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Topic 3

Topic 3. Integers. Lesson 7.3.1 Integers and Absolute Value. Integers less than zero are negative integers. Integers greater than zero are positive integers. Lesson 7.3.1 Integers and Absolute Value, continued.

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Topic 3

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  1. Topic 3 Integers

  2. Lesson 7.3.1 Integers and Absolute Value • Integers less than zero are negative integers. Integers greater than zero are positive integers.

  3. Lesson 7.3.1 Integers and Absolute Value, continued • The absolute value of an integer is the distance the number is from zero on a number line. Two vertical bars are used to represent absolute value. The symbol for absolute value of 3 is |3|.

  4. Example 1 Write an integer that represents 160 feet below sea level. Because it represents below sea level, the integer is –160. Example 2 Evaluate | –2 |. On the number line, the point –2 is 2 units away from 0, so | –2 | = 2.

  5. Lesson 7.3.2 Adding Integers • To add integers with the same sign, add their absolute values. The sum is: • positive if both integers are positive. • negative if both integers are negative. • To add integers with different signs, subtract their absolute values. The sum is: • positive if the positive integer's absolute value is greater. • negative if the negative integer's absolute value is greater.

  6. Example 1 Example 2 Find 4 + (–6). Find –2 + (–3). Use a number line. Use a number line. • Start at 0. • Start at 0. • Move 4 units right. • Move 2 units left. • Then move 6 units left. • Move another 3 units left.

  7. 7.3.3 Subtracting Integers • Subtracting an integer is just like adding the negative. • Subtracting a negative is like adding the positive. (The two negatives cancel each other out.)

  8. Example 1 Find 6 – 9. 6 – 9 = 6 + (–9) = –3 Example 2 Find –10 – (–12). –10 – (–12) = –10 + 12 = 2 Example 3 Evaluate a – b if a = –3 and b = 7. a – b = –3 – 7. = –3 + (–7). = –10

  9. 7.3.4 Multiplying Integers • To multiply integers: • Multiply the absolute values of the integers • Count the number of NEGATIVE integers • If the number is an EVEN number, the answer is positive • If the number is an ODD number, the answer is negative

  10. Example 1 5(–2) = –10 There is 1 negative integer, so the product is negative. Example 2 –6(–9) = +54 There are 2 negative integers, so the product is positive. Example 3 (–7)2=(–7)(–7)= +49There are 2 negative integers, so the product is positive. Example 4 (4)(2)(–9) = -72 There is 1 negative integer, so the product is negative. Example 5 (-1)(2)(-3)(4)(-5)(6)(-7) = ? Example 6 (-1)(2)(-3)(4)(-5)(6)(-7)(8)(-9) = ?

  11. 7.3.5 Dividing Integers • To divide integers: • Divide the absolute values of the integers • If both integers are positive, the quotient is positive • If both integers are negative, the quotient is positive (the 2 negatives cancel each other) • If one integer is positive and one is negative, the answer is negative. (Does not matter which is positive and which is negative.)

  12. Example 1 6 ÷ 2 = +3Both integers are positive, quotient is positive. • Example 2 -9 ÷ -3 = +3Both integers are negative, quotient is positive. • Example 3 -12 ÷ 4 = -3Only one of the integers is negative, quotient is negative. • Example 4 16 ÷ -4 = -4Only one of the integers is negative, quotient is negative. • Remember: Fractions are actually division problems, these same rules apply. -18 = +9 -2

  13. 7.4.3Add & Subtract Like Fractions • “Like fractions” have the same denominator • Such as 5/8 or 3/8 or -7/8 • To add/subtract like fractions: • Add/subtract the numerators • Keep the denominator • Simplify if needed

  14. Example 1 Find . Write in simplest form. Add the numerators. Write the sum over the denominator. = 1 Simplify. Example 2 Find . Write in simplest form. Subtract the numerators. Write the difference overthe denominator.

  15. 7.4.4Add & Subtract Unlike Fractions • “Unlike fractions” has denominators that are NOT the same. • For example: 2/3 and ¾ and 7/8 • To add/subtract unlike fractions: • Rename the fractions using the least common denominator (LCD). • Add or subtract as with like fractions. • If necessary, simplify the sum or difference.

  16. Example Find . Use the LCD. Rename using the LCD, 12. or Add the fractions.

  17. 7.4.5Add & Subtract Mixed Fractions • Convert mixed numbers to improper fractions. • Convert to to like fractions if needed. • Then, add or subtract the like fractions. • Simplify if necessary.

  18. Example 1 Find . Convert to improper fractions. Subtract. 2Simplify

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