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Num
ber SeNSe
Name ____________________________________________
Period ____________
Number
S
eNSe
+ x
÷
IN
TE
GE
RS
—
L
ike
Sign
s
Diff
eren
t Si
gns
L
ike
Sign
s
Add
and
ta
ke th
e si
gn
Subt
ract
and
ta
ke si
gn o
f la
rges
t
abso
lute
val
ue
Cha
nge
to
Add
ition
by:
“K
eep—
Cha
nge–
C
hang
e”
Ans
wer
is
Po
sitiv
e
Ans
wer
is
N
egat
ive
-2 +
(-4)
= -6
4
+ 6
= 10
-4 +
8 =
4
6
+ (-
12) =
-6
(-
9) -
(-2)
=
(-
9) +
(+2)
= -7
8 x
6 =
48
(-
45) ÷
(-9)
= 5
9 x
(-3)
= -2
7
(-72
) ÷ 1
2 =
-6
D
iffer
ent
Sign
s
Unit B Vocabulary:
1
2
Math www.CommonCoreSheets.com
Name:
Answers
1-10 92 83 75 67 58 50 42 33 25 1711-12 8 0
1) 78.9 - 55.779 = 23.121
2) 73 + 48.7 = 121.7
3) 41.3 - 20.65 = 20.65
4) 46 + 39.5 = 85.5
5) 72 - 67.01 = 4.99
6) 65 + 56.8 = 121.8
7) 58 - 45.183 = 12.817
8) 79.3 + 10.21 = 89.51
9) 17 - 1.2 = 15.8
10) 92 + 8.83 = 100.83
11) 67.15 - 24.302 = 42.848
12) 96 + 37.367 = 133.367
1. 23.121
2. 121.7
3. 20.65
4. 85.5
5. 4.99
6. 121.8
7. 12.817
8. 89.51
9. 15.8
10. 100.83
11. 42.848
12. 133.367
Adding & Subtracting DecimalsSolve each problem.
13
Math www.CommonCoreSheets.com
Name:
Answers
Modified 1-10 90 80 70 60 50 40 30 20 10 0
1) 78.9 - 55.779 = 23.121
2) 73 + 48.7 = 121.7
3) 41.3 - 20.65 = 20.65
4) 46 + 39.5 = 85.5
5) 72 - 67.01 = 4.99
6) 65 + 56.8 = 121.8
7) 58 - 45.183 = 12.817
8) 79.3 + 10.21 = 89.51
9) 17 - 1.2 = 15.8
10) 92 + 8.83 = 100.83
20.65 15.8 23.121 85.5 89.51
12.817 121.7 100.83 4.99 121.8
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Adding & Subtracting DecimalsSolve each problem.
14
Math
Name:
www.CommonCoreSheets.com
Answers
1-10 92 83 75 67 58 50 42 33 25 1711-12 8 0
1) 63 .9× 7 .0
0+ 44730
447 .30
2) 44 .84× 9 .84
17936358720
+ 4035600441 .2256
3) 88 .6× 5 .01
8860
+ 443000443 .886
4) 39 .6× 5 .20
07920
+ 198000205 .920
5) 28 .15× 5 .5
14075+ 140750
154 .825
6) 14 .36× 4 .9
12924+ 57440
70 .364
7) 63 .14× 2 .08
505120
+ 1262800131 .3312
8) 18 .65× 6 .8
14920+ 111900
126 .820
9) 16 .92× 8 .4
6768+ 135360
142 .128
10) 80 .1× 2 .8
6408+ 16020
224 .28
11) 5 .9× 3 .9
531+ 1770
23 .01
12) 5 .6× 6 .2
112+ 3360
34 .72
1. 447.30
2. 441.2256
3. 443.886
4. 205.920
5. 154.825
6. 70.364
7. 131.3312
8. 126.820
9. 142.128
10. 224.28
11. 23.01
12. 34.72
Multiplying with DecimalsSolve each problem.
15
Math
Name:
www.CommonCoreSheets.com
Answers
Modified 1-9 89 78 67 56 44 33 22 11 0
1) 63 .9× 7 .0
0+ 44730
447 .30
2) 44 .84× 9 .84
17936358720
+ 4035600441 .2256
3) 88 .6× 5 .01
8860
+ 443000443 .886
4) 39 .6× 5 .20
07920
+ 198000205 .920
5) 28 .15× 5 .5
14075+ 140750
154 .825
6) 14 .36× 4 .9
12924+ 57440
70 .364
7) 63 .14× 2 .08
505120
+ 1262800131 .3312
8) 18 .65× 6 .8
14920+ 111900
126 .820
9) 16 .92× 8 .4
6768+ 135360
142 .128
447.30 126.820 154.825
131.3312 441.2256 70.364
142.128 205.920 443.886
1.
2.
3.
4.
5.
6.
7.
8.
9.
Multiplying with DecimalsSolve each problem.
16
6-1 Repeating Decimals
Key Concept Part One Repeating Decimals
92
= 112
=
7
Part Two Work Space:
8
Part Three
=
9
Practice 6-‐1 Repeating Decimals
Gary brings 391pounds of hamburger to cook at Bobby’s cookout. Bobby already bought 5
114pounds.
a.) Express each amount as a decimal.
b.) How much hamburger do they have total? Round to the nearest hundredth.
c.) If they are making hamburgers that are each 31pound, how many hamburgers can they make?
