1 / 31

RATIONAL NUMBERS

RATIONAL NUMBERS. Fractions. INTEGERS. WHAT IS AN INTEGER? The integers consist of the positive natural numbers ( 1 , 2 , 3 , …), their negatives (−1, −2, −3, ...) and the number zero . . RATIONAL NUMBERS. WHAT IS A RATIONAL NUMBER?

vaughan
Télécharger la présentation

RATIONAL NUMBERS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. RATIONAL NUMBERS Fractions

  2. INTEGERS • WHAT IS AN INTEGER? • The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.

  3. RATIONAL NUMBERS • WHAT IS A RATIONAL NUMBER? • In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fractiona/b, where b is not zero.

  4. RATIONAL NUMBERS • WHAT IS A RATIONAL NUMBER? • In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fractiona/b, where b is not zero. • EXAMPLES: • , 0.25, , -0.125 1 4 -5 4

  5. ADDING FRACTIONS • To add two fractions with the samedenominator, add the numerators and place that sum over the common denominator • EXAMPLE: 3 5 1 5 4 5 + =

  6. ADDING FRACTIONS • To Add Fractions with different denominators: • Find the Least Common Denominator (LCD) of the fractions • Rename the fractions to have the LCD • Add the numerators of the fractions • Simplify the Fraction

  7. EXAMPLE 1 4 1 3 +

  8. Adding Fractions • To make the denominator of the first fraction 12, multiply both the numerator and denominator by 3. 1 4 1 3 x3 ? + = x3 ? 12 + =

  9. Adding Fractions • To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4. 1 4 1 3 x4 ? + = x4 3 12 ? 12 + =

  10. Adding Fractions • To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4. 1 4 1 3 x4 ? + = x4 3 12 4 12 + =

  11. Adding Fractions • We can now add the two fractions. 1 4 1 3 ? = + 7 12 3 12 4 12 + =

  12. TRY THIS 1 3 2 5 ? + =

  13. TRY THIS 1 3 2 5 x5 x3 ? + = x5 x3 5 15 6 15 ? + =

  14. TRY THIS 1 3 2 5 x5 x3 ? + = x5 x3 11 15 5 15 6 15 + =

  15. SUBTRACTING FRACTIONS • To Subtract Fractions with different denominators: • Find the Lowest Common Denominator (LCD) of the fractions • Rename the fractions to have the LCD • Subtract the numerators of the fractions • The difference will be the numerator and the LCD will be the denominator of the answer. • Simplify the Fraction

  16. TRY THIS 2 5 1 3 ? - =

  17. TRY THIS 2 5 1 3 x3 x5 ? - = x3 x5 6 15 5 15 ? - =

  18. TRY THIS 2 5 1 3 x3 x5 ? - = x3 x5 1 15 6 15 5 15 - =

  19. MULTIPLYING FRACTIONS • To Multiply Fractions: • Multiply the numerators of the fractions • Multiply the denominators of the fractions • Place the product of the numerators over the product of the denominators • Simplify the Fraction

  20. Multiplying Fractions • To multiply fractions, simply multiply the two numerators x = 3 5 ? ? 1 3 x =

  21. Multiplying Fractions • Then simply multiply the two denominators. 3 5 3 ? 1 3 x = x =

  22. Multiplying Fractions • Place the numerator over the denominator. 3 5 3 15 1 3 x = x =

  23. Multiplying Fractions • State in simplest form. 3 5 3 15 1 5 1 3 x = =

  24. DIVIDING FRACTIONS • To Divide Fractions: • Multiply the reciprocal of the second term ( fraction) • Multiply the numerators of the fractions • Multiply the denominators of the fractions • Place the product of the numerators over the product of the denominators • Simplify the Fraction

  25. Dividing Fractions • Example: 3 5 1 3 = ÷ Multiply by the reciprocal… 9 5 3 5 3 1 x =

  26. TRY THESE • 1) • 2) 1 4 2 3 x = 2 5 1 3 ÷ =

  27. TRY THESE • 1) • 2) 2 3 1 4 2 12 x = 2 5 1 3 ÷ =

  28. TRY THESE • 1) • 2) 2 3 1 4 1 6 2 12 x = = 2 5 1 3 ÷ =

  29. TRY THESE • 1) • 2) 2 3 1 4 1 6 2 12 x = = 2 5 1 3 ÷ = 2 5 3 1 x =

  30. TRY THESE • 1) • 2) 2 3 1 4 1 6 2 12 x = = 2 5 1 3 ÷ = 2 5 3 1 6 5 x =

  31. TRY THESE • 1) • 2) 2 3 1 4 1 6 2 12 x = = 2 5 1 3 ÷ = 1 5 2 5 3 1 6 5 1 x = =

More Related