To multiply two signed numbers, multiply their absolute values and use the following rules for the sign of the product:
- Two numbers with the same sign yield a positive product
- Two numbers with opposite signs yield a negative product
In algebra, if there is no indicated operation between quantities, it represents multiplication. For example, xy means x * y. However, if there is a + or - between parentheses and a quantity, it represents combining terms rather than multiplication.
Fundamentals of AlgebraChu v. NguyenIntegral ExponentsDustiBuckner14
Fundamentals of Algebra
Chu v. Nguyen
Integral Exponents
Exponents
If n is a positive integer (a whole number, i.e., a number without decimal part) and x is a number, then
The number x is called the base and n is called the exponent.
The most common ways of referring to are “ x to the nth power,”
“ x to the nth,” or “the nth power of x.”
Integral Exponents (cont.)
For any non-zero number x and a positive integer n
and
Note: is not defined
and
Rules Concerning Integral Exponents
Following are five rules in which m and n are positive integers:
Rule 1: ; for example,
Rule 2: ; for example
or
Rules Concerning Integral Exponents (Cont.)
Rule 3: ; for example
or
Rule 4: ; for example
or
Rule 5: ; for example
or
Basic Rules for Operating with Fractions
Since dividing by zero is not defined, we assume that the denominator
is not zero.
Following are the eight basic rules for operating with fractions.
Rule 1: ; for example
Rule 2: ; for example
Rule 3: ; for example
Basic Rules for Operating with Fractions (cont.)
Rule 4: ; for example
Rule 5: ; for example
Rule 6: ; for example
Basic Rules for Operating with Fractions (cont.)
Rule 7: ; for example
Rule 8: ; for example
Notes: a*b +a*x may be expressed as a(b + x)
a*b + 1 may be written as a(b + ), and
m*x – y may be expressed as m(x - )
Square Root
Generally, for a>0 , there is exactly one positive number x such that
, we say that x is the root of a, written as
for
When n = 2, we say that x is the square root of “a” and is denoted by
or or
For example:
or
Practices
Carrying out the following operations:
24 ; 2-2 ; 2322, ; 252-5 ; and (2x3)5
; ; ; and
3.
4.
5.
n
m
n
m
x
x
x
+
=
n
x
1
0
)
2
(
2
2
2
=
=
=
-
+
-
x
x
x
x
1
0
=
x
0
0
n
n
n
x
x
x
x
=
=
+
0
0
n
n
x
x
1
=
-
3
2 ...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
3. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
Multiplication and Division of Signed Numbers
4. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
Multiplication and Division of Signed Numbers
5. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
6. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield positive
products.
7. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
8. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
Example A.
a. 5 * (4) = –5 * (–4)
9. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
Example A.
a. 5 * (4) = –5 * (–4) = 20
10. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
Example A.
a. 5 * (4) = –5 * (–4) = 20
b. –5 * (4) = 5 * (–4)
11. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
Example A.
a. 5 * (4) = –5 * (–4) = 20
b. –5 * (4) = 5 * (–4) = –20
12. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
Example A.
a. 5 * (4) = –5 * (–4) = 20
b. –5 * (4) = 5 * (–4) = –20
In algebra, multiplication operation are not always written
down explicitly.
13. Rule for Multiplication of Signed Numbers
To multiple two signed numbers, we multiply their absolute
values and use the following rules for the sign of the product.
+ * + = – * – = + ;
+ * – = – * + = – ;
Multiplication and Division of Signed Numbers
Two numbers with the same sign multiplied yield a positive
product.
Two numbers with opposite signs multiplied yield a negative
product.
Example A.
a. 5 * (4) = –5 * (–4) = 20
b. –5 * (4) = 5 * (–4) = –20
In algebra, multiplication operation are not always written
down explicitly. Instead we use the following rules to identify
multiplication operations.
14. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two quantities, the
operation between them is multiplication.
15. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
16. Multiplication and Division of Signed Numbers
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
17. Multiplication and Division of Signed Numbers
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
18. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
19. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
20. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
However, if there is a “+” or “–” sign between the ( ) and a
quantity, then the operation is to combine.
21. ● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
However, if there is a “+” or “–” sign between the ( ) and a
quantity, then the operation is to combine.
Hence 3(+5) = (+5)3 =15,
22. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
However, if there is a “+” or “–” sign between the ( ) and a
quantity, then the operation is to combine.
Hence 3(+5) = (+5)3 =15, but 3 + (5) = (3) + 5 = 8,
23. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
However, if there is a “+” or “–” sign between the ( ) and a
quantity, then the operation is to combine.
Hence 3(+5) = (+5)3 =15, but 3 + (5) = (3) + 5 = 8,
and –5(–5) = (–5)(–5) = 25,
24. Multiplication and Division of Signed Numbers
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
However, if there is a “+” or “–” sign between the ( ) and a
quantity, then the operation is to combine.
Hence 3(+5) = (+5)3 =15, but 3 + (5) = (3) + 5 = 8,
and –5(–5) = (–5)(–5) = 25, but (–5) – 5 = –5 – (5) = –10.
25. Multiplication and Division of Signed Numbers
However, if there is a “+” or “–” sign between the ( ) and a
quantity, then the operation is to combine.
Hence 3(+5) = (+5)3 =15, but 3 + (5) = (3) + 5 = 8,
and –5(–5) = (–5)(–5) = 25, but (–5) – 5 = –5 – (5) = –10.
● If there is no operation indicated between two sets of ( )’s,
the operation between them is multiplication.
Hence (x + y)(a + b) = (x + y) * (a + b)
● If there is no operation indicated between a set of ( ) and a
quantity, the operation between them is multiplication.