10
6-2 Terminating Decimals
Key Concept A TERMINATING DECIMAL is a decimal the ENDS! Part One Part Two
11
Part Three
12
Any Rational Number (a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal. Just divide the numerator by the denominator.
Directions:
-‐ Change the following fractions to decimals. -‐ Put a “T” or “R” next to your answer for either terminating or repeating decimals.
1) 51 2)
21 3)
53
4) 41 5)
32 6)
85
7) 92 8)
52 9)
103
10) 72 11)
74 12)
127
13) 5021
14) 43 15)
54
16) 65 17)
98 18)
83
13
Comparing Integers (A)Compare the pairs of integers using <, >, or =
14 12 5 4 10 9 -12 -13
-15 -14 -5 -6 -8 -7 13 15
6 7 0 2 10 9 9 8
-2 -3 1 3 -14 -13 -4 -3
-4 -3 -4 -2 -10 -11 15 14
1 0 7 5 -8 -7 -3 -1
-13 -15 -5 -3 11 10 12 13
-4 -5 3 5 -3 -1 0 1
10 9 -2 -1 3 2 15 13
8 6 -14 -12 -10 -8 14 13
Math-Drills.com14
Student Name: __________________________ Score:
Free Math Worksheets @ http://www.mathworksheets4kids.com
Use > or < or = sign to compare the integers:
- 5 - 5 - 9 - 1 - 2 - 6
- 7 - 4 - 1 - 6 - 7 - 2
- 6 - 3 - 2 - 5 - 7 - 3
- 5 - 9 - 8 - 8 - 6 - 9
- 4 - 6 - 6 - 3 - 1 - 7
- 3 - 8 - 9 - 8 - 4 - 1
- 7 - 9 -3 - 9 - 8 - 5
- 2 - 7 - 9 - 2 - 8 - 1
- 6 - 5 - 5 - 4 - 3 - 2
Compare
15
Student Name: __________________________ Score:
Free Math Worksheets @ http://www.mathworksheets4kids.com
Answers
- 5 = - 5 - 9 < - 1 - 2 > - 6
- 7 < - 4 - 1 > - 6 - 7 < - 2
- 6 < - 3 - 2 > - 5 - 7 < - 3
- 5 > - 9 - 8 = - 8 - 6 > - 9
- 4 > - 6 - 6 < - 3 - 1 > - 7
- 3 > - 8 - 9 < - 8 - 4 < - 1
- 7 > - 9 -3 > - 9 - 8 < - 5
- 2 > - 7 - 9 < - 2 - 8 < - 1
- 6 < - 5 - 5 < - 4 - 3 < - 2
16
4-1 Rational Numbers
Part One
W I R
17
Example
18
Rational Number Practice
Part I - Place each of the following numbers in the correct column(s). Some numbers might belong in more than one column, so be careful! Make sure you list each number in EVERY column it belongs in.
0 3 -3 1.5 5.1− 32
32
− 25.0 25.0−
Whole Numbers Integers Rational Numbers
Part II - Place each of the following numbers in the correct set below.
0 3 -3 1.5 5.1− 32
32
− 25.0 25.0−
Real Numbers
Integers
Whole Numbers
Rational Numbers
19
Rational
Number
Whole
Yes/No?
Integer Yes/No?
Rational: Yes/No?
WHY?
(Terminating vs. Non-terminating) (Repeating vs. Non-repeating)
1) 0.36
2) 36.0
3) -7
4) 6.8556546
5) 0.121314151...
6) 3.6198
7) 0.24682
8) 3.0
9) 1.45454545…
10) 0.12112111211112
20
4-1 Absolute Values and Opposites
Part Two
21
Part Three Define Opposites:
22
Name: __________________________ Score:
Free Math Worksheets @ www.mathworksheets4kids.com
Find the value:
1)
|4| =
2)
|−13| =
3)
−|10| =
4)
−|−7| =
5)
|11| =
6)
|−2| =
7)
−|12| =
8)
−|5| = −
9)
|1| =
10)
|−14| =
11)
−|8| = −
12)
−|−13| =
13)
|3| =
14)
|−7| =
15)
−|4| =
16)
−|−15| =
17)
|9| =
18)
|−12| =
19)
−|14| =
20)
−|−2| =
21)
|5| =
22)
|−8| =
23)
−|11| =
24)
−|−10| =
Absolute Value
23
Name: __________________________ Score:
Free Math Worksheets @ www.mathworksheets4kids.com
Find the value:
1)
|−7| − |3| =
2)
|12| + |8| =
3)
|13| − |−7| =
4)
|−14| + |−4| =
5)
|−9| + |7| =
6)
|6| − |1| =
7)
|11| + |−12| =
8)
|−10| − |−2| =
9)
|−13| + |4| =
10)
|10| + |8| =
11)
|12| − |−7| =
12)
|−15| + |−4| =
13)
|9| − |4| =
14)
|14| + |3| =
15)
|10| − |−6| =
16)
|−11| + |−3| =
17)
|−15| − |7| =
18)
|9| − |2| =
19)
|14| + |−5| =
20)
|−11| − |−6| =
21)
|−5| + |4| =
22)
|12| − |8| =
23)
|7| − |−1| =
24)
|−10| + |−5| =
Absolute Value
24
Practice with Absolute Value
Directions: Find the absolute value of each of the following. 1) | + 6 | 2) | - 4 | 3) - | 19 | 4) - | - 5.3 |
5) - | 42 | 6) | 20 - 19 | 7) - | 60 + 13 | 8) | 10.6 - 3 |
9) | 87 -
87 |
10) | 100 | - | -8 | 11) | 100 | + | -8 | 12) - | 4.6 - 4 |
13) 5 | - 4 | 14)
2|10| −
15) -2 | 15 - 8 | 16) - | 8 - 2 |
25
4-1 Opposites
Examples : -6 and 6 since -6+6=0
½ and -½ since ½+-½=0
Absolute Value
The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive.
