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
= 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 =
5/6 =
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
(-8.6)
-21.72
– (-42.5)
10.25

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