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Fractions

Fractions. Fractions. Numbers such as ½ and -¾ are called fractions . The number above the fraction line is called the numerator. The number below the fraction line is called the denominator. Reducing Fractions.

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Fractions

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  1. Fractions

  2. Fractions • Numbers such as ½ and -¾ are called fractions. • The number above the fraction line is called the numerator. • The number below the fraction line is called the denominator.

  3. Reducing Fractions • When both the numerator and denominator have a common divisor, we can reduce the fraction to its lowest terms. • A fraction is said to be in its lowest terms (or reduced) when the numerator and denominator are relatively prime (have no common divisors other than 1).

  4. To reduce a fraction to its lowest terms, divide both the numerator and the denominator by the GCD. • The fraction 6/10 is reduced to its lowest terms as follows.

  5. You Try… • Reduce to its lowest terms

  6. Mixed Numbers and Improper Fractions • The number 2¾ is an example of a mixed number. It is called a mixed number because it is made up of an integer and a fraction. • 2¾ means 2 + ¾ • An improper fraction is a fraction whose numerator is greater than its denominator.

  7. The figure shows improper fractions and mixed numbers….

  8. How do you convert mixed numbers to improper fractions?

  9. Example: Convert to Improper Fractions.

  10. How do you convert improper fractions to mixed numbers?

  11. Example: Convert to a mixed number.

  12. Example: Convert to a mixed number.

  13. Multiplication of Fractions • Multiply the numerators and multiply the denominators together then reduce if necessary.

  14. Examples

  15. Reciprocal • The reciprocal of any number is 1 divided by that number. • The product of a number and its reciprocal must equal 1.

  16. Division of Fractions • To find the quotient of two fractions, multiply the first fraction by the reciprocal of the second fraction.

  17. Example: Evaluate

  18. Addition and Subtraction of Fractions • Before we can add or subtract fractions, the fractions must have a lowest common denominator.

  19. Adding or Subtracting Fractions with Unlike Denominators • Use prime factorization to find the LCD for the denominator. • Example:

  20. Addition Example Now Reduce!

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