On a number line it is the distance between the number and zero.
The symbol for absolute value is to enclose the number between vertical bars such as |-20| = 20 and read "The absolute value of -20 equals 20".
Examples: |-19| = |25| = 53
− = |0.02| = |5-2| = |4| + |-9| =
Order of Operations (PEMDAS)
Step 1: Parentheses; Operations within the grouping symbols. ( ) [ ],,
Step 2: Exponents, Evaluate all powers. Step 3: Multiplication and Division in order from left to right. Step 4: Addition and Subtraction in order from left to right.
* Using these rules with ensure that numerical expressions have only one value. * Simplify:
A. 5 + (12 - 3) B. (5 - 1)³ ÷ 4 C. ( )[ ] 1223 −+−•
D. 20 – 2(4 - 1) * 3 E. 5 * 3² - 7 F. 10210 3
−
−
26
Order of Operations
Directions: Solve each expression using the order of operations (use PEMDAS to help you) 1) 321025 +÷−
2) )23(15 +÷
3) 2412 •÷
4) 45218 +•−
5) 12824 −•÷
6) 2)31220( ÷÷−
7) 4556325100 −•−•+
8) 245315 −•÷
9) 277 23 −
10) 395)34( 2
+
••
27
Order of Operations
Directions: Solve each expression using the order of operations (use PEMDAS to help you)
1) 2478 ÷+•
2) 6)34(2 −+
3) 323 •
4) 2)43(2 +
5) 4
5102 ÷+
6) 4)416( 2 ÷+
7) 10)24(6 32 −−
8) 7
)423( 2 −•
9) 12)546(916 2 ÷•−−
10) ⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−
1141058 2
23
28
4-2 Additive Inverse Property of Addition & Adding Integers
Examples:
Adding Integers using a Number Line:
Adding Integers using “chips”: =+− 58
Zero Pairs:
=−+ 47
=−+− 510 =+− 1012
29
Lesson 4-2 Adding Rational Numbers on a Number Line
5 and (-5) are called: - Additive Inverse Examples: - Opposites - Zero Pairs
• To ADD a positive integer start at the first number and move to the
_____________________ on the number line.
• To ADD a negative integer start at the first number and move to the
_____________________ on the number line.
Directions: Use these number lines to solve the following problems.
1. –2 + +5 =
2. –9 + –3 =
3. +5 + –7 =
4. –4 + +4 =
5. –8 + –2 =
6. +1 + –8 =
30
Try to solve #7 without a number line.
7. -25 + +30 =
You Try:
1) Which of the following number sentences represents the number line above? A) − 4 + 2 = 6 B) − 4 + 6 = 2 C) 2 + 6 = − 4 D) 2 + − 4 = 6
Directions: Use these number lines to solve the following problems.
2. –8 + +7 =
3. –2 + –6 =
4. +10 + –15
5. –6 + +9 =
6. –1 + –9 =
7. +8 + –8 =
31
Lesson 4-2 Adding Rational Numbers with Chips
Sample: 4 + − 6 = ___________
There are 4 zero pairs, which only leaves two negative chips, so the answer is − 2
Directions: Use your chips to set up each problem below. For #1-6, Draw the Integer Chip model to demonstrate how to find the solution. Then, find the solution.
1) − 5 + −8 = ______ 2) + 2 + −7 =______
3) + 8 + −3 = ______ 4) − 4 + +3 + − 2 =______
5) − 2 + −4 = ______ 6) + 4 + 5 =______
7) − 3 + 6 =______ 8) − 9 + −12 =______
9) 6 + + 13 + −4 =______ 10) 7 + − 13 =______
32
11) −5 + 12 = ______ 12) −5 + 3 =______
13) 5 + −4 + 4 = ______ 14) 5 + − 5 =______
15) −6 + −11=______ 16) +6 + +11 =______
17) −7 + −6 + 9 =______ 18) −8 + −2 + −4 =______
19) At 10 pm on New Years Eve, the temperature in West Seneca was 24 degrees. At midnight, the temperature dropped 36 degrees! What was the temperature at midnight?
Write a number sentence to describe this situation: ______________________
Solve:
20) Bob got on an elevator on the 5th floor. He traveled 2 floors up, and 4 floors down before he reached his destination. At which floor did Bob get off the elevator?
Write a number sentence to describe this situation: ______________________
Solve:
33
ADDING INTEGERS
SAME SIGNS DIFFERENT SIGNS
( ) ( )=+++ 19
( ) ( ) =++− 66 ( ) ( ) =−++ 47
( ) ( ) =−++ 97 ( ) ( ) =−+− 51
( ) ( ) =+++ 99
34
Adding Integers (A)Use an integer strategy to find each answer.
