Section 1.3 Addition of Real Numbers

Objective: Add positive and negative real numbers. 1.3 Lecture Guide: Addition of Real Numbers There is a difference in the process for adding two numbers with like signs versus adding two numbers with unlike signs.

Adding Numbers with Like Signs: Verbally Numerical Examples Graphical Examples To add numbers with like signs: 1. add the absolute values of the terms 2. and use the same sign as the terms.

Adding Numbers with Unlike Signs: Verbally Numerical Examples Graphical Examples To add numbers with unlike signs: 1. subtract the smaller absolute value from the larger absolute value 2. and use the sign of the term with larger absolute value.

1. Find each sum where each term has the same sign

5. Find each sum where each term has the same sign

9. Find each sum where the terms have opposite signs

Summary of Addition of Real Numbers: Determine if the terms have like or unlike signs. If the terms have like signs, add the absolute values. The sum will have the same sign as both terms. If the terms have unlike signs, subtract the absolute values. The sum will have the same sign as the term with the larger absolute value.

Algebraically Verbally Numerical Example Addition of Fractions To add fractions with the same denominator, add the numerators and use the common denominator. for

Algebraically Verbally Numerical Example Addition of Fractions To add fractions with unlike denominators, first express each fraction in terms of a common denominator and then add the numerators using this common denominator. forand

13. Find each sum where each term has the same sign. 14.

15. Find each sum where each term has the same sign. 16.

17. Find each sum where each term has the same sign. 18.

19. Find each sum where each term has the same sign. 20.

21. Find each sum where each term has the same sign. 22.

23. Find each sum where each term has the same sign. 24.

25. Find each sum.

26.

Algebraically Verbally Numerical Example Commutative Property of Addition: Objective: Use the commutative and associative properties of addition. The sum of two terms in either order is the same.

Algebraically Verbally Numerical Example Associative Property of Addition: Terms can be regrouped without changing the sum.

27. Explain the distinction between the commutative property of addition and the associative property of addition.

28. There are two different ways to use the commutative property of addition to rewrite the following expression: _____________________ and _____________________ Can you write both?

Mentally add the following terms. (Hint: You may want to first use the commutative and associative properties of addition to mentally reorder and regroup the terms.) 29.

Mentally add the following terms. (Hint: You may want to first use the commutative and associative properties of addition to mentally reorder and regroup the terms.) 30.

Mentally add the following terms. (Hint: You may want to first use the commutative and associative properties of addition to mentally reorder and regroup the terms.) 31.

Mentally add the following terms. (Hint: You may want to first use the commutative and associative properties of addition to mentally reorder and regroup the terms.) 32.

Objective: Evaluate an algebraic expression for given values of the variables. 33. Evaluate the following expressions forand Show your work below and then use your calculator to check your work. (Hint: See Calculator Perspective ) It may be helpful to use parentheses when making substitutions for the variables.

34. Evaluate the following expressions forand Show your work below and then use your calculator to check your work. (Hint: See Calculator Perspective ) It may be helpful to use parentheses when making substitutions for the variables.

35. Evaluate the following expressions forand Show your work below and then use your calculator to check your work. (Hint: See Calculator Perspective ) It may be helpful to use parentheses when making substitutions for the variables.

Phrases Used To Indicate Addition: Key PhraseVerbal ExampleAlgebraic Example Plus"12 plus 8" Total"The total of $25 and $40" Sum"The sum of x and y" Increased by"An interest rate r is increased by 0.5%" More than"7 more than x"

36. Translate each verbal statement into algebraic form. x plus three

37. Translate each verbal statement into algebraic form. The total of t and six

38. Translate each verbal statement into algebraic form. Five more than z