University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2021
Views:

45

Pages:

2
Author:

Adriel Nicholson

Section 1.2: Addition and subtraction with signed numbers Chapter 1: Introduction to Algebra Opposite of a number The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero. OPPOSITE NOTATION: –x means the opposite of x. • –5 is read as “the opposite of 5” (It is also correct to read this as negative 5.) • It is proper to say that 5 is the opposite of (-5) since they are both 5 units from 0 on a number line. • It is equally correct to say that (-5) is the opposite of 5 for the same reason. • Thus 5 and -5 are opposites. Absolute Value The absolute value of a number is its distance from 0 on the number line. Absolute values are always greater than or equal to zero. • • • The absolute value of a number n is written as |n|. Example: –5 is five units away from 0, so | − 5| = 5. Similarly: 5 is five units away from 0, so |5| = 5. Section 1.2: Addition and subtraction with signed numbers Chapter 1: Introduction to Algebra Addition with signed numbers • Adding numbers with the same sign: add the values and keep the common sign. For example: 6+3=9 For example: (−5) +(−3) (add the 5 and the 3, then make negative) (−5) + (−3) = −8 • Adding numbers with different signs: subtract the values and use the sign of the largervalued number. For example: −6 + 3: The answer should be negative since the “larger number” (−6) is negative. Subtract 6 – 3 and make the result negative. −6 + 3 = −3 For example: 6 + (−4): The answer should be positive as the larger number 6 is positive. Subtract 6 – 4 and keep the result positive. 6 + (−4) = 2 Subtraction with signed numbers Subtraction Property: • 𝑎 − 𝑏 = 𝑎 + 𝑡ℎ𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑜𝑓 𝑏 • 𝑎 − 𝑏 = 𝑎 + (−𝑏) Subtracting a number is the same as adding its opposite. Use the subtraction property and turn the problem into an addition problem then follow the rules of addition with signed numbers. For example: 6–8 change to addition: 6 – 8 = 6 + 𝑡ℎ𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑜𝑓 8 = 6 + (−8) = −2 For example: −10 – (−3) Change to addition: − 10 – (−3) = −10 + 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑜𝑓 (−3) = −10 + 3 = −7