(-3) + (+12) = (-15) + (-10) = (+15) + (-10) =
(-15) + (-3) = (+6) + (+5) = (-7) + (-5) =
(+9) + (+4) = (+9) + (+11) = (+10) + (+11) =
(-15) + (+15) = (-7) + (+5) = (-2) + (+11) =
(+11) + (-3) = (-9) + (-14) = (+14) + (+11) =
(-5) + (-7) = (-10) + (+2) = (+4) + (+13) =
(+11) + (+13) = (-7) + (-12) = (-4) + (-7) =
(-14) + (+5) = (-1) + (+10) = (-5) + (-11) =
(+5) + (-14) = (-3) + (-10) = (-8) + (-5) =
(+8) + (-12) = (-10) + (-9) = (-1) + (+3) =
Math-Drills.Com35
Adding Integers (A)Use an integer strategy to find each answer.
(-11) + (-5) = 12 + 2 = 10 + (-13) =
(-8) + (-5) = 13 + 14 = (-7) + 15 =
11 + 15 = (-3) + (-1) = (-12) + (-1) =
(-2) + (-15) = 10 + (-12) = (-5) + 7 =
13 + (-4) = 12 + 2 = 12 + (-13) =
(-9) + (-1) = 9 + (-6) = 3 + (-3) =
2 + (-13) = 14 + (-9) = (-9) + 2 =
(-3) + 2 = (-14) + (-5) = (-1) + 7 =
(-3) + (-3) = 3 + 1 = (-8) + 13 =
10 + (-1) = (-13) + (-7) = (-15) + 12 =
Math-Drills.Com36
Adding Integers (A)Use an integer strategy to find each answer.
14 + 12 = 4 + -2 = 13 + 9 =
-11 + -11 = -8 + 13 = 6 + 14 =
10 + 7 = 15 + 9 = 2 + 6 =
15 + -15 = -11 + -3 = -6 + -3 =
6 + -9 = -2 + 2 = 15 + -1 =
11 + -5 = 12 + -8 = 4 + 2 =
9 + 5 = 4 + -7 = -8 + -12 =
-2 + 14 = 10 + 6 = 6 + -14 =
13 + 4 = -13 + -15 = -4 + -8 =
-6 + 7 = -7 + 12 = -6 + 9 =
Math-Drills.Com37
Adding Integers (A)Use an integer strategy to find each answer.
28 + -82 = 10 + 36 = 39 + 95 =
66 + 36 = 66 + 81 = -69 + 5 =
48 + 77 = -12 + -4 = -38 + -19 =
49 + -76 = 6 + 47 = 79 + 98 =
20 + -56 = 67 + -23 = -85 + -78 =
-57 + -22 = -36 + -32 = -81 + -5 =
-11 + 98 = -26 + 17 = -49 + -20 =
-93 + -20 = -10 + 58 = -58 + -21 =
-70 + 5 = 20 + 88 = 20 + 6 =
28 + 52 = 14 + 72 = 18 + -56 =
Math-Drills.Com38
4.3 ~ Addition with Rational Numbers When adding two numbers with the same sign: When adding two numbers with different signs:
39
ADDING RATIONAL NUMBERS
Signs: Operation: Solution: SUM: 1)
95
98+−
Same or
Different
Add or
Subtract
Positive or
Negative
95
98+−
2)
106
51 −−
+
Same or
Different
Add or
Subtract
Positive or
Negative
106
51 −−
+
3) 14.07 + − 3.9 =
Same or
Different
Add or
Subtract
Positive or
Negative
14.07 + − 3.9 =
4)
10910
6519 +−
Same or
Different
Add or
Subtract
Positive or
Negative
10910
6519 +−
5)
Same or
Different
Add or
Subtract
Positive or
Negative
40
8) At 10 pm, the temperature in Alaska was − 12 degrees.
At midnight, the temperature dropped 24 degrees.
Write an addition problem that represents this situation.
What was the temperature at midnight?
9) Justin opened a bank account by depositing (putting in) $50.80 in it on Monday. He withdrew (took out) $36.11 on Tuesday. Then deposited his check worth $77.92 on Wednesday.
Write an addition problem that represents Justin’s situation.
How much money does Justin currently have in his account?
6)
Same or
Different
Add or
Subtract
Positive or
Negative
7)
Same or
Different
Add or
Subtract
Positive or
Negative
41
10) Write in words one addition problem as a real world example. Be sure it includes positive and negative numbers. Then write it as a mathematical sentence with a solution!
Sample: I deposit $20 and then withdraw $17 the next day. + 20 + − 17 = + 3
11) − 20 + + 14 + − 2 = 12) + 12 + − 4 + − 10 =
13) 7.26 + − 9.4 = 14) 17.08 + − 5.2 =
15) =+−
72
75
16) =−
+−
127
61
17) 532.6 +−
= (Remember: you can’t compare apples to oranges!)
42
Practice 4-‐3
Adding Rational Numbers
1) Which of the following numbers are not a whole number?
0, 5, -‐3, 24
Explain why.
2) Tell whether each statement is true or false.
a) All whole numbers are integers True or False
b) All rational numbers are integers True or False
c) 3.7 is a rational number True or False
d) All integers are whole numbers True or False
3) Find the sum of the following:
a) 15 + 27 = b) -‐25 + 31 = c) -‐73 + (-‐10) =
d) 35 + (-‐17) = e) -‐105 + 26 = f) -‐53 + 19 =
4) Find the sum of the following:
a) 95 + 92 = b) 3.7 + 29.5 =
c) 6.2 + (-‐17.2) = d) 65 + -‐
83 =
e) 658 +
312 = f)
749 + -‐
215 =
43
Adding Rational Numbers
Examples: Add. 1) 4 + 7 = 11 3) 4 + (-7) = -3 2) - 4 + 7 = 3 4) - 4 + (-7) = -11 Add.
