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7th Grade Math Summer Homework
Due: Tuesday, August 11, 2015
Adding and Subtracting Positive and Negative Numbers
Examples:
1.) 2 + 3 = 5
2.) 2 + (-3) = -1
3.) 2 – 3 = -1
4.) 2 – (-3) = 5
Notice: + 3 is the SAME as – (-3) AND + (-3) is the SAME as - 3
Now You Try: Use the number line to find the solutions to the
problems below.
Great Job! Here is A DIFFERENT WAY to Add and Subtract postive
and negative numbers.
Key Points:
1. ) Adding and Subtracting Positive and Negative numbers is the
same as Combing the numbers.
2.) Just like Combing (Mixing) Tea and Lemonade.
If there is more Tea it tastes more like Tea, if there is more
Lemonade it tastes more like Lemonade.
3.) Positives and Negatives cancel each other out.
and
= 0
4.) Cross out one negative for every positive and what is left is your
answer.
Your answer is +1 (Positive 1)!
Examples:
1+2=3
1 + (-2) = -1
+3
-1
** Two negatives together make a positive. -(-2) changes to +2
1 – 2 = -1
1 – (-2) = 3
1 + (+2) = 3
-1
+3
Notice: + 2 is the SAME as – (-2) AND + (-2) is the SAME as – 2
Now You Try: Draw positive and negative circles and cross out
equivalent positive and negatives to solve the problems below.
Fantastic! Number lines and pictures help us understand THE RULES
of Adding and Subtracting Positive and Negative numbers. However,
when we add and subtract LARGER numbers it does not make sense
to draw a number line or pictures. Here is a method you can use for
LARGER numbers.
Key Points:
1.)
Same sign: Add the numbers and keep the sign.
43 + 56 = 99
OR
-22 – 67 = -89
You can use these boxes to help you organize your work.
2.)
Different Sign: Subtract the number and keep the sign of the
larger number.
-43 + 56 = 13
OR
22 – 67 = -45
When numbers are on different sides move the smaller number
and subtract.
Examples:
25 + 34 = 59
** Two negatives together make a positive. -(-34) changes to +34
25 + (-34) = -9
25 – 34 = -9
25 – (-34) = 59
25 + (+34) = 59
Notice: +34 is the SAME as – (-34) AND + (-34) is the SAME as – 34
Now You Try: Draw a box with a positive and negative sign (+/-) to
solve the problems below.
Now You Try: Use your favorite method to solve the mixed practice
problems below.
Challenge: Try these challenge problem below!
Rules for Multiplying and Dividing Integers
Positive x Positive = Positive
(4) x
(6)
=
24
Positive x Negative = Negative
(10) x
(-4)
= -40
You can also use the Triangle Trick to remind you.


+
-
-
Cover up the sign (positive/negative) of the numbers you are multiplying.
The remaining sign that is left, will tell you whether the answer is positive
or negative.
For example, (+8) times (-7). Cover up a + and a – sign on the triangle.
What is left? A negative sign, so my answer is -56. 
Positive ÷ Positive = Positive
(24) ÷
(6)
=
4
Negative x Negative = Positive
Positive ÷ Negative = Negative
(40) ÷
(-4)
= -10
Negative x Positive = Negative