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7th Grade Math / Lesson 7A: Basic Operations

OPERATIONS
What will we be learning in this unit?


  • In this lesson you will learn how the effects of operations on numbers.

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


Adding


  1. If adding numbers that have the same sign, just add the numbers and use the sign that the numbers have.

    Ex) -3 + -4 = -7     Ex) 3 + 4 = 7

  2. If adding numbers that have different signs, subtract the numbers and use the sign from the number that is "bigger".

    Ex) -3 + 4 = 1 It is positive because the 4 was the "bigger" number.

    Ex) 3 + (-4) = -1 It is negative because the -4 is the "bigger" number.


    Adding


    Practice adding integers

    1. 45 + 23 =

    2. -34 + (-21) =

    3. - 45 + 75 =

    4. -65 + 20 =


    Adding


    Practice adding integers

    1. 45 + 23 = 68

    2. -34 + (-21) =-55

    3. - 45 + 75 =30

    4. -65 + 20 =-45


    Subtraction


    Use the same rules as addition because all subtraction problems can be changed to addition by adding the opposite of the second number. Don't do anything to the first number, change the subtraction to addition and use the opposite of the second number, then use the addition rules.

  3. Ex) -3 - (-4) = -3 + 4    Change - to + and change -4 to 4. Now use the rules for addition.
    -3 + 4 = 1

  4. Ex) 12 - 8 = 12 + -8    Change - to + and change 8 to -8. Now use the rules for addition.
    12 + -8 = 4


  5. Subtraction


    Practice changing these to addition of the opposite and get the answer.

    1. 10 - (-2) =

    2. -30 - 4 =

    3. 15 - (-3) =

    4. 35 - 29 =


    Subtraction


    Practice changing these to addition of the opposite and get the answer.

     

    1. 10 - (-2) =   10 + 2 =
     
     
    2.  -30 - 4 =    -30 + (-4) =
     
     
    3.  15 - (-3) =   15 + 3 =
     
     
    4.  35 - 29 =   35 + (-29) =
     


    Subtraction


    Practice changing these to addition of the opposite and get the answer.

     

    1.   10 - (-2) =   10 + 2 =     12
       
    2.   -30 - 4 =    -30 + (-4) =  -34
       
    3.   15 - (-3) =   15 + 3 =    18
       
    4.   35 - 29 =   35 + (-29) =    6
     


    Word Problems
     
    • A football team heading for their end zone has the following results on their 4 tries with the ball. First try, they run the ball for a gain of 4 yards. Second try, they pass the ball for a short 5 yard gain. Third try, the quarterback gets sacked for a loss of 20 yards. The last try, they complete a 10 yard pass. What is the total gain or loss in yards for the 4 plays?
       
    • Solution   

                   first try         4 yards

                    second try    5 yards

                    third try        -20 yards

                   fourth try        10 yards

     
    Add these together and you get   -1 yards  which means they lost 1 yard from when they began