Name _______________________________
Date ___________
UNIT 1 MATH REVIEW (Math 7)
KEY IDEAS
 Adding Rational
Numbers
Ex 1: -3 + -4
 (keep sign)

(add)
Case I
Rational numbers with
the same sign.
(neg + neg)
(pos + pos)
 Keep the sign
 Add the numbers
neg + neg = neg
4+3=7
The answer:
-
Put this number on the answer line
-7
Ex 2: -2.5 + -7.08
 (keep sign) neg + neg = neg

write a neg sign on answer line
write a neg sign on answer line
-
(add)
Line up the decimal points!
2.50
+ 7.08
The answer: -9.58

4
1
+9
7
7
(keep sign) neg + neg = neg

(add)
Ex 3:
2
write a neg sign on answer line
-
Remember – you need like denominators
4
7
1
+9
7
5
11
7
2
(add)
Practice
4)
5
5)
1
5
+ 8 = _____
3
6
The answer:
-
-
45 + 32 = _____
-11
6)
5
7
–
12.7 + -37.25 = ______
KEY IDEAS
 Adding Rational
Numbers
Case II
Rational numbers with
different signs.
(pos + neg)
(neg + pos)
 Keep the sign of the
number with the highest
absolute value
 Subtract the numbers
Ex 7: -3 + 4
4 bigger #
(subtract) 3 smaller #
1
1
Ex 8:
neg + pos
SO
subtract
Since 4 is bigger, the answer is positive
2.5 + -7.08
pos + neg
SO
Answer:
subtract
(line up the decimals!)
(subtract)
7.08 bigger #
- 2.50 smaller #
Since 7.08 is bigger, the answer is negative
Ex 9:
-2
4
1
+9
7
7
neg + pos
Since you can’t subtract
1
7
4
-2
7
9
(subtract)
bigger #
SO
1
7
-
9
1
7
-4.58
subtract
4
7
7 1
8 +
7 7
smaller #
Since
Answer:
is bigger, the answer is positive
you need to borrow from 9
8
7
4
-2
7
8
Answer:
6
4
7
Practice
10)
7 + 3 =_____
11)
13) 6 + -15 =_____
14) –7 + -3 =____
15) 62 + -35 = ______
16) -58 + -27 =______
17) -10.3 + -19.7 = ____
18) -7.5 + 2.3 = ______
12)
3
1

2

4
7
= _____
8
19.31 + -4.58 = _____
1
5
19)  8  ( 4 ) = _____
3
9
20) 3
2

3

6
2

7 _______
Use the number lines and show the sum of each addition problem below.
21)
-
4 + 9 = ____
22) -3 + -8 = ____
How do we use the calculator?
Show the keys you would press to solve
a)
-
4 + 8 + -3 + -9 + 10
1
5
b)  8  ( 4 )
3
9
c) -10.3 + -19.7
KEY IDEAS
SUBTRACTING
INTEGERS
1st Rewrite as addition by
adding the opposite
*Keep the 1st integer
* turn subt.(-) to add (+)
* write the opposite of
the second integer
Add the opposite

Then, use addition
rules
Ex 23:
-
4 - 6
Step 1: rewrite subtraction as an addition problem by adding the opposite
-
4
Keep
+
ADD
Step 3: use the addition rules
Ex 24:
-
6
OPPOSITE
-
4 + -6 =
-
10
-
3 - -5
Step 1: rewrite subtraction as an addition problem by adding the opposite
-
3
Keep
+
5
ADD
Step 3: use the addition rules
OPPOSITE
-
3 + 5= 2
Practice
-
26) -50 - 38 = _____
27)
28) 8 - -5 = _____
29) 35 - -2 = _____
30) –11 + 6.5 =______
31) 19.31 - -4.58 =_____
32) 3.7 – 4.8 = ______
33) –8.36 – 4.2 = _____
1
2
35) 3  7  _______
4
3
36) 3 + 4 – 8 - -7 + -3 =_____
25)
4 - 3= _____

3
5

34) 4  2
5
 ______
8
Use the number lines to show each subtraction problem.
37) 4 - 12 = ___
-
35 - 35 = ______
38)
-
9 - -4 = ___
39) -6 - 3 = ___
KEY IDEAS
 Absolute Value
Ex 40:
-The distance a number
is from zero
-Always a positive answer!
Ex 42:
Practice
43)
7  15
5
= _____
44)
KEY IDEAS
= 5
Ex 41:
 100
23  43 =  20 = 20
25
= ______
45)
36  24
= _______
Ex 43: State the opposite of each.
Comparing and Ordering Integers
 Use the number line to
help you.
 Numbers to the right are
always greater!
 Opposites are numbers
that are the same distance
from 0 but on different
sides of 0.
a) -2
_2_
b) +5
_-5__
Ex 44: Compare using >, <, =.
3 > -4
-
b) -6 < 5
Practice
45) State the opposite of each.
a) -27 ___
b) 57 ___
c) -13 ___
d) 0 ___
46) Compare using >, <, =.
a) -13 ___ 0
b) 99 ___ -100
= 100
c)  5 ___  6
d)  4 ___ 4
47) Order the integers in each set from least to greatest.
{ -57, 2, 16, -89, -90, 0 } __________________________________
48) Place the following number’s on the number line below.
-4, 3, -5, 1.5, -3, 2
KEY IDEAS
 Word Problem
-Read
-Plan
-Solve
Ex 49:
If the overnight temperature at the Arctic Circle was
-14.8F, and the temperature rose28.5F during the day,
how many degrees was it during the day than during the
overnight? Write a math sentence to answer.
Math sentence: __________________________________
Show Your Work!
50) The highest recorded temperature on Earth51) The temperature in Alaska was 4oC at
was recorded in Africa at 136F, while the
1:00 A.M. The temperature decreases 2oC
lowest was -129F in Antarctica. What is the per hour. What was the temperature at
difference between these extreme
5:00A.M.?
temperatures?
Practice
Write a
52) A research team aboard an underwater
53) You park in a garage 2 floors below ground
research vessel descends 1,500 feet beneath level. Then you get in the elevator and go up
the surface of the water. They then rise
9 floors. What floor are you on now?
525 feet and descend again 350 feet.
How many feet below the surface are they?
54) The overnight temperature at the Arctic Circle
was -14F. The temperature rose 8F during
the day. What is the temperature now?
Review it all
1. Write each statement as an integer.
a)A gain of 4 yards ____ b) A loss of $5 ____
c) 25 feet below sea level____
3. Write the absolute value of
a)  -4 _______
b)  7 _______
2. Write the opposite of each number:
a) –74_____
b) 65 ______
4. Use < , > or =
a) 4 ___-2
b) -7 ___ 7
5. Order the numbers from least to greatest
a) 24, -42, -12, 6, 0 ___________________ b) 25, -26, 26, 0, -25 _____________________
6. Which of the following integers is the
greatest?
a. –99
b.  98
c. 97
d. –100
7. Which of the following integers is the least?
8. Simplify  -7
a. 1
b. 0
c. 7
d. –7
9. Compare the following integers
–54 ___ 45
a. <
b. >
c. =
10. Add the following integers:
11. Subtract the following integers:

2
1
3   4 = ________
3
9
Explain how you got your answer
a. –15
b.  -20
c. –19
d. 0
5.78 - -14.2 = __________
Explain how you got your answer
12.
Math sentence: ________________________________