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Adding and Subtracting Real Numbers
Unit 1 Lesson 5
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ADDING AND SUBTRACTING REAL NUMBERS
Students will be able to: add and subtract integers and rational numbers. Key Vocabulary: Rules of Addition Rule of Subtraction Opposites Additive Inverse
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ADDING AND SUBTRACTING REAL NUMBERS
We can use a number line to add any real numbers. Adding a positive number by moving to the right. Adding a negative number by moving to left. 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 Negative Numbers Positive Numbers
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 1: Use a number line to find the sum. Β a. βπ+π=π Β b. π+ βπ =βπ Β c. βπ+π=π 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 1: Use a number line to find the sum. Β a. βπ+π=π Β b. π+ βπ =βπ Β c. βπ+π=π Move 9 units to the right 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 Move 7 units to the left 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 Move 8 units to the right
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ADDING AND SUBTRACTING REAL NUMBERS
RULES OF ADDITION: without a number line To add two numbers with the same sign: Add their absolute values. Attach the common sign. To add two numbers with opposite signs: Subtract the smaller absolute value from the larger absolute value. Attach the sign of the number with the larger absolute value.
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 2: Find the sum. Β a. π.π+ βπ.π +π.π Β b. β π π +π+ π π Β c. βππ+ βπ
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 2: Find the sum. Β a. π.π+ βπ.π +π.π =βπ.π+π.π =π.π Β b. β π π +π+ π π =β π π + π π +π =π Β c. βππ+ βπ =βππ
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ADDING AND SUBTRACTING REAL NUMBERS
RULE OF SUBTRACTION: without a number line To subtract π from π, add the opposite of π to π: πβπ=π+ βπ The result is the difference of π and π.
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 3: Find the difference. Β a. βπβπ Β b. β π π β β π π Β c. ππβππ
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 3: Find the difference. Β a. βπβπ =βππ Β b. β π π β β π π =β π π + π π =β π π =βπ Β c. ππβππ
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ADDING AND SUBTRACTING REAL NUMBERS
OPPOSITES are pair of positive real numbers with its negative. Opposites are additive inverse of each other. ADDITIVE INVERSE of a number π is the number that when add to π will yield zero. π+ βπ =π The opposite of βπ is π. The opposite of π is βπ. 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 4: Evaluate each expression. Β a. πβ βπ βπ+π Β b. βπβπ+ βπ Β c. βππ+ βππ +ππ
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 4: Evaluate each expression. Β a. πβ βπ βπ+π =π+π+π =π+π =ππ Β b. βπβπ+ βπ =βππβπ =βππ Β c. βππ+ βππ +ππ =βππ+ππ =βπ
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 5: The average height of a NBA player is 79 inches while the height of an average man is 69 inches. What is the difference between their heights?
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ADDING AND SUBTRACTING REAL NUMBERS
Sample Problem 5: The average height of a NBA player is 79 inches while the height of an average man is 69 inches. What is the difference between their heights? =ππβππ =ππ ππππππ
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