Section 1'4 Subtracting Integers

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Section 1.4 Subtracting Integers
Opposites The opposite of x is x. To find the
opposite of a number, change the sign.

• 1. The opposite of 3 is ________
• 2. The opposite of -2 is ________

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3. The opposite of -5 is _______ 4. The
opposite of a positive number is a
___________number. 5.The opposite of a negative
number is a ___________number.
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Property of Opposites
If x is a positive number, then (x) x
(two negatives make a positive)
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Definition of Subtraction To subtract a number,
add its opposite
a b a (-b) a (b) a b
All subtraction problems can be written as
____________ problems.
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Steps for Subtracting Negative numbers 1.
Change all subtraction problems to addition
problems. ? when subtracting a negative number,
remember to change to addition. example 3
(4) 3 4 7
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Steps for Subtracting Negative numbers
2. Add negative numbers as before. ? If the
signs are the same, _____________ the numbers and
copy the sign. ? If the signs are different,
______________ the smaller number from the larger
number and copy the sign of the larger number.
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Simplify the following without a calculator.
6. 10 5 ___________ 7. 5 10
___________ 8. 5 10 ___________ 9. 5
10 ___________
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Simplify the following without a calculator.
10. 5 (10) ___________ 11. 10 (5)
___________ 12. 10 (5) ___________ 13.
10 (10) ___________
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Simplify the following without a calculator.
14. 10 1 6 ___________ 15. 3 6 (2)
___________ 16. 4 3 ___________ 17.
4 3 3 ___________
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Homework

• Pg. 27
• 7 47 odd,
• 22, 34, 40, 46,
• 51 56 all

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Section 1. 5 Rounding and Estimating
Rounding Numbers We would round numbers when
describing Driving Distance Population
Estimating
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Steps for Rounding Numbers 1. Place an arrow
under the digit you wish to round
2. Look at the number to the right of the arrow
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3. If the next digit is a __________ keep the
number above the arrow the same and replace
remaining number with zeros.
4. If the next digit is a __________ add one to
the number above the arrow and replace remaining
numbers with zeros.
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Example Round 567,234 to the nearest
thousand.
?
Digit to the right is a 2 so keep number above
the arrow the same
567,234 rounded to the nearest thousands is
567,000
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• Round the following numbers
• 1. 4,586 to the nearest tens
• __________________
• 248 to the nearest hundreds
• ____________________

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3. 10,964 to the nearest thousands
____________________ 4. 42,318 to the nearest
ten thousand ____________________
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5. 499,651 to the nearest ten thousand
____________________ 6. 39,837,241 to the
nearest hundred thousand ____________________
7. 39,837,241 to the nearest million
____________________
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8. In 1987, the enrollment of students in public
schools in the United States was 39,837,241.
Round this number to the nearest ten-million.
39,837,241 _________________
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Estimating Estimating is used to find an answer
quickly. One common method is to round each
number so that you can do the arithmetic
mentally.
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Estimate the following problems by rounding to
the indicated place value
9. 399 610 744 298 (hundred)
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Estimate the following problems by rounding to
the indicated place value
10. 27,365 (thousand) 18,670
3,500 9,912
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Estimate the following problems by rounding to
the indicated place value
11. (ten thousand) 12,455 68,321 8,477
91,670
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Use rounding to estimate each answer. Then find
the exact answer.
12. 251 (249) is closest to which of the
following numbers? a. 500 b. 0 c. -500
Exact Answer _______________
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Use rounding to estimate each answer. Then find
the exact answer.
13. 77 22 is closest to which of the
following numbers? a. 100 b. 60 c.
60 d. 100 Exact Answer _______________
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Use rounding to estimate each answer. Then find
the exact answer.
14. Is the difference of 553 50 closer to 600
or 500? Exact Answer _______________
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Use rounding to estimate each answer. Then find
the exact answer.
15. 37 (61) is closest to which of the
following numbers? a. 100 b. 20 c.
20 d. 100 Exact Answer _______________
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Use rounding to estimate each answer. Then find
the exact answer.
16. 37 (61) is closest to which of the
following numbers? a. 100 b. 20 c. 20
d. 100 Exact Answer _______________
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Homework Pg. 35 1 61 every other
odd, 8, 10, 18, 22, 44, 50, 60
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Section 1.6 Multiplying Integers
10 10 10 3(10) _________ (-10) (-10)
(-10) 3(-10) _________ ex1. 4(-3)
__________ ex2. -5(2) __________
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Therefore, the product of a positive number and a
negative number is a ______________________
number.
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-3(2) ______ -3(1) ______ -3(0)
______ -3(-1) _____ ex1. (-2)( -2) _____
ex2. (-5)( -1) _____
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Therefore, the product of a negative number and a
negative number is a ______________________
number.
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Rules for multiplying integers 1. The product of
an __________ number of negatives is _______.
2. The product of an ________ number of
negatives is_______.
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• Simplify the following without a calculator.
• -1(2)( -3) __________
• 2. (-3)(-1)(-2)(2) __________

3. 2(-1)(-5)( -2)( -1) __________ 4.
(-15)(0)( -3)( -2) __________
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Multiplication Property of Zero A 0 0 0 A
0 A number multiplied by zero is always zero.
Multiplication Property of One A 1 A 1
A A A number multiplied by one is always the
original number.
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Commutative Property of Multiplication A
B B A In multiplication, the order does
not affect the product.
Associative Property of Multiplication (A B)
C A (B C) The grouping of three or more
terms does not affect the product.
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Rewrite the following using the commutative
property of multiplication 5. 2 3
___________ 6. 5 -4 __________
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Rewrite the following using the associative
property of multiplication 7. (-3 -1) 9
_______________ 8. (-5 2) -3
_______________
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Distributive Property A(B C) AB AC
We say multiplication distributes over addition.
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Example 4(3 6) 4(3) 4(6) 12
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Rewrite the following using the distributive
property and simplify 9. 2(3 4) 10. 3(4
10)
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Rewrite the following using the distributive
property and simplify 11. 6(7 5) 12. 5(4
7)
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Use rounding to estimate each answer. Then use
your calculator to find the exact answer. 13.
77 22 Estimate ______Exact Answer
______ 14. 553 50 Estimate
______Exact Answer ______
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15. 37 61 Estimate _____Exact Answer
____ 16. 52 98 Estimate _____ Exact
Answer ____
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Homework
Pg. 45 1 45 every other odd, 10,
18, 30, 44, 51 56 all, 57, 59, 61, 65 76
all