Introduction | Lesson Goals | Definitions | Procedures | Testing | Summary

Introduction

Operations with fractions can be confusing for many students. This is because a fraction has more than one number. Thus, addition-subtraction and multiplication-division are different for fractions than with whole numbers. And though operations with fractions are more complex than with whole numbers, there are just a few rules to learn. By learning and practicing these rules, operations with fractions can be handled with a minimum of difficulty.

Lesson Goals  (top)

By completing this lesson students should be able to:

  • Define a fraction and understand what it is.
     
  • Understand what numerators and denominators are.
     
  • Find common and least common denominators.
     
  • Multiply or divide numerators and denominators of a fraction by the same
      number, without changing the value of a fraction.
     
  • Understand what the bar of a fraction is.
     
  • Add fractions.
     
  • Subtract fractions.
     
  • Understand what an improper fraction is, and change it to a mixed number.
     
  • Understand what a mixed number is, and change it to an improper fraction.

Definitions  (top)

Fraction - A fraction is an indicated division, thus  indicates 3 is to be divided. A fraction is a portion of a whole number; thus  represents 3 of 4 parts of a quantity.
Numerator - the top number in a fraction. In  the number 3 is the numerator.

Denominator - the bottom number in a fraction. In  the number 4 is the denominator.
The bar of the fraction - In  the bar  () means 3 is to be divided by 4.Improper fraction - A fraction with a larger numerator than denominator, such as  which represents more than a whole number.

Mixed number - A whole number plus a fraction, such as 

Least common denominator - The smallest whole number that denominators of different fractions will divide into evenly. Thus,  for  and , the least common common denominator is 12.

Equivalent fractions - Different fractions that represent the same value. Thus,  and  are equivalent fractions.

 

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