1. Algebra 2-4 Dividing Rational Numbers1. 2. 3.
Note: For this problem, 2 × 3 is considered different from 3 × 2
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2. Algebra 2-4 Dividing Rational Numbers
Since multiplication and division are inverse operations, the rule for finding the sign of the quotient of two numbers is similar to the rule for finding the sign of a product of two numbers.
Dividing Integers
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3. Algebra 2-4 Dividing Rational Numbers
Dividing Numbers with the Same Sign
The quotient of two numbers with the same sign is positive.
Examples:
Dividing Integers
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4. Algebra 2-4 Dividing Rational Numbers
Dividing Numbers with Different Signs
The quotient of two numbers with different signs is negative.
Examples:
Dividing Integers
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5. Divide Integers
Find .
Answer:
positive quotient
Example 4-1a

6. Divide Integers
Find .
Divide.
negative quotient
Answer:
Example 4-1b

7. Divide Integers Find each quotient. a. Answer: 20 b. Answer: –15
Example 4-1c

8. Simplify Before Dividing
Simplify the numerator first.
Multiply.
Answer:
different signs  negative quotient
Example 4-2a

9. Simplify Before Dividing
Answer: 3
Example 4-2b

10. Algebra 2-4 Dividing Rational Numbers
The rules for dividing positive and negative integers also apply to division with rational numbers.
Dividing Integers
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11. Divide Rational Numbers
Find .
Estimate: – 108 ÷ 9 = – 12
Answer: Use a calculator. different signs  negative quotient
Example 4-3a

12. Algebra 2-4 Dividing Rational Numbers
Remember that to divide by any nonzero number, multiply by the reciprocal of that number.
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13. No calculator!! – Divide Rational Numbers Find .
Multiply by the reciprocal of –
Answer:
same signs  positive quotient
Example 4-3b

14. Divide Rational Numbers
Find each quotient. a. b.
Answer: 15.3
Answer:
Example 4-3c

15. Algebra 2-4 Dividing Rational Numbers
Page 86 #18 – 36 even (10 problems – 10 points)
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16. Divide Rational Numbers
Baseball The perimeter of a square baseball diamond is 360 feet. Find the length of one side of the diamond.
To find the length of one side, divide the perimeter by the number of sides.
same signs  positive quotient
Answer: The length of one side is 90 feet.
Example 4-4a

17. Divide Rational Numbers
The perimeter of a triangular building is 450 feet. Find the length of each side.
Answer: 150 feet
You can use the Distributive Property to simplify fractional expressions.
Example 4-4b

18. Simplify Algebraic Expressions
The fraction bar indicates division.
Multiply by the reciprocal of 13.
Distributive Property.
Answer: Simplify.
Example 4-5a

19. Do this one in your notes, PLEASE!!
Simplify Algebraic Expressions
Simplify
Answer:
Example 4-5c

20. Evaluate Algebraic Expressions
Evaluate if w = 2, x = –9.1 and y = 4.
Replace w with 2, x with –9.1 and y with 4.
Find the numerator and denominator separately.
Answer: Use a calculator. different signs  negative quotient
Example 4-6a

21. Evaluate Algebraic Expressions
Evaluate if s = 2.3, t = 5 and u = –4.
Answer: –14.375
Example 4-6b