Ch. 4 Notes

Algebra I Chapter 4 Mrs. Cataldo Class Notes Chapter 4.1-4.5 Short Quiz: Write as addition problems. Use the distributive rule. 1. 7 ( 9 + y) 2. (c – d) d Solve. 3. -7 --6 = 4. 12 • -4 = 5. 16/-4 = 4.1: Rational Numbers A rational number is any number that can be written as the _________________________ of two _________________________. Example: The number 12 ½ is rational because it can be written as the quotient of the integer 25 and the integer 2, 25/2 = 12 ½. Based on this definition, is any fraction a rational number? ______ List two examples of fractions. ______ ______ Are they expressed as the quotient of two integers? _____ A fraction can be divided out to get its decimal form. Example: 25/2 = 12.5 What is the decimal form of 1/5? _______ How about ¾ ? _______ These fractions result in a terminating decimal, i.e. the decimal ends. Some fractions like 1/3 divide out to repeating decimals. What does 1/3 divide out to? ________________ Is 1/3 a rational number? Can it be written as the quotient of two integers? _____ So the decimal form of a rational number is a repeating or terminating decimal. Later we will look at irrational numbers. These are non-repeating, non-terminating decimals like π. What is a decimal? It is a fraction with a multiple of 10 in the denominator. Example: Write 0.2 as a fraction. 2/10 Write 0.25 as a fraction. _________ Every integer can be written as a fraction with the denominator of 1 and the numerator as the number. Example: 5 can be written as the fraction 5/1 How would you write -2 as a fraction? _______ Rational numbers can be represented as points on a _______________________. This means they can be ordered. Fill in the blank with a < or > sign. -5.5 ___ 4.5 -7.3 ____ 8.1 -1/3 ____-3 HOMEWORK NOTE: Remember how to subtract decimals. Example: 6.23 -7.321 = _________ Write 6.230 OR -7.321 -7.321 + 6.230 4.2 Absolute Value and Addition The absolute value is the distance between two numbers on a number line or the distance between a number and zero. Remember we talked about the distance between -3 and 2 is 5. Draw a number line below to represent this distance. Another way to think of absolute value is the positive value of whatever is within the absolute value signs. Example: The absolute value of -5 is 5. What is the absolute value of 6 ? ____ Addition: The sum of 2 numbers having the same sign can be found by adding their __________________________________, the answer having the same sign as the numbers. The sum of 2 numbers having opposite signs can be found by subtracting their __________________________________, the answer having the same sign as the number having the __________________ absolute value. Note: When using symbols for a value, the absolute value of x if x>0 is x. The absolute value of x if x<0 is –x. Example: If x = 9, the absolute value of 9,9 = 9 = x. If x = -9, 9 = 9 = -x. 4.3 Operations with Rational Numbers This lesson just repeats what we learned in Chapter 3 about adding, subtracting, multiplying and dividing integers with positive and negative signs. Review: 1. What is the difference between 6.2 and -1.3? Write 6.2 --1.3 as an addition problem and solve. 2. Subtract -5.4 from -3. 3. Find the product of -3.1 and 0.5. 4. Divide 8.4 by -2.1. The product or quotient of 2 numbers having the same sign can be found by multiplying or dividing their ______________________________________. The answer always being _______________________. The product or quotient of 2 numbers having opposite signs can be found by multiplying or dividing their ______________________________________. The answer always being _______________________. 4.4 Approximations (Rounding) When rounding decimals, round down if the following digit is less than 5 and round up if it is greater than or equal to 5. Example: Round 1.267 to the nearest 100th. The hundredth’s place is 6, what is the next digit in the 1000th place? 7. 7 > 5 so round up. The answer would be 1.27. Round 5.463 to the hundredth’s place. The thousandths place is 3 which is less than 5 so round down to 5.46. Practice: Round the following to the nearest 10th. 1. 8.905 ______ 2. 7.55 _____ 3. 3.486 ______ 4. 12.97 ______ What about negative integers? Round those to the next higher absolute value if the following digit is 5 or greater. Example: Round – 1.25 to the nearest tenth. The answer is -1.3. Note: If you include a zero at the end of a decimal that indicates that the place value is significant or meaningful. If you round 3.499 to the nearest hundredth you would get 3.50. The zero shows the significant place. 4.5 Graphing Using Negative Numbers This lesson is drawing graphs after making tables but this time using x,y coordinates that are positive and negative. Attach graph paper. Graph y = 3x -1 using x = -2, -1, 0, 1 and 2.