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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?

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RATIONAL NUMBERS

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  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 = =

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