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Fraction Worksheets

Click on the Fraction worksheet set you wish to view below.

  1. Addition and Subtraction of Rational Fractions
  2. Adding and Subtraction Algebraic Fractions
  3. Adding and Subtracting Mixed Numbers and Fractions
  4. Adding Mixed Numbers
  5. Adding Mixed Numbers
  6. Color Fractions Objects and Shapes
  7. Coloring Fractions
  8. Color Modeling Fractions
  9. Comparing Fractions
  10. Converting Percentages to Fractions and Decimals
  11. Decimals to Fractions and Percentages
  12. Dividing Mixed Numbers
  13. Dividing Mixed Numbers
  14. Division of Rational Fractions
  15. Evaluate Expressions with Fractional Exponents
  16. Fraction Addition
  17. Fraction Division
  18. Fraction Multiplication
  19. Fractions of Numbers
  20. Fractions of Simple Numbers
  21. Fractions to Decimals and Percentages
  22. Fraction Word Problems (Easy)
  23. Fraction Word Problems (with words)
  24. Fraction Word Problems
  25. Fraction Word Problems (Moderate)
  26. Making Mixed Numbers (Improper Fractions and Fractions)
  27. Matching Pictures, Words and Fractions
  28. Modeling Fractions
  29. Multiplication and Division of Algebraic Fractions
  30. Multiplication of Rational Fractions
  31. Multiplying Mixed Numbers
  32. Multiplying Mixed Numbers
  33. Reciprocals of Fractions and Whole Numbers
  34. Review of Fractions
  35. Rewriting Fractions
  36. Shade and Reduce Fractions
  37. Simple Fraction Word Problems
  38. Simplifying and Reducing Algebraic Fractions
  39. Simplify Complex Fractions
  40. Solving Fractional Equations
  41. Subtraction of Fractions
  42. Subtracting Mixed Numbers
  43. Subtracting Mixed Numbers
  44. Undefined Algebraic Fractions
  45. Undefined Fractions
  46. Visualizing Fractions

Fraction Worksheet Makers

  1. Basic Math Worksheet Maker
  2. Basic Operation Math Quiz Maker
  3. Decimals/Fractions
  4. Fractions
  5. Fractions with Models

What are fractions?

The word fraction means 'a part of the whole', it comes from the Latin word frangere which means to break. They are written with one number on top of another, the lower number tells you the size of the piece, and the upper number tells you how many pieces of that size you have. So, one piece, that is a quarter of the whole is written as 1/4 and two pieces would be written as 2/4. The lower number is called the denominator and the upper number (the 2 in 2/4) is the numerator.

One important rule with fractions is that when adding two fractions, the denominators must match. If they do, the numerators are added to get the final answer.

Example: 1/5 + 2/5 = 3/5. Only the top numbers add, and only when the bottom numbers match up.

 

How is this topic used in the real world?

The US Customary System of measurement is the official name for the system that uses inches, feet, and miles to measure lengths. The inch is too big for most accurate measurements (the kind you find in the building trades and in automobile repair work). Because of this, fractions of an inch often appear and have to be added and subtracted.

It is still common to find wrenches that are sized by fractions of an inch ( 5/8, 9/16 or 11/2 inch) and the standard two-by-four used in house construction is really 1 1/2 inches by 3 1/2 inches. Workers have to be able to add, subtract and multiply fractions.

A problem with fractions.

Fractions can be either proper or improper. An improper fraction has a numerator that is larger than the denominator: 6/5, 10/5 and 3/2 are all improper fractions. They are called improper because they represent an amount that is greater than one. 3/2 means three halves. Three halves is the same as one and a half. 11/2 is called a mixed fraction, because it has both a whole number (1 ) and a fraction (1/2). In mathematics, improper fractions are usually easier to use, but when talking about amounts in the real world, we usually say, "Add 1 and 1/4 cups of flour..." instead of saying, "Add 5/4 cups of flour."

A basic problem would be to convert a mixed fraction into an improper fraction.

2 1/2 = 2 + 1/2

2 = 4 X 1/2 = 4/2

finally, 4/2 + 1/2 = 5/2

Who invented fractions?

Simple fractions, like 1/2 or 1/3 are probably older than recorded history. They would have arisen naturally when some quantity had to be evenly divided. Think about how we cut a pie or a cake into equal fractions so that no one person gets more than a fair share.

Using fractions in a more formal, mathematical way is at least as old as the Egyptians (1000 BC) who only used fractions that had one as the numerator. In their system, there was no such thing as 3/4, rather, they would have to write 1/4 three times.

An interesting fact about coordinate fractions:

Zeno of Elea was famous for his paradoxes. Although he lived in the 5th century BC, the problems he posed are still talked about today, 2,400 years after his death.

Zeno said, if an arrow is shot toward a target, it first must travel half-way, and then it must travel half-way from this new place toward the target, and so on. At each step, the arrow travels half the remaining distance.

The distance traveled is 1/2 + 1/4 + 1/8 + 1/16 and so on forever.

To get to the target, the arrow has to travel all these smaller and smaller distances. Zeno claimed that since the series of fractions is infinite, the arrow can never reach the target, as it will always have just a little bit farther to go.


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