Then, around 1 st grade, you learned about zero, and you started calling them whole numbers. 0, 1, 2, 3, …0, 1, 2, 3, … The first kind of rational number you learned was called a natural number. 1, 2, 3, …1, 2, 3, … integers Around 4 th grade, you start hearing about negative numbers, and you start calling them integers. -2, -1, 0, 1, 2…-2, -1, 0, 1, 2… rational number If a number doesn’t fall into any of those categories – but you can write it as a fraction, it’s just called a rational number If you can’t write the number as a fraction, it’s an irrational number. These are all the real numbers.4.561…π

CLASSIFYING RATIONAL NUMBERS N, W, Z, Q Q Q Z, Q Z, Q Q W, Z, Q W, Z, Q Q N, W, Z, Q Q Q Q Z, Q Z, Q

irrational rational integer whole natural

irrational rational integer whole natural

irrational rational integer whole natural 1 π π 1 π 1 π

irrational rational integer whole natural

irrational rational integer whole natural

ABSOLUTE VALUE For each value, write it opposite, then its absolute value. Watch this: opposite absolute value 1) ) ) ) ) ) ) ) ) )

ABSOLUTE VALUE – │14│ – │14│ – 14 – 14 -│7│ -│7│ – 7 – │ 10 │ 16 - │ 10 │ – – – 19 4 – 19 – 15 – – 5 16 – – │2│+ 19 – │2│+ 19 – –

Integer Addition - Number Line 1. – It’s an addition problem. The first integer, -3, is the location, The second integer, 9, is the movement = – 7 It’s an addition problem. The first integer, 2, is the location, The second integer, – 7, is the movement. 2 + – 7 = – 6 + – 4 = -10 It’s an addition problem. The first integer, -6, is the location, The second integer, – 4, is the movement – 4

1. – – 3 9 – – 8 8 – 5 8 – 5 3 – 3 – 3 3. – 2 + – – 8 – 8 1.Signs are DIFFERENT. 2.SUBTRACT the absolute values. 3.Write down that number. 4.The answer is POSITIVE because the bigger absolute value (9) is positive. 1.Signs are DIFFERENT. 2.SUBTRACT the absolute values. 3.Write down that number. 4.The answer is NEGATIVE because the bigger absolute value (-8) is negative. 1.Signs are SAME. 2.ADD the absolute values. 3.Write down that number. 4.The answer is NEGATIVE because both integers are negative. Integer Addition - The Rules

Integer Addition - Practice = – 34 = – 15 = – 31 = – 26 = – 28 = 1 = 6 = – 7 = 9 = – 8 = – 7 = 14 = – 12 = 25 = – 31 = – 11 = 6 = 65 = – 80 = 41 = – 11 = 6 = 65 = – 80 = 41

1. 3 – 9 It’s a subtraction problem. The first integer, + 3, is the location,...the second integer, + 9, means move 9 spaces. 3 – 9 = – 2 – – 7 – 2 – – 7 = 5 3. – 6 – 3 = -9 –6 – 3–6 – 3–6 – 3–6 – 3 Integer Subtraction - Number Line The subtraction sign means move to the left... It’s a subtraction problem. The first integer, – 2, is the location, The subtraction sign means move to the left......but, the second integer, – 7, means reverse direction, then move 7 spaces. It’s a subtraction problem. The first integer, – 6, is the location, The subtraction sign means move to the left......the second integer, + 3, means move 3 spaces.

1.4 – – – – 4 10 – 4 6 – 6 – 6 2. – 7 – 1 – 7 + – 1 – 7 + – – 8 – 8 3. – 1 – – 3 – – – 1 3 – Change the subtraction to addition, then change the sign of the 2 nd integer. 3.Signs are DIFFERENT. 4.SUBTRACT the absolute values. 5.Write down that number. 6.The answer is NEGATIVE because the bigger – 10 absolute value ( – 10) is negative. 1.Change the subtraction to addition, then change the sign of the 2 nd integer. 3.Signs are SAME. 4.ADD the absolute values. 5.Write down that number. 6.The answer is NEGATIVE because both integers are negative. 1.Change the subtraction to addition, then change the sign of the 2 nd integer. 3.Signs are DIFFERENT. 4.SUBTRACT the absolute values. 5.Write down that number. 6.The answer is POSITIVE because the bigger + 3 absolute value ( + 3) is positive. Integer Subtraction - The Rules

Integer Subtraction - Practice = – 85 = – 54 = – 65 = – 56 = – 59 = – 15 = – 84 = 79 = 4 = – 37 = – 15 = – 84 = 79 = 4 = – 37 = 60 = 93 = 98 = 97 = 36 – 16 – ( – 95) – 5 – ( – 9)

Integer Multiplication Watch this: –7(8) = Why is this multiplication ? There’s a number smashed next to parenthesis. When you multiply or divide integers, it’s easy: Step 1: Multiply (or divide) the absolute values Step 2: Now, look the signs: If they match...it’s positive If they’re different...it’s negative – Integer Division 2. Why is this division? Fractions are division. When you multiply or divide integers, it’s easy: Step 1: Multiply (or divide) the absolute values. Step 2: Now, look the signs: If they match...it’s positive If they’re different...it’s negative =+10 or 10

Integer Multiplication and Division - Practice = – 48 = – 50 = 143 = 168 = – 105 = – 24 = 168 = – 105 = – 24 = – 70 = 70 = – 96 =288 = 24 =– 200 =288 = 24 =– 200 = – 21 = – 11 = 17 = – 5 = – 20 =

Integers Operations

Integers Operations 4. Samantha has $ in her checking account. If she makes a withdrawal of $127.78, what will be the new balance? 5. Jared and Natalie were playing basketball. After playing for a long time, Jared was losing by six points. Then he scored ten points in a row, but Natalie scored the next five points. Then they had to stop playing. Who won and by how many points? 3. The temperature at 10 P.M. one evening was 7 o C. At 4 A.M. the next morning the temperature was - 3 o C. What was the change in temperature from 10 P.M to 4 A.M.? 2. Lina started the week with a checking account balance of $496. During the week, she wrote a check in the amount of $58.50, another check in the amount of $147.29, and then made a deposit in the amount of $ What was her checkbook balance after this deposit? 6. Gertrude plays bingo every Tuesday. In the last 5 weeks, she has lost $7, lost $4, won $8, lost $9, and won $2. What was her average weekly gain or loss? hiked? 1. The change in elevation from the top to the bottom of the Grand Canyon is km. A tour guide hikes down to the bottom every day for a week, but rides an ATV back up. For the week, what is the total change in elevation that he hiked? km $ o C $ Natalie won by a point. $-2 or $2 loss