0-3: Operations with Integers

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

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

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

0-4: Adding and Subtracting Rational Numbers

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

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

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

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

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

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

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