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Integer Operations Guide: Addition, Subtraction, Multiplication, Division

Learn how to add, subtract, multiply, and divide integers efficiently with simple rules and examples. Easily compare and compute rational numbers using different methods. Practice exercises included.

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Integer Operations Guide: Addition, Subtraction, Multiplication, Division

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  1. 0-3: Operations with Integers

  2. 0-3: Operations with Integers • You can use a number line to add integers • Example 1: Use a number line to find -3 + (-4) • Start at 0 • Negative numbers move left • Positive numbers move right • Resulting position -4 -3

  3. 0-3: Operations with Integers • When the signs of two integers are the same • Add the two integers together, and keep their sign • 3 + 5 = 8 • -3 + (-5) = -8 • When the signs of two integers are different • Subtract the smaller integer from the larger, and keep the sign of the larger • 3 + (-5) = -2 • -3 + 5 = 2

  4. 0-3: Operations with Integers • Integers can also be multiplied and divided • When the signs of two integers are the same • The product/quotient is positive • 3(5) = 15 • -3(-5) = 15 • When the signs of two integers are different • The product/quotient is negative • 3(-5) = -15 • -3(5) = -15

  5. 0-4: Adding and Subtracting Rational Numbers

  6. 0-4: Adding and Subtracting Rational Numbers • You can use different methods to compare rational numbers. One way is to compare two fractions with common denominators. A second is to compare as decimals • Example 1: Replace ? with <, >, or = to make 2/3 ? 5/6 a true sentence • Common denominator • The common denominator of 3 & 6 is 6 • 2/3 = 4/6 • 5/6 = 5/6 • Since 4 < 5, 2/3 < 5/6

  7. 0-4: Adding and Subtracting Rational Numbers • Example 1: Replace ? with <, >, or = to make 2/3 ? 5/6 a true sentence • Write as decimals • 2/3 = 0.666666666667 • 5/6 = 0.833333333333 • Since 0.6 < 0.8, 2/3 < 5/6

  8. 0-4: Adding and Subtracting Rational Numbers • When fractions have the same denominator, simply add or subtract the numerator. • Remember to simplify, if possible • Find each sum or difference • 3/5 + 1/5 • 4/5 • 7/16 – 1/16 • 6/16 = 3/8 • 4/9 – 7/9 • -3/9 = -1/3

  9. 0-4: Adding and Subtracting Rational Numbers • When fractions have unlike denominators, find the least common denominator. • Convert each fraction using the least common denominator, then add or subtract • Simplify, if possible. • Find each sum or difference • 1/2 + 2/3 • 3/6 + 4/6 = 7/6 • 3/8 – 1/3 • 9/24 – 8/24 = 1/24 • 2/5 – 3/4 • 8/20 – 15/20 = -7/20

  10. 0-4: Adding and Subtracting Rational Numbers • To subtract a negative number, change it to adding its inverse (opposite) • When dealing with decimals, use the rules about adding/subtracting integers from earlier. (Repeated here as a reminder) • When the signs of two decimals are the same • Add the two decimals together, and keep their sign • When the signs of two decimals are different • Subtract the smaller from the larger, and keep the sign of the larger

  11. 0-4: Adding and Subtracting Rational Numbers • Find each sum or difference • -13.12 + (-8.6) • -21.72 • -32.25 – (-42.5) • -32.25 + 42.5 • 10.25

  12. 0-4: Adding and Subtracting Rational Numbers • Assignment • Page P16 • 1 – 39 (odds)

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