Section 1.5 Subtraction of Real Numbers 51 1e. - 1 2 - 3 5 =- 1 2 + a- 3 5 b =- 5 10 + a- 6 10 b =- 11 10 Student Check 1 Perform the indicated operation. Rewrite as adding the opposite of 3 5 , which is - Convert the fractions to equivalent fractions with their common denominator of 10. Add the numbers. a. 1 - 4 b. 11.3 - (-4.3) c. -75 - 15 d. -32 - (-8) e. - 2 3 - a- 1 4 b 3 5 . ������������ Instead of rewriting a subtraction problem as adding the opposite, we observe that, after any double negative signs are eliminated, the operation connecting the numbers is equivalent to the sign of the number being added. This enables us to use the rules for addition to simplify the expression. For instance, -6 - 2 → Both numbers are negative, so we get -8. 6 - 10 → These numbers have opposite signs, so we get -4. -1 - (-5) = -1 + 5 → These numbers have opposite signs, so we get 4. Also, note that -(-a ) = a . More about the Order of Operations In Section 1.3, we learned the order of operations. We will use that again to simplify expressions, but this time, we will apply the rules for adding and subtracting signed numbers. ���������������������� Order of Operations When simplifying a numerical expression, perform the operations in the following order. Step 1: Simplify expressions inside grouping symbols first, starting with the innermost set. If there is a fraction bar, simplify the numerator and denominator separately. Step 2: Evaluate any exponential expressions. Step 3: Perform multiplication or division in order from left to right. Step 4: Perform addition or subtraction in order from left to right. �� ������������������������ ������������������ Simplify each expression. 2a. -4 - (-3) + 5 - 7 2b. -42 + 6 - u-10 + 3u 2c. 5 - {4 - 6 - (1 - 12 - (-2))} Solutions 2a. -4 - (-3) + 5 - 7 = -4 + 3 + 5 + (-7) Rewrite. = -1 + 5 + (-7) Add the fi rst two numbers, -4 + 3 = -1. = 4 + (-7) Add the fi rst two numbers, -1 + 5 = 4. = -3 Add the fi nal numbers. Objective 2 ▶ Apply the order of operations.
hendricks_beginning_algebra_1e_ch1_3
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