1) -5 + (-6) 2) -8 + 3 3) -5 + 5 4) -14 + (-13) 5) 4 + (-5)
6) -3 + 10 7) -6 + (-15) 8) 2 + (-8) 9) -7 + 5 10) -1 + (-4)
11) 16 + (-12) 12) -4 + (-8) 13) -7 + (-5) 14) -6 + 7 15) 10 + (-6)
16) 103
109 −+ 17)
73
72 −+
− 18) 25
21 −+
19) -2.1 + 3.5 20) -0.8 + (-0.3)
44
4-‐3 Practice – Adding Rationals Find the sum of the following:
1) !!!+ !
!!= 2)
!!+ !
!=
3) !
!+ − !
!= 4)
!!+ !
!=
5) 2 !!+ 4 !
!= 6) 2 !
!+ 3 !
!"=
7) 1 !!+ 4 !
!= 8) 3 !
!+ −4 !
!=
45
4-‐4 Subtracting Integers
1) Re-‐write Subtraction expressions into Addition:
ADD THE OPPOSITE! 2) Follow the Adding Integer Steps:
Examples:
=−− 65
( )=−−− 86
=−− 122
Write and simplify a subtraction expression for the temperature at 5:00 P.M. and at 8:00 P.M. Model each expression on the thermometer
=−− 73 =−− −61 =−1510
46
Subtracting Integers (A)Use an integer strategy to find each answer.
(-6) - (+2) = (-3) - (+8) = (+5) - (-5) =
(-9) - (-8) = (+9) - (-4) = (+6) - (-9) =
(-6) - (+6) = (+8) - (-7) = (+7) - (-5) =
(-8) - (-8) = (-6) - (+3) = (+2) - (+1) =
(+5) - (+1) = (-3) - (+4) = (-6) - (+3) =
(+6) - (-2) = (-4) - (+3) = (+2) - (+9) =
(-3) - (+5) = (-6) - (+1) = (+1) - (+1) =
(-8) - (+5) = (+8) - (-8) = (-2) - (+3) =
(-9) - (-4) = (+1) - (+4) = (+3) - (+4) =
(+1) - (+3) = (+7) - (+9) = (+8) - (-9) =
Math-Drills.Com47
Subtracting Integers (A)Use an integer strategy to find each answer.
-4 - 10 = -10 - -1 = 1 - 2 =
-1 - -11 = -5 - -2 = -3 - -11 =
11 - -14 = -3 - -10 = 1 - 2 =
3 - 3 = 1 - -10 = 13 - 14 =
-2 - -14 = 10 - 12 = 13 - 12 =
4 - 15 = -5 - -1 = -14 - -7 =
-6 - -10 = 5 - 5 = 8 - -6 =
-7 - 2 = -8 - 3 = -5 - -12 =
12 - 2 = -6 - 11 = -3 - 2 =
-9 - -6 = 11 - -8 = 5 - -10 =
Math-Drills.Com48
Integer Addition and Subtraction (A)
3 + (-8) = (-9) - (-4) = 7 - 5 =
6 - (-4) = (-4) - (-2) = (-4) - 10 =
6 - 5 = (-2) - 5 = (-2) - 7 =
(-8) + (-2) = 8 + 6 = (-9) + 10 =
8 + (-10) = 2 - (-10) = 8 - 5 =
8 - (-2) = 1 - (-7) = 4 + 2 =
(-2) + 6 = (-4) - 4 = 9 - (-7) =
(-1) - 0 = 7 - 5 = (-5) + (-10) =
(-1) - (-2) = (-5) - (-6) = 9 - (-9) =
7 - 4 = (-2) + 5 = (-4) - (-10) =
8 - (-2) = (-6) + 2 = 4 + 1 =
-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS49
Integer Addition and Subtraction (B)
(-8) + 6 = (-3) - 6 = 7 + (-3) =
(-1) + (-3) = 7 + (-10) = (-8) - (-2) =
1 - (-6) = (-6) + (-1) = (-2) - (-7) =
2 + (-2) = 3 + (-6) = 7 - 4 =
(-5) - (-8) = 2 - (-6) = (-8) - 10 =
2 - (-1) = (-1) - 8 = (-10) + 10 =
4 - 9 = 3 + 6 = 5 - 0 =
6 - 3 = 5 + 2 = (-2) + 1 =
(-4) + (-2) = (-8) + (-8) = (-4) - (-1) =
10 + 4 = 7 + 9 = (-9) - 1 =
8 - 5 = (-10) - (-3) = (-7) + 4 =
-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS50
4.5 Subtracting Rationals
Rewrite as an addition problem, then decide if the answer is positive, negative, or zero.
51
Adding & Subtracting Rational Numbers
1) ( ) ( )61811 −−+−−
2) ( ) 571010 −−−−
3) 98.36 −
4) ( )5.28.5 −+
5) ( )7.38.1 −−
6) 8.27 −
7) ( ) ( ) 4.52.78.0 −−+−
8) ( ) 013.48.07.1 +−−
9) 58
23
+⎟⎠
⎞⎜⎝
⎛−
10) ⎟⎠
⎞⎜⎝
⎛−−21
47
11) 47
51+⎟⎠
⎞⎜⎝
⎛−
12) 54
52−
52
Adding & Subtracting Rational Numbers:
1)
2)
3)
4)
5)
6)
7)
8)
8)
9)
10)
11)
12)
13)
53
14)
15)
16)
( )5.85.8 −−−
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
What is the difference between -‐424 and 125 on the number line? Explain how you found your answer!
