Simplify the fraction:
Find the greatest common divisor (GCD) of 1350 and 1575. Once you have the GCD, divide both the numerator and the denominator by this number to simplify the fraction.
The GCD of 1350 and 1575 is 225.
4. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{1350 \div 225}{1575 \div 225} = \frac{6}{7}
\][/tex]
Therefore, the ratio of 13.5 to 15.75 in fractional notation in its lowest terms is [tex]\( \boxed{\frac{6}{7}} \)[/tex].
