Fractions

Things one must know:

• Proper fractions - the numerator is smaller than the denominator
• Improper fractions - the numerator is greater than the denominator
  
• Multiplying two proper fractions yields a smaller number
• Dividing two proper fractions yields a larger number
• Comparing fractions: multiply the numerator of one fraction with the denominator of the other fraction and vice versa
• When simplifying fractions that incorporate sums or differences, you may split up the terms of the numerator, but you may never split the terms of the denominator
• Two numbers are reciprocals of each other if their product equals 1. 
  
• When using benchmark values round some numbers up and others down
• Smart numbers: choose numbers equal to common multiples of the denominators of the fractions in the problem (MGMAT FDP p37)
• Pick smart numbers when no amounts are given in the problem, do not pick smart numbers when any amount or total is given
  
  Rules of positive fractions:
• Numerator goes up, the fraction increases
• Denominator goes up, the fraction decreases
• Adding the same number to both the numerator and the denominator brings the fraction closer to 1.
  - Adding to a proper fraction increases its value
  - Adding to an improper fraction decreases its value
  
• Multiplying or dividing both the numerator and the denominator by the same number does not change the value of the fraction