54
4-‐6 Distance on a Number Line
55
Practice 4-‐6
Distance on a Number Line
Ex 1) Find the distance between 18 and -‐25 on a number line.
Ex 2) Find the distance between -‐12.4 and -‐2.6 on a number line.
Ex 3) Kim is standing on a diving platform that is 15 feet above the pool. She dives in and
her dive takes her 6 feet below the water. How far apart is it from where Kim started to
where she finished the dive?
56
Absolute Value/Integer Practice
1.) Insert <, >, or = between the pair of numbers. a) −13 ____ 19 b) −2.7 ____ −2. 6 c) 1 !
! ____ − !
!
d) 3 + 8 ____ 2 − 11 e) −3.2 ____ −3 !
! f) 3 − (−4) ____ −8
2.) Place each set of numbers in order from smallest to largest. Set 1: -‐0.4, − !
!, 3, −0.5 ___________________________________________________
Set 2: −12 , −10 , 6.5, −6. 5 _______________________________________________ Set 3: 2 !
!, 2.7 , − !
!, -‐1 ___________________________________________________
3) Write 2 absolute value expressions that could be used to find the distance between 3.9 and 8.3. 4) Circle all expressions that represent the distance between -‐8 and 7? a) −8 + 7 b) 7 + 8 c) −7 + 8 d) 8 − 7 e) 7 − 8 f) −8 − 7 5) Which pairs of numbers are 13.7 units apart on a number line? Circle all that apply. a) -‐26.3 and -‐12.6 b) -‐26.3 and 12.6 c) -‐3.2 and -‐10.5 d) 3.2 and 10.5 e) -‐3.2 and 10.5 f) 26.3 and -‐12.6 6) Suppose a diver is swimming 13.2 feet below sea level. A whale is 851 feet below sea level. How much lower is the whale than the diver? 7) Which pair of numbers is farther apart? a) -‐20,593 and 814.18 b) -‐20,593 and -‐814.18
57
Topic 4: RATIONAL NUMBER REVIEW
1. Determine whether the given number belongs to each set. Write Yes or No in each box.
Whole Number Integer Rational Number
12
-‐125
67
2. Compare the numbers below using the <, >, or = symbol. a.) b.) │-‐2│___ │-‐18│ b.) 25 ___ │-‐25│
c.) │-‐14 │___ -‐9 d.) -‐16 ___ -‐18
3. Evaluate: 810 +− = __________
4. Evaluate: │-‐7│+ │1│= __________
5. Which of these situations can be represented by the opposite of 15?
Check all answers that apply.
o A. You win a $15 bet. o B. A football player is tackled for a loss of 15 yards. o C. You deposit $15 into your bank account. o D. An elevator descends 15 floors.
58
6. Which of the following are Sums of Additive inverses? Check all answers that apply. o A. 6+ (-‐8) o B. 6 + (-‐6) o C. -‐8 + (-‐8) o D. 8 + (-‐8)
7. Complete the number line below to show the addition problem 9 + (-‐3). Then solve the
problem.
-‐3 -‐2 -‐1 0 1 2 3 4 5 6 7 8 9 10
9 + (-‐3) = ______
8. Use the chip board below to find the sum of 3 + (-‐12).
○○○ ○○○○ ○○○○ 3 + ( -‐12) = ______
○○○○ 9. Suppose a deep sea diver dives from the surface to 50 feet below the surface. He then dives down 120
more feet. The diver’s depth is represented by the sum -‐50 + (-‐120). Find the sum.
-‐50 + (-‐120) = ________
10. -‐8 + (-‐10) = ______
11. -‐9 + 9 = _________
12. -‐16 + 10 = _______
13. Write each subtraction problem as an addition problem, then solve it.
Subtraction problem Addition problem Answer
a.) -‐8 -‐ 4 = _______________________ = _______
b.) 12 -‐ -‐ 5 = _______________________ = _______
c.) -‐3 -‐ -‐15 = _______________________ = _______
59
Topic 4 Review
1) What type of number is − !
!? Circle all that apply.
Integer Rational Whole 2) Fill in the blank with <, >, or =. −1 _____ −16 3) Which pairs of numbers are additive inverses? 9, 9 6, -‐6 -‐9, -‐9 -‐9, 9 -‐6, -‐6 4) In her garden, Pam planted a seed 4 !
!in. below the ground. After one month, the plant has grown a
total of 10 !!in. How many inches is the plant above the ground?
5) The temperature in town is 28.3°F during the day and -‐6.7°F at night. Find the difference in the temperatures. 6) Find the distance between -‐55 and -‐24 on a number line. 7) Evaluate the following: a) 13 + −7 b) −12 − −16 c) −3 !
!+ −4 !
! d) !
!− !
!
60
5-1 Multiplying Integers
Part One
Part Two
61
Key Concept
Part Three = = = = = = = = =
62
©J X2Y0c1q2Q 8KvuMt8af vSTogfbtQw9airweG NLDLeCX.E q EAQlylL 1reiVgchgtWsX 4rdeRsAegrZvoe5dT.X I 0MNaTdAeB hwfi5tVh8 dI6nIfkiBnliutlex SPArAeC-GATlVgFeYbvrzaG.Q Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Multiplying Integers
Find each product.
