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2.2 Adding and Subtracting Rational Numbers• Use a number line to find each sum.
a. -3 + (- 4)
Step 1 – Draw an arrow from 0 to -3.
Step 2 – Draw a second arrow 4 units to the left to represent adding -4.
Step 3 – The second arrow ends at the sum of -7, so -3 + (-4) = -7.
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Adding and Subtracting Rational Numbers• Use a number line to find each sum.
b. 2.5 + (-3.5)
Step 1 – Draw an arrow from 0 to 2.5.
Step 2 – Draw a second arrow 3.5 units to the left.
Step 3 – The second arrow ends at the sum of -1, so 2.5 + (-3.5) = -1.
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Addition of Rational Numbers
• To add rational numbers with the same sign, add their absolute values. The sum has the same sign as the addends.
• To add rational numbers with different signs, subtract the lesser absolute value from the greater absolute value. The sum has the same sign as the number with the greater absolute value.
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Add Rational Numbers• Find each sum.
a. -11 + (-7)
= -18
b. 7 3
16 8
7 6
16 16
1
16
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Subtract Rational Numbers
• Every positive rational number can be paired with a negative rational number. These pairs are called opposites.
• A number and its opposite are additive inverses of each other.– When you add two opposites, the sum is
always 0.
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Additive Inverse Property
• The sum of a number and its additive inverse is 0.
• For every number a, a + (-a) = 0.
• Examples:
2 + (-2) = 0 -4.25 + 4.25 = 0
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Subtraction of Rational Numbers
• To subtract a rational number, add its additive inverse.
• For any numbers a and b, a – b = a + (-b).
• Examples:
8 – 15 = 8 + (-15) = -7
-7.6 – 12.3 = -7.6 + (-12.3) = -19.9
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Subtract Rational Numbers to Solve a Problem• During a five-day period, a telecommunications
company’s stock price went from $17.82 to $15.36 per share. Find the change in the price of the stock.
15.36 – 17.82
= -2.46
The price of the stock changed by -$2.46.
The problem asks for the change in a stock’s price from the beginning of a week to the end. Since the change was negative, the price dropped. This makes sense since the ending price is less than the beginning price.
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More Practice!!!!!
• Textbook p. 76 – 77 #17 – 36, 39 – 56.