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Literal Equations, Numbers, and Quantities

Literal Equations, Numbers, and Quantities. Module 1 Lesson 2. What is a Literal Equation?. A Literal Equation is an equation with two or more variables. You can "rewrite" a literal equation to isolate any one of the variables using inverse operations.

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Literal Equations, Numbers, and Quantities

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  1. Literal Equations, Numbers, and Quantities Module 1 Lesson 2

  2. What is a Literal Equation? A Literal Equationis an equation with two or more variables. • You can "rewrite" a literal equation to isolate any one of the variables using inverse operations. • When you rewrite literal equations, you may have to divide by a variable or variable expression.

  3. Solving a Literal Equation

  4. –y –y x = –y + 15 Example: Solving Literal Equations A. Solve x + y = 15 for x. x + y = 15 Since y is added to x, subtract y from both sides to undo the addition. B. Solve pq = x for q. pq= _x_ p p Since q is multiplied by p, divide both sides by p to undo the multiplication.

  5. Your Turn: Solve 5 – b = 2t for t. 5 – b = 2t Locate t in the equation. Since t is multiplied by 2, divide both sides by 2 to undo the multiplication.

  6. Your Turn! Solve for the indicated variable. 1. 2. 3. 2x + 7y = 14 for y 4. for h P = R – C for C for m 5. for C

  7. Your Turn Solutions H = 3V A 2. y = 14 – 2x 7 3. C = R – P 4. m = x(k – 6) 5. C = Rt + S

  8. Example: Application The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol  in your answer. Locate d in the equation. Since d is multiplied by , divide both sides by  to undo the multiplication. Now use this formula and the information given in the problem.

  9. The bowl's diameter is inches. Example: Continued The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol  in your answer. Now use this formula and the information given in the problem.

  10. The Real Number System Every Real Number is either rational or irrational. We refer to these sets as subsets of the real numbers, meaning that all elements in each subset are also elements in the set of real numbers.

  11. Examples of each Subset

  12. Example Consider the following set of numbers. List the numbers in the set that are: • Natural Numbers • Whole Numbers • Integers • Rational Numbers • Irrational Numbers • Real numbers

  13. Example Consider the following set of numbers. List the numbers in the set that are: • Natural Numbers: √16 = 4, so that is the only Natural Number • Whole Numbers: 0 , √16 • Integers: -3, 0, √16 • Rational Numbers: -3, 0, ½ , .95, √16 • Irrational Numbers: √8 • Real numbers: All of the numbers listed above!

  14. Properties of Real Numbers

  15. Communitive Property It doesn’t matter how you swap addition or multiplication around…the answer will be the same! Rules: Commutative Property of Addition a+b = b+a Commutative Property of Multiplication ab = ba Samples: Commutative Property of Addition 1+2 = 2+1 Commutative Property of Multiplication (2x3) = (3x2)

  16. Associative Property It doesn’t matter how you group (associate) addition or multiplication…the answer will be the same! Rules: Associative Property of Addition (a+b)+c = a+(b+c) Associative Property of Multiplication (ab)c = a(bc) Samples: Associative Property of Addition (1+2)+3 = 1+(2+3) Associative Property of Multiplication (2x3)4 = 2(3x4)

  17. Identity Property Rules: Identity Property of Addition a+0 = a Identity Property of Multiplication a(1) = a What can you add to a number & get the same number back? ZERO What can you multiply a number by and get the number back? ONE Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication 2(1)=2

  18. Inverse Property Rules: Inverse Property of Addition a+(-a) = 0 Inverse Property of Multiplication a(1/a) = 1 Think opposites! The Inverse property uses the inverse operation to get to the identity! Samples: Inverse Property of Addition 3+(-3)=0 Inverse Property of Multiplication 2(1/2)=1

  19. Distributive Propety You can distribute the coefficient through the parenthesis with multiplication and remove the parenthesis. Rule: a(b+c) = ab+bc • Samples: • 4(3+2)=4(3)+4(2)=12+8=20 • 2(x+3) = 2x + 6 • -(3+x) = -3 - x

  20. Identify the property that justifies each of the following. • 6 + 8 = 8 + 6 • 5 + (2 + 8) = (5 + 2) + 8 • 12 + 0 =12 • 5(2 + 9) = (5  2) + (5  9) • 4  (8  2) = (4  8)  2 • 5/9  9/5 = 1 • 5  24 = 24  5 • 18 + -18 = 0 • -34 1 = -34

  21. Solutions • Commutative • Associative • Identity • Distributive • Associative • Inverse • Commutative • Inverse • Identity

  22. Closure Property All real numbers have closure. The Closure property states the if a and b are real numbers then: • a + b is a real number • ab is a real number. So, if you add two rational numbers, your sum will be rational. Also, if you add two irrational numbers, that sum will be irrational.

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