Hence x(a + b) = x * (a + b ) and (a + b)x = (a + b) * x.
To multiply many signed numbers together, we always
determine the sign of the product first, then multiply just the
numbers themselves. The sign of the product is determined by
the following Even–Odd Rules.
● If there is no operation indicated between two quantities, the
operation between them is multiplication. Hence xy means x * y.
26. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
Multiplication and Division of Signed Numbers
27. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Multiplication and Division of Signed Numbers
28. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1)
Multiplication and Division of Signed Numbers
29. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1)
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
30. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1) = – 4
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
4 came from 1*2*2*1 (just the numbers)
31. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1) = – 4
b. (–2)4
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
32. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1) = – 4
b. (–2)4 = (–2 )(–2)(–2)(–2)
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
33. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1) = – 4
b. (–2)4 = (–2 )(–2)(–2)(–2)
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
four negative numbers, so the product is positive
34. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1) = – 4
b. (–2)4 = (–2 )(–2)(–2)(–2) = 16
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
four negative numbers, so the product is positive
35. Even-Odd Rule for the Sign of a Product
• If there are even number of negative numbers in the
multiplication, the product is positive.
• If there are odd number of negative numbers in the
multiplication, the product is negative.
Example B.
a. –1(–2 ) 2 (–1) = – 4
b. (–2)4 = (–2 )(–2)(–2)(–2) = 16
Fact: A quantity raised to an even power is always positive
i.e. xeven is always positive (except 0).
Multiplication and Division of Signed Numbers
three negative numbers, so the product is negative
four negative numbers, so the product is positive
37. Rule for the Sign of a Quotient
Multiplication and Division of Signed Numbers
In algebra, a ÷ b is written as a/b or .
a
b
38. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Multiplication and Division of Signed Numbers
In algebra, a ÷ b is written as a/b or .
a
b
39. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Multiplication and Division of Signed Numbers
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
40. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Multiplication and Division of Signed Numbers
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
41. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
42. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
43. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
= 5
44. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
b . –20 / 4 = 20 / (–4)
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
= 5
45. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
b . –20 / 4 = 20 / (–4) = –5
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
= 5
46. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
b . –20 / 4 = 20 / (–4) = –5
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
= 5
c.
(–6)2
=
–4
47. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
b . –20 / 4 = 20 / (–4) = –5
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
= 5
c.
(–6)2
=
36
–4–4
48. Rule for the Sign of a Quotient
Division of signed numbers follows the same sign-rules for
multiplications.
Two numbers with the same sign divided yield a positive
quotient.
Two numbers with opposite signs divided yield a negative
quotient.
Multiplication and Division of Signed Numbers
Example C.
a.
b . –20 / 4 = 20 / (–4) = –5
In algebra, a ÷ b is written as a/b or .
a
b
+
+
=
–
– = +
+
+
=
–
–=
–
20
4
= –20
–4
= 5
c.
(–6)2
=
36
–4 =
–4 –9
49. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
50. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
Example D. Simplify.
(– 4)6(–1)(–3)
(–2)(–5)12
51. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
Example D. Simplify.
(– 4)6(–1)(–3)
(–2)(–5)12
five negative numbers
so the product is negative
52. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
Example D. Simplify.
(– 4)6(–1)(–3)
(–2)(–5)12
= –
five negative numbers
so the product is negative
53. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
Example D. Simplify.
(– 4)6(–1)(–3)
(–2)(–5)12
= –
five negative numbers
so the product is negative
simplify just the numbers4(6)(3)
2(5)(12)
54. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
Example D. Simplify.
(– 4)6(–1)(–3)
(–2)(–5)12
= –
five negative numbers
so the product is negative
simplify just the numbers4(6)(3)
2(5)(12)
= –
3
5
55. The Even–Odd Rule applies to more length * and / operations
problems.
Multiplication and Division of Signed Numbers
Example D. Simplify.
(– 4)6(–1)(–3)
(–2)(–5)12
= –
five negative numbers
so the product is negative
simplify just the numbers4(6)(3)
2(5)(12)
= –
3
5
Various form of the Even–Odd Rule extend to algebra and
geometry. It’s the basis of many decisions and conclusions in
mathematics problems.
The following is an example of the two types of graphs there
are due to this Even–Odd Rule. (Don’t worry about how they
are produced.)
56. The Even Power Graphs vs. Odd Power Graphs of y = xN
Multiplication and Division of Signed Numbers
57. Make sure that you interpret the operations correctly.
Exercise A. Calculate the following expressions.
1. 3 – 3 2. 3(–3) 3. (3) – 3 4. (–3) – 3
5. –3(–3) 6. –(–3)(–3) 7. (–3) – (–3) 8. –(–3) – (–3)
B.Multiply. Determine the sign first.
9. 2(–3) 10. (–2)(–3) 11. (–1)(–2)(–3)
12. 2(–2)(–3) 13. (–2)(–2)(–2) 14. (–2)(–2)(–2)(–2)
15. (–1)(–2)(–2)(–2)(–2) 16. 2(–1)(3)(–1)(–2)
17. 12
–3
18. –12
–3
19. –24
–8
21. (2)(–6)
–8
C. Simplify. Determine the sign and cancel first.
20. 24
–12
22. (–18)(–6)
–9
23. (–9)(6)
(12)(–3)
24. (15)(–4)
(–8)(–10)
25. (–12)(–9)
(– 27)(15)
26. (–2)(–6)(–1)
(2)(–3)(–2)
27. 3(–5)(–4)
(–2)(–1)(–2)
28. (–2)(3)(–4)5(–6)
(–3)(4)(–5)6(–7)
Multiplication and Division of Signed Numbers