1. Rules for expressing numbers often differ from place to place. Schools and companies often have "best usage guides" for students and employees to help them. In general, a number like 23 is too cumbersome to express in words, so you may express it in Arabic numbers. Then, according to a lot of people, once a writer uses Arabic numbers for one quantity in a passage, all the numbers should be expressed that way. The numerator is always over the denominator, no matter how large the quantities in a fraction. 2. She divided the cake into three equal pieces. You lost me on the eight-twenty thirds. Additional: yes, if the cake was divided into 8 equal pieces, you can say divided into "eighths". Likewise, if the cake is cut into 23 pieces, say divided into "twenty-thirds".

you can say "x over y" for any number. it's the most formal way and you can use it with any fraction. however, for certain more common fractions, there is an easier way to say it, so we usually prefer that. the following are the same way of saying the same fraction: (1/2) one over two （二分之一） => one half (一半） (1/3) one over three => one third (1/100) one over one hundred => one hundredth but we would never say: (572/175) five hundred twenty two over one hundred and seventy five ==XXXX==> five hundred twenty two "one hundred seventy fifths" as you can see, it would be ambiguous if we used this way of speaking for such a complicated number (since I cannot add quotation marks when i am speaking!), so we would instead use the standard form: five hundred twenty two OVER one hundred and seventy five

Yes, if the cake was divided into 8 equal pieces, you can say divided into "eighths". Likewise, if the cake is cut into 23 pieces, say divided into "twenty-thirds".