Unit 1 Rational Numbers Integers

Adding Integers The sum of two positive integers is always positive. 5+4=9. The sum of two negative integers is always negative. -5 +(-3)= -8. The sum of a positive integer and a negative integer is sometimes positive, sometimes negative and sometimes zero. 5 + (-1)=4 -5 +1=-4 -5 +5=0

Positive+ Negative 4+ (-2)= 7+ (-8)= 5 + (-5)= 9+ (-13)=

Negative + Positive (-9) + 5= (-4) + 7= (-6) + 5= (-3) + 10=

Negative + Negative (-4) + (-4)= (-7) + (-2)= (-1) + (-6)= (-8) + (-5)=

Subtracting Integers To subtract an integer, add its opposite. 4-9=4 + (-9)=-5 Or Keep, Change, Change -5 – (+7) Keep the 5, change the – to + and the + to - -5 + (-7)=-12 11- (-3)= 11 + 3=14

Positive – Positive 4 – 8= 5 – 6= 7 – 9= 3 – 12=

Positive - Negative 4 – (-5)= 8 – (-1)= 12 – (-7)= 3 – (-9)=

Negative - Positive (-9) - 5= (-4) - 7= (-6) - 5= (-3) - 10=

Negative - Negative (-2) - (-4)= (-7) - (-5)= (-5) - (-6)= (-8) - (-10)=

Multiplying Integers The product of two integers with the same sign is positive. 5X5=25 -5X-5=25 The product of two integers with different signs is negative. -5X4=-20 5X-4=-20

Negative x Negative -4 x -7 -4(-3) -14(-6) -8 x -9 What pattern do you see?

Negative x Positive -4 x 8 -12(6) 15(-3) 9 x -7 What pattern do you see?

Dividing Integers The quotient of two integers with the same sign is positive. 25÷5=5 -25÷-5=5 The quotient of two integers with different signs is negative. -25÷5=-5 -20÷5=-4

Negative ÷ Negative -48 ÷ -12 -108 ÷ -3 -64 ÷ -4 -72 ÷ -6 What pattern do you see?

Negative ÷ Positive Positive ÷ Negative -144 ÷ 4 84 ÷ -6 45 ÷ -3 -168 ÷ 8 What pattern do you see?

Summary Multiplying and Dividing Integers- If the signs are the same, the answer is positive. If the signs are different, the answer is negative.

Warm Up -4 +8= 5+ -2= (-3) – 6= 5 – (-5)=

Practice Problems: (-8) × 4 =_______ 9 × (-6) =_______ (-1) × (-10) =_______   16 ÷ (-4) = _______ 20 ÷ (-2) = _______ -35 ÷(- 5) = _______

Exit Ticket 4(-12) 64 ÷ -8 -56 ÷ -7 (-5)(-9)