1)
6 × −4 2)
4 × 2
3)
3 × −4 4)
−6 × 4
5)
5 × −4 6)
−3 × 4
7)
−5 × 6 8)
−2 × −1
9)
−8 × −2 10)
11 × 12
11)
−7 × 5 12)
9 × −6
13)
10 × 5 14)
9 × 2
15)
−12 × 7 16)
8 × −12
17)
9 × 10 × 6 18)
−6 × −10 × −8
19)
7 × 9 × 7 20)
6 × 6 × −2
21)
−5 × −4 × −10 22)
9 × 9 × −5
23)
8 × 3 × 8 24)
7 × 5 × −5
63
5-2 Multiplying Rationals
Key Concept Part One Write if each product is positive or negative. = = = = = = = =
Part Two Find the product.
Part Three
64
Multiplying Rational Numbers
1) ⎟⎠
⎞⎜⎝
⎛−•87
32
2) ⎟⎠
⎞⎜⎝
⎛−•−212
81
3) ⎟⎠
⎞⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛322
512
4) ( )3415 −
5) ⎟⎠
⎞⎜⎝
⎛−•−910
109
6) ⎟⎠
⎞⎜⎝
⎛−⎟
⎠
⎞⎜⎝
⎛512
316
7) 1812
92
−•
8) ⎟⎠
⎞⎜⎝
⎛−−4135
65
Multiplying Rational Numbers
Multiply.
1)
=•2112
43
-‐
2)
=•−81
41
3)
=−•−322
211
4)
=−•−322
213
5)
( )( )=06.05.0
6)
( )( )=−− 9.007.0
7)
What is the sign of ba 2 when
72 −== ba ? Evaluate!
8) A farmer has 140 bushels of wheat to sell. He sells an
average of 5116 bushels each day.
Represent the total change in the number of bushels he has for sale after 6 days.
66
Multiplying Rational Numbers-‐ word problems
1) The width of a vegetable garden is 31 times its length. If the length of the garden is
437 ft, what is the width?
2) Mark left 83 of a pizza in the refrigerator. On Friday, he ate
21 of what was left.
What fraction of the entire of the pizza did he eat on Friday?
3) Alano wants to make one and a half recipes of the pasta salad recipe shown below.
Fill in each blank with the amount of ingredient needed to make the recipe.
Ingredient Amount Alano’s Recipe Broccoli cup
411
Cooked Pasta
cup433
Salad Dressing
cup32
Cheese cup311
67
5-3 Dividing Integers
Key Concept
Part One A B C D E F G H I
68
Part Two Part Three
An elevator descends 1,000 feet in 8 seconds. Express the movement of the elevator as a unit rate.
69
©q h2e0f1522 WKyuIt4a2 ZS4ozfCtVwtazr1eI QL3LACR.o R PAIl3lX qrUiogthytxsF 2rVeysRevr2vAegd7.C C 8MVaEdHeq 6wUiUtOhk GIXnJfqienHiOt0eQ rPOrBeJ-8ATlcgbe5bQrRa6.M Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra Name___________________________________
Period____Date________________Dividing Integers
Find each quotient.
1)
35 ÷ −5 2)
−8 ÷ 4
3)
−24 ÷ 4 4)
−8 ÷ −2
5)
8 ÷ 4 6)
−24 ÷ 8
7)
−21 ÷ 7 8)
6 ÷ −6
9)
−132 ÷ −11 10)
−60 ÷ −15
11)
−52 ÷ −4 12)
60 ÷ 12
-1-
70
©P L2I0w1N2L tKzu1t6aB bS4o1fetBwQavrHeF mLbLAC9.j G vAulnla xr3i3gBhkt7sQ trzeusHeNrMvjeVdk.K O VMlaDdMeK dwUiutWha pIEnYfSiznKiCtGeU cPur6eI-TALlLgQeCb8rtab.F Worksheet by Kuta Software LLC
13)
6 ÷ −1 14)
75 ÷ 15
15)
65 ÷ −13 16)
12 ÷ 4
17)
−168 ÷ −12 18)
−8 ÷ 2
19)
−105
720)
−4
−1
21)
−10
−222)
−144
12
23)
24
−1224)
60
−15
-2-
71
5-4 Dividing Rationals
Part One
Part Two
72
Part Three
73
5-5 Operations with Rationals
A complex fraction is a fraction within another fraction. Always re-write them as a division problem. Then apply “Keep-Switch-Flip”
Extra Practice ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺
1) 43
2) 1210
−
85
315
3) 92
− 4) 813
531− 11
32−
74
Practice with Complex Fractions:
1. 12 4
2. 38
−2
3. −6
23
4. 5
− 57
5.
−23 2
6. 13
−3
7. −4
15
8.
− 56 − 14
9.
− 35 23
75
10. 15
− 23
11. − 12 25
12. 45 34
13. 12 23
14. − 35− 47
15. − 1011 12
16. −35
− 13
17. − 13 34
18. 45
− 13
76
19. 212 23
20. − 23 1 34
21. −125 1−3
22. 15
2 13
23. 325 34
24.
−312 3 45
25. 438
−1 89
26. −423 3 38
27.
−523 3 56
77
Order of Operations Practice
1) 8 + 4 x 22 - 6 2) 2 + 24 ÷ (6 - 4)3
3) 30 - 6 ÷ 2 x 32 4) 52 - (2 + 3) ÷ 5 8 - 2
5) 17 − (5 + 3)6 ÷ 42 6) 2 + 5(6 + 1) ÷ 7
7) (3 – 5)2
÷ 2 • 2
9) 432 −
97
31−
78
Order of Operations Practice
1) 8 + 4 x 22 - 6 2) 2 + 24 ÷ (6 - 4)3
3) 30 - 6 ÷ 2 x 32 4) 52 - (2 + 3) ÷ 5 8 - 2
5) 17 − (5 + 3)6 ÷ 42 6) 2 + 5(6 + 1) ÷ 7
7) (3 – 5)2
÷ 2 • 2 8) Use the distributive property toeliminate the parenthesis:
2( x + 7 – y) =
Now evaluate if x = -6 and y = 9.
