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## Rational Numbers and Opposites

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**Rational Numbers**and Opposites Technology 1.1 For Figure 1.1, Figure 1.1 Enter the fraction, , as a quotient, and choose to have your answer displayed as a fraction by selecting ► FRAC, option 1, under the MATH menu. The negative symbol is . (-) (-) 2 3 MATH 1 ENTER Enter the mixed number, 2 as a sum of a whole number, 2, and the fraction, Choose to have the answer displayed as a fraction. 2 + 3 4 MATH 1 ENTER 1 of 2**Technology**1.1 Rational Numbers and Opposites Figure 1.1 Enter the negative mixed number as the opposite of a sum of the whole number, 3, and the fraction, Use as an opposite sign. Choose to have the answer displayed as a fraction. (-) (-) ( 3 + 1 4 ) MATH 1 ENTER Note that the mixed-number answers are displayed as improper fractions. Directions for changing an improper fraction to a mixed number are given in Section 1.2, “Calculator Exercises.” 2 of 2**Technology**1.2 Absolute Value For Figure 1.2, Figure 1.2 To enter an absolute-value expression on your calculator, use the abs function found under the MATH NUM menu option 1. Close the set of parentheses that are opened for you to enclose each of the numbers, 3.5 and , in each set of parentheses. MATH ► 1 3 . 5 ) ENTER MATH ► 1 (-) 1 2 ) MATH 1 ENTER**Technology**1.4 Adding Rational Numbers c. d. Figure 1.4 For Figure 1.4, Enter the fractions, and in parentheses for proper grouping and ease in reading. Choose to have the answer displayed as a fraction. This option, FRAC, is located under the MATH menu option 1. ► ( 1 2 ) + ( (-) 2 3 ) MATH 1 ENTER 1 of 2**Technology**1.4 Adding Rational Numbers c. d. Figure 1.4 Mixed numbers are written as the sum of the whole number and the fraction. Negative mixed numbers have the negative sign outside the parentheses. Choose to have the answer displayed as a fraction by using option 1 under MATH menu. (-) ( 1 + 2 3 ) + ( 2 + 3 5 ) MATH 1 ENTER 2 of 2**Technology**1.5 Subtracting Rational Numbers a. d. Figure 1.5 For Figure 1.5, Negative integers and decimals may be entered without parentheses. Note the difference in the negative, , and the minus, . (-) - 9 . 6 - (-) 3 . 8 ENTER 1 of 2**Technology**1.5 Subtracting Rational Numbers a. d. Figure 1.5 Enter the fraction, , in parentheses for proper grouping and ease in reading. Negative numbers have the negative signs outside the parentheses. Choose to have the answer displayed as a fraction. This option, ► FRAC, is located under the MATH menu option 1. ( 1 4 ) - (-) ( 1 + 1 2 ) MATH 1 ENTER 2 of 2**Technology**1.7 Multiplying Rational Numbers a. d. Figure 1.7 For Figure 1.7, There is no need to place decimal numbers in parentheses. You may use the multiplication sign instead. (-) 4 . 8 9 (-) 6 . 4 ENTER Place the negative mixed number as a sum in parentheses with the negative outside the grouping. Choose to have your answer displayed as a fraction. This option, ► FRAC, is located under the MATH menu option 1. (-) ( 1 + 2 3 ) ( 2 + 3 5 ) MATH 1 ENTER**Technology**1.8 Dividing Rational Numbers c. d. d. Figure 1.8a Figure 1.8b For Figure 1.8a and 1.8b, There is no need to enter the whole number 0 in the decimal -0.34. 0 (-) . 3 4 ENTER Since it is not possible to divide by 0, an error is displayed on the screen when you enter the expression. (-) 8 . 9 0 ENTER Press to quit the error screen and return to the default home screen. ENTER**Technology**1.9 Integer Exponents a. Figure 1.9a To enter an exponent, use the key. For Figure 1.9a, There is a special key, , that may be used to square a number. To square a number, enter the base followed by . ^ x2 x2 ( 2 3 ) x2 MATH 1 ENTER or ( 2 3 ) ^ 2 MATH 1 ENTER 1 of 3**Technology**1.9 Integer Exponents b. Figure 1.9b For Figure 1.9b, There is a special function under the MATH menu option 3 that may be used to cube a number. 1 . 5 MATH 3 ENTER or 1 . 5 ^ 3 ENTER 2 of 3**Technology**1.9 Integer Exponents d. For Figure 1.9c, Figure 1.9c Enter the mixed number 9 , as the sum of 9 and enclosed in parentheses. Use the for inserting the exponent. ^ ( 9 + 1 3 ) ^ 5 MATH 1 ENTER Since the result is not a fraction, enter the fraction answer that we are checking, and compare the decimal values. 1 7 2 1 0 3 6 8 2 4 3 ENTER 3 of 3**Technology**1.10 Square Roots c. d. e. Figure 1.10a For Figure 1.10a and Figure 1.10b, To enter a square root, enter . Close the parentheses that are opened for you in order to enclose the number in a set of parentheses. 2nd 2nd 4 9 ) MATH 1 ENTER (-) 2nd 2 5 ) ENTER 1 of 2**Technology**1.10 Square Roots e. Figure 1.10b Since the square root of a negative number is not defined as a real number, if your calculator is in Real mode (the default mode), an error will be displayed when you enter the expression. 2nd (-) 2 5 ) ENTER Press to quit the error screen and return to the default home screen. ENTER 2 of 2**Technology**1.11 Cube Roots a. b. c. For Figure 1.11, Figure 1.11 The cube root is located under the MATH menu option 4. Remember to close the set of parentheses that is opened for you. MATH 4 (-) 2 7 ) ENTER MATH 4 3 0 ) ENTER MATH 4 1 2 7 ) MATH 1 ENTER**Technology**1.13 Order of Operations c. d. e. Figure 1.13 For Figure 1.13, It is necessary to enter both the numerator and the denominator in a set of parentheses to ensure proper grouping. ( 1 6 - 2 x2 + 3 ) ( 3 + 2 ) ENTER 1 of 2**Technology**1.13 Order of Operations c. d. e. Figure 1.13 Use a set of parentheses instead of brackets and braces. 2 ( ( 2 ( 3 - 4 ) + 7 ) - 8 ) + 3 ( (-) 5 ) ENTER Enclose the radicand in a set of parentheses. (-) 2nd 2 5 + 1 1 ) + 6 ENTER 2 of 2