There are may ways on telling which fraction or ratio is largest. There is the LCD (least common denominator), percentages, visualization, and criss-cross multiplication. Here are some ways to tell which fraction is greater.

1. LCD

So most people know what least common multiple, right?

Least Common Multiple- The smallest number two or more numbers share.

LCD is the same thing except the LCM is the denominator. For example let's say our two fractions were 7/8 and 8/9. If we look at the two denominators, they're both 8 and 9. Now we have to find the LCM of the two numbers.

8•9= 72

Our LCM is 72. So now we have to change the numerators to the numbers we multiplied to get the denominator 72.

7/8•9/9=63/72 (7 *9 and 8*9)

8/9*8/8=64/72 (8*8 and 9*8)

Now your new fractions that can be reduced to your regular fractions (7/8 and 8/9) are now 7/8=63/72 and 8/9=64/72. You can easily see the greatest fraction is 64/72 or 8/9 because 64 is greater than 63.

2. Percentages

From fourth grade, all of you are supposed to know your percents and what fraction and decimal they equal. We could easily tell which fraction is greater by turning them into percents. So let's say we have 4/5 and 2/3. We could easily tell which one is greater by turning them into percents.

4/5=80%

2/3=66 2/3%

As you can see, the greatest fraction out of 4/5 and 2/3 is 4/5.

3. Visualization and explanation

This way is for people who like to be thorough in their math. For this way you'll need a fraction chart of all of the fractions from parts to 1/2 to 1/12.

Let's say we have the fractions 1/3 and 3/5. If we look on the fraction diagram 3/5 should be your answer. Your explanation should be close to this.

Ex. 1-3/5 is greater than 1/3 because on the fraction diagram for 3/5, you only have 2/5 more to get to a whole. For 1/3 however you'll need 2/3 more to get to a whole. Since 2/5 is a smaller amount to get to a whole than 1/3, 3/5 is greater.

4. Criss Cross Multiplication

This is a real shortcut in math when you're in a big hurry. Since I can't explain it or draw it very well here's a link that could help you.

https://www.mathsisfun.com/algebra/cross-multiply.html
If you have any questions, need any help or have any more advice to add please comment or answer below! Hope these tips are useful!