79
Order of Operations with Rational Numbers
( )3295
−= FC 3259
+= CF
1) Convert 14°F into Celsius. 2) Convert 10°C into Fahrenheit.
3) Convert -13°F into Celsius. 4) Convert -30°C into Fahrenheit.
5) 124
86+ 6) 4
32 −
321836 •÷− 97
31−
7) Use the distributive property to eliminate the parenthesis:
½( x - 8 + y) =
Now evaluate if x = -10 and y = 12.
80
Name: __________________________ Score:
Free Math Worksheets @ www.mathworksheets4kids.com
1)
−13 + | − 2 + 5| − 6 =
2)
|−8| + |−14| − 9 =
3)
|−7| + |−11| =
4)
|−9| − |−5 + 7| + |12| =
5)
|32 − 95 + 6| + |−15| − 4 =
6)
|−41| − |18| + 12 =
7)
| − 64 + 7| + 2 − 6 =
8)
17 + |−14 − 65| − 8 =
9)
|−44 + 62| + |11| − |28| =
10)
|−71| − |−23 + 57| − 22 =
11)
82 + |−15 − 75| − |3| =
12)
54 + 47 − | − 25 + 19| =
13)
|−3 + 14| + |8 + 5| − 2 =
14)
−9 + 74 − |87 − 33 − 7| =
15)
|56| − |−21 − 10| − 8 =
16)
47 + |−72| − 69 =
17)
|−8 + 11 − 4| + |4 + 7| =
18)
|12 − 4| − |−8 + 8| − 1 =
19)
|31| − |−51| + 82 =
20)
|−7 + 14| + |8| − |2 + 9| =
Solve each absolute value problem
81
Name: __________________________ Score:
Free Math Worksheets @ www.mathworksheets4kids.com
Find the value:
1)
|−8| × |9| =
2)
|30| ÷ |5| =
3)
|11| × |−4| =
4)
|−21| ÷ |−7| =
5)
|−3| × |5| =
6)
|10| ÷ |2| =
7)
|3| × |−6| =
8)
|−24| ÷ |−8| =
9)
|−12| × |9| =
10)
|10| ÷ |10| =
11)
|7| × |−6| =
12)
|−9| ÷ |−1| =
13)
|−6| × |−5| =
14)
|36| ÷ |3| =
15)
|4| × |−4| =
16)
|−27| ÷ |−9| =
17)
|−4| × |6| =
18)
|56| ÷ |8| =
19)
|5| × |−7| =
20)
|−55| ÷ |−5| =
21)
|−10| × |3| =
22)
|12| ÷ |2| =
23)
|5| × |−8| =
24)
|−12| ÷ |−6| =
Absolute Value
82
Name: __________________________ Score:
Free Math Worksheets @ www.mathworksheets4kids.com
1)
|56 − 15| × 8 +|�|
�=
2)
|�|
�× |4 − 1| =
3)
|−8| ×|��|
|�|− |7| =
4)
|���|
�×|�|
|��|=
5)
|−1 + 4| +|�|
|��| =
6)
3 +|����|
�× 7 =
7)
|��|
|�|+
|�|
�=
8)
−|3| × |6 − 2| =
9)
|3| ×|����|
�=
10)
|���|
�− |8| × | − 5| =
11)
|��|
�+
|��|
�− | − 3 × 4| =
12)
|��|
�×
|�|=
13
9 ×|���|
|�|=
14)
|��|
|�|+
|����|
�× 8 =
15)
|13| − 7 ×|����|
�=
16)
|���|
�− |9 × 2| + |4| =
17)
|���|
|���|− |3| =
18)
|��|
|�|× 5 × | − 2 − 3| =
19)
|9 + 2| −|��|
|�|=
20)
|22 + 1| +||
|�|× 6 =
Solve each absolute value problem
83
Name: __________________________ Score:
Free Math Worksheets @ www.mathworksheets4kids.com
1)
|2 − 3| +||
|�| =
2)
| �|
|�|+
|���|
�× 8 =
3)
2 +|�|
× |−1| =
4)
−|−5| × |7 − 1| =
5)
−|−4| ×|���|
�=
6)
|� |
�− |−9| × | − 6| =
7)
2 × −|6 + 3| −|� |
|�|=
8)
|����|
||×||
|�|=
9)
|�|
+
|� |
�− |−2 × 6| =
10)
| �|
� − |2 × 4| + |4| =
11)
|18| ×| ��|
�=
12)
−5 + |−1 + 6| ×|�|
=
13)
−|3| ×|���|
×
| �|
|�|=
14)
| ��|
||× 3 =
15)
|12 − 19| × 4 +| �|
�=
16)
|−5 − 2| +||
�× |8| =
18)
|��|
|�|− |6| =
18)
| �|
�×
|�|
|��|=
19)
|9 − 5| +|�|
|�| =
20)
|�|
|�|+
|� |
× 6 =
Solve each absolute value problem
84
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R ÷
OF
IN
TE
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RS
+
OR
- O
F I
NT
EG
ER
S
85
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