Comparing fractions and mixed numbers

The  exercise appears under the Arithmetic Math Mission and Pre-algebra Math Mission. This exercise practices the ability to recognize relative sizes between mixed numbers and improper fractions.

Types of Problems
There is one type of problem in this exercise:


 * 1) Compare the mixed number and improper fraction: This problem provides two numbers, one of which is a mixed number and the other, an improper fraction. The student is asked to select which of the symbols <, >, or = can be placed between the numbers to make a true sentence. Cfamn1.png

Strategies
Knowledge of fractions as part of a whole will ensure success on this exercise.


 * 1) In most mathematics, improper fractions are preferred because operations can be performed more mechanically. However, in common conversation mixed numbers occur more frequently.
 * 2) Dividing the improper fraction (seeing how many wholes it contains) can often determine which fraction is larger quickly.
 * 3) A calculator would go against the spirit of the problem, but can transfer numbers into decimals which may increase efficiency for some.
 * 4) An equivalent improper fraction and mixed number does occur on this problem, so the equals sign will be used occasionally.

Real-life Applications

 * 1) Fractions can be a source of weakness for many students but are important in measurement, science and economics. The strengthening of fractions via geometric models will increase proficiency with fractions.