AI Tutor
Would you rather have 12\frac{1}{2} of 10 cookies or 14\frac{1}{4} of 40 cookies?
Even though 14\frac{1}{4} looks smaller than 12\frac{1}{2}, 14\frac{1}{4} of 40 is 10 cookies, while 12\frac{1}{2} of 10 is only 5 cookies! To compare fractions of different groups, we have to find the actual amount first.

Finding a Fraction of a Number

A fraction has two parts: the denominator (bottom number) tells you how many equal groups to make, and the numerator (top number) tells you how many of those groups to take.
To find a fraction of any total, first divide the total by the denominator, then multiply your answer by the numerator.
Now that we know how to find one amount, how do we compare two different fractions with different totals?

Step-by-Step Comparison

Let's compare 23\frac{2}{3} of 30 and 34\frac{3}{4} of 28 using the symbols << (less than), >> (greater than), or == (equal to).
First, calculate the left side: 30÷3=1030 \div 3 = 10, and 10×2=2010 \times 2 = \mathbf{20}.
Next, calculate the right side: 28÷4=728 \div 4 = 7, and 7×3=217 \times 3 = \mathbf{21}.
Since 2020 is smaller than 2121, we write: 23 of 30<34 of 28\frac{2}{3} \text{ of } 30 < \frac{3}{4} \text{ of } 28