1. RATIONAL NUMBERS

2. Mental Math Warm Up Number from 1-6 48+ 21= 56+38= 15+18+17= 125+186= 530+280= 176+125=

3. INTEGERS WHAT IS AN INTEGER?WHAT IS AN INTEGER? The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3,...) and the number zero.The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3,...) and the number zero.natural numbers123negativeszeronatural numbers123negativeszero

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

5. RATIONAL NUMBERS WHAT IS A RATIONAL NUMBER?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 fraction a/b, where b is not zero.In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.mathematicsfractionratio integers fractionzeromathematicsfractionratio integers fractionzero EXAMPLES:EXAMPLES: 1414

6. RATIONAL NUMBERS WHAT IS A RATIONAL NUMBER?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 fraction a/b, where b is not zero.In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.mathematicsfractionratio integers fractionzeromathematicsfractionratio integers fractionzero EXAMPLES:EXAMPLES:, 0.25, 0.25 1414

7. RATIONAL NUMBERS WHAT IS A RATIONAL NUMBER?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 fraction a/b, where b is not zero.In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.mathematicsfractionratio integers fractionzeromathematicsfractionratio integers fractionzero EXAMPLES:EXAMPLES:, 0.25,, 0.25, 1414 -5 4

8. RATIONAL NUMBERS WHAT IS A RATIONAL NUMBER?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 fraction a/b, where b is not zero.In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.mathematicsfractionratio integers fractionzeromathematicsfractionratio integers fractionzero EXAMPLES:EXAMPLES:, 0.25,, -0.125, 0.25,, -0.125 1414 -5 4

9. ADDING FRACTIONS  To add two fractions with the same denominator, add the numerators and place that sum over the common denominator  EXAMPLE: 3535 + 1515 = 4545

10. 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

11. EXAMPLE 1414 + 1313

12.  To make the denominator of the first fraction 12, multiply both the numerator and denominator by 3. Adding Fractions 1414 + 1313 ? = x3 ? 12 +=

13.  To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4. Adding Fractions 1414 + 1313 ? = x4 3 12 + ? 12 =

14.  To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4. Adding Fractions 1414 + 1313 ? = x4 3 12 + 4 12 =

15.  We can now add the two fractions. Adding Fractions 1414 + 1313 ? = 3 12 + 4 12 = 7 12

16. TRY THIS 1313 + 2525 ? =

17. 1313 + 2525 ? = 5 15 + 6 15 ? = x5 x3

18. TRY THIS 1313 + 2525 ? = 5 15 + 6 15 = x5 x3 11 15

19. 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

20. TRY THIS 2525 - 1313 ? =

21. 2525 - 1313 ? = 6 15 - 5 15 ? = x3 x5

22. TRY THIS 2525 - 1313 ? = 6 15 - 5 15 = x3 x5 1 15

23. 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

24. To multiply fractions, simply multiply the two numerators Multiplying Fractions 3535 x 1313 = x = ????

25. Then simply multiply the two denominators. 3535 x 1313 = x= 3?3? Multiplying Fractions

26. Place the numerator over the denominator. 3535 x 1313 = x= 3 15 Multiplying Fractions

27. If possible, state in simplest form. 3535 x 1313 = 3 15 = 1515 Multiplying Fractions

28. 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

29.  Example: 3535 ÷ 1313 Dividing Fractions = 3535 x 3131 = Multiply by the reciprocal… 9595

30. TRY THESE  1)  2) 2323 x 1414 = 2525 1313 = ÷

31. TRY THESE  1)  2) 2323 x 1414 = 2525 1313 = ÷ 2 12

32. TRY THESE  1)  2) 2323 x 1414 = 2525 1313 = ÷ 1616 = 2 12

33. TRY THESE  1)  2) 2323 x 1414 = 2525 1313 = ÷ 1616 = 2 12 2525 3131 x=

34. TRY THESE  1)  2) 2323 x 1414 = 2525 1313 = ÷ 1616 = 2 12 2525 3131 x= 6565

35. TRY THESE  1)  2) 2323 x 1414 = 2525 1313 = ÷ 1616 = 2 12 2525 3131 x= 6565 = 1515 1