1 / 18

Integers: Addition, Subtraction, Multiplication, and Division

Learn how to work with integers; add, subtract, multiply, and divide them; master absolute values, and apply operations on number lines. Practice problems included.

garber
Download Presentation

Integers: Addition, Subtraction, Multiplication, and Division

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related