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Integers and Introduction to Solving Equations

Chapter 2. Integers and Introduction to Solving Equations. Introduction to Integers. 2.1. Numbers greater than 0 are called positive numbers . Numbers less than 0 are called negative numbers. Positive and Negative Numbers. -6. -5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5. 6. zero.

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Integers and Introduction to Solving Equations

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  1. Chapter 2 Integers and Introduction to Solving Equations

  2. Introduction to Integers 2.1

  3. Numbers greater than 0 are calledpositive numbers.Numbers less than 0 are callednegative numbers. Positive and Negative Numbers -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 zero negative numbers positive numbers

  4. Integers –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Some signed numbers are integers. Theintegersare { …, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, …} zero negative numbers positive numbers

  5. Negative and Positive Numbers –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –3 indicates “negative three.” 3 and +3 both indicate “positive three.” The number 0 is neither positive nor negative. zero negative numbers positive numbers

  6. We compare integers just as we compare whole numbers. For any two numbers graphed on a number line, the number to theright is the greater number and the number to theleft is the smaller number. Comparing Integers < means “is less than” > means “is greater than”

  7. Graphs of Integers –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 The graph of –5 is to the left of –3, so –5 is less than –3, written as –5 < –3 . We can also write –3 > –5. Since –3 is to the right of –5, –3 is greater than –5.

  8. The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is | |. Absolute Value is 2 because 2 is 2 units from 0. is 2 because –2 is 2 units from 0. –6 –6 –5 –5 –4 –4 –3 –3 –2 –2 –1 –1 0 0 1 1 2 2 3 3 4 4 5 5 6 6

  9. Helpful Hint Since the absolute value of a number is that number’s distance from 0, the absolute value of a number is always 0 or positive. It is never negative. zero a positive number

  10. Two numbers that are the same distance from 0 on the number line but are on the opposite sides of 0 are calledopposites. Opposite Numbers 5 units 5 units –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 5 and –5 are opposites.

  11. Opposite Numbers 5 is the opposite of –5 and –5 is the opposite of 5. The opposite of 4 is –4 is written as –(4) = –4 The opposite of –4 is 4 is written as –(–4) = 4 –(–4) = 4 If ais a number, then–(–a)=a.

  12. Helpful Hint Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0.

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