Operations with Signed Numbers
Operations with Signed Numbers
Slide: 1
Section 2.1
Real Numbers Whole numbers Natural numbers
−5 −4 −3 −2 −1
0
1
2
3
4 5
Negative integers Neither positive nor negative integer Slide: 2
Positive integers
Section 2.1
Absolute Value The absolute value of a number is its distance from the origin ‘0’ on the number line. Since it is a distance, it is always positive and the direction does not matter.
−5 −4 −3 −2 −1 3 units
0
1
2
3
4 5
3 units
For example, −3 and +3 are 3 units from the origin ‘0’ The absolute value of a is denoted as a Slide: 3
Section 2.1
Signed Numbers Every positive number has an opposite, called a negative number. They are represented as numbers to the left of zero on the number line.
−5 −4 −3 −2 −1
0
1
2
2 is greater than −4 −1 is greater than −5 −2 is less than 1 −4 is less than −3 Slide: 4
3
4 5
Operations with Signed Numbers - Addition
Section 2.1
When signed numbers (e.g., −5, +12) are added together, the result will be a number with a sign.
(+5) + (+8) = 5 + 8 = 13
(+) + (+) = (+)
When both numbers are positive, the final answer will be positive. (−) + (−) = (+)
(−7) + (−2) = −7 −2 = −9
When both numbers are negative, the final answer will be negative. (+) + (−) = (+/−)
(+2) + (−5) = 2 − 5 = −3 (+8) + (−3) = 8 − 3 = 5
When adding numbers that have different signs, subtract the smaller of the two and the answer will be either positive or negative Slide: 5
What is the value of the following expression: (−12) + 7 + (–16) = a. –21. a.
b. 11 . c. 21 . d. −11 . Slide: 6
What is the value of the following expression: (−12) + 7 + (–16) = a. –21. a.
b. 11 . c. 21 . d. −11 . Slide: 7
Operations with Signed Numbers - Subtraction When subtracting signed numbers, change the sign of the number being subtracted to its opposite, change subtraction to addition, and follow the addition rules for signed numbers.
(+5) − (−8) = 5 + 8 = 13 (−7) − (−2) = −7 + 2 = −5 (−2) − 5 = −2 + (–5) = –7 (−8) − 3 = −8 + (–3) = −11
Slide: 8
Section 2.1
What is the value of the following expression: (−12) – (−6) – 5 = a. b. c. d.
Slide: 9
–1 –11 1 11
What is the value of the following expression: (−12) – (−6) – 5 =
Slide: 10
Section 2.1
Operations with Signed Numbers Multiplication and Division
When signed numbers are multiplied or divided, the result will be a number with a sign.
+16 = (+4) (+) = (+) +4 (+) When both numbers are positive, the final answer will be positive. (−)(−) = (+) −24 = (+3) (−) (−7)(−2) = (+14) = (+) −8 (−)
(+)(+) = (+)
(+3)(+8) = (+24)
When both numbers are negative, the final answer will be positive. (+)(−) = (−)
(+2)(−3) = (−6)
(−)(+) = (−)
(−1)(+5) = (−5)
+42 = (−6) −7 −90 = (−10) +9
(+) = (−) (−) (−) = (−) (+)
When only one of the numbers is negative, the final answer will be negative. Slide: 11
Section 2.1
What is the value of the following expression: (−6)(2)(−5)(−1)÷(−4) = a. 15 b. −15
Slide: 12
Section 2.1
What is the value of the following expression: (−6)(2)(−5)(−1)÷(−4) =
Slide: 13
Slide: 1
Section 2.1
Real Numbers Whole numbers Natural numbers
−5 −4 −3 −2 −1
0
1
2
3
4 5
Negative integers Neither positive nor negative integer Slide: 2
Positive integers
Section 2.1
Absolute Value The absolute value of a number is its distance from the origin ‘0’ on the number line. Since it is a distance, it is always positive and the direction does not matter.
−5 −4 −3 −2 −1 3 units
0
1
2
3
4 5
3 units
For example, −3 and +3 are 3 units from the origin ‘0’ The absolute value of a is denoted as a Slide: 3
Section 2.1
Signed Numbers Every positive number has an opposite, called a negative number. They are represented as numbers to the left of zero on the number line.
−5 −4 −3 −2 −1
0
1
2
2 is greater than −4 −1 is greater than −5 −2 is less than 1 −4 is less than −3 Slide: 4
3
4 5
Operations with Signed Numbers - Addition
Section 2.1
When signed numbers (e.g., −5, +12) are added together, the result will be a number with a sign.
(+5) + (+8) = 5 + 8 = 13
(+) + (+) = (+)
When both numbers are positive, the final answer will be positive. (−) + (−) = (+)
(−7) + (−2) = −7 −2 = −9
When both numbers are negative, the final answer will be negative. (+) + (−) = (+/−)
(+2) + (−5) = 2 − 5 = −3 (+8) + (−3) = 8 − 3 = 5
When adding numbers that have different signs, subtract the smaller of the two and the answer will be either positive or negative Slide: 5
What is the value of the following expression: (−12) + 7 + (–16) = a. –21. a.
b. 11 . c. 21 . d. −11 . Slide: 6
What is the value of the following expression: (−12) + 7 + (–16) = a. –21. a.
b. 11 . c. 21 . d. −11 . Slide: 7
Operations with Signed Numbers - Subtraction When subtracting signed numbers, change the sign of the number being subtracted to its opposite, change subtraction to addition, and follow the addition rules for signed numbers.
(+5) − (−8) = 5 + 8 = 13 (−7) − (−2) = −7 + 2 = −5 (−2) − 5 = −2 + (–5) = –7 (−8) − 3 = −8 + (–3) = −11
Slide: 8
Section 2.1
What is the value of the following expression: (−12) – (−6) – 5 = a. b. c. d.
Slide: 9
–1 –11 1 11
What is the value of the following expression: (−12) – (−6) – 5 =
Slide: 10
Section 2.1
Operations with Signed Numbers Multiplication and Division
When signed numbers are multiplied or divided, the result will be a number with a sign.
+16 = (+4) (+) = (+) +4 (+) When both numbers are positive, the final answer will be positive. (−)(−) = (+) −24 = (+3) (−) (−7)(−2) = (+14) = (+) −8 (−)
(+)(+) = (+)
(+3)(+8) = (+24)
When both numbers are negative, the final answer will be positive. (+)(−) = (−)
(+2)(−3) = (−6)
(−)(+) = (−)
(−1)(+5) = (−5)
+42 = (−6) −7 −90 = (−10) +9
(+) = (−) (−) (−) = (−) (+)
When only one of the numbers is negative, the final answer will be negative. Slide: 11
Section 2.1
What is the value of the following expression: (−6)(2)(−5)(−1)÷(−4) = a. 15 b. −15
Slide: 12
Section 2.1
What is the value of the following expression: (−6)(2)(−5)(−1)÷(−4) =
Slide: 13
