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Learning Goals
7th Grade Extended Class
Chapter 2: Properties of Real Numbers
1. To graph real number using a number line.
2. To compare real numbers.
3. To find the opposites and absolute values of real numbers.
4. To add integers with the same sign and different signs.
5. To subtract integers.
6. To add real numbers.
7. To subtract real numbers.
8. To organize data in a matrix.
9. To add and subtract matrices.
10. To multiply and divide integers.
11. To multiply real numbers.
12. To divide real numbers.
13. To use real numbers to model real-life problems.
14. To use all four operations of real numbers to solve a real-life problems.
15. To use the distributive property.
16. To simplify expressions by combining like terms.
7th Grade Extended Class
Name: _________________________________
Chapter 2 Binder Sheet
Class Color: _____________________________
Day
1
Lessons and Homework
Lesson 2.1 The Real Number Line
Homework: The Real Number Line Wksht
2
Lesson Adding and Subtracting Integers
Homework: Adding and Subtracting Integers Wksht
3
Lesson 2.2 Addition of Real Numbers
Homework: Addition of Real Numbers Wksht
4
Lesson 2.3 Subtraction of Real Numbers
Homework: Subtraction of Real Numbers Wksht
5
Quiz Lesson 2.1-2.3
6
Lesson 2.4 Adding and Subtracting Matrices
Homework: Matrices Wksht (Both Sides)
7
Lesson Multiplying and Dividing Integers
Homework: Multiplying and Dividing Integers Wksht
8
Lesson 2.5 Multiplication of Real Numbers
Homework: Multiplication of Real Numbers Wksht
9
Lesson 2.7 Division of Real Numbers
Homework: Division of Real Numbers Wksht
10
Review of Multiplying and Dividing Real Numbers
Homework: More Practice of Multiplication and Division of Real Numbers Wksht
11
Quiz Lesson 2.4, 2.5, 2.7
12
Lesson 2.6 Combining Like Terms
Homework: Combining Like Terms Wksht
13
Lesson 2.6 The Distributive Property
Homework: The Distributive Property Wksht
Due Date
14
Lesson 2.6 Combining Like Terms and the Distributive Property
Homework: Combining Like Terms and the Distributive Property Wksht
15
Quiz Lesson 2.6
16
Review Chapter 2
Homework: Chapter 2 Practice Test
17
Review Chapter 2
Homework: Study for Test
18
Chapter 2 Test
Homework: Review Question A
19

Review Question B
The binder sheet is subject to change.
* Worksheets have been adapted from Algebra 1 (2004) McDougall Littell Inc
Name _________________________________________________________
The Real Number Line
Tell whether each number is an integer. Write Yes or No.
1. -3
2. 4.1
3. -1/2
4. 2
5. 0
6. -3.14
Use positive and negative signs to write each number.
7. Earned $50
8. 5 ft below sea level
9. Lost 10 yards
Write the opposite of each number.
10. 3
11. -56.2
12. 250
13. 2.8
14. -245
16. 1 4
3
Find the absolute value of each number.
17. |23|
18. |-2.3|
20. |-1089|
21. |9|
19. |6.61|
1
1
22. |-4 2|
Complete the statement using < or >.
23. 4 _____ -2
24. 2.4 _____ -2.5
25. -3.2 _____ -3.02
26. 5.1 _____ 5.01
27. 2.8 _____ 2.79
28. -4 _____ -44
Tell whether the equation or inequality is true for some values of x, all values
of x, or no values of x. If it is true for some values, describe when it is
true and when it is false.
29. │x│≥ 0
30. │x│= x
Name _________________________________________________________
Adding and Subtracting Integers Worksheet
Add or subtract the integers. Don’t forget to use the rules.
ifferent
ame
ign
um
Signs
ifference
Subtraction
Stay, change, change
Follow Addition Rules
1. -23 + 57 =
2. -18 + (-13) =
3. 34 + 82=
4. -17 + 8 =
5. -67 + (-17) =
6. -71 + (-22) =
7. -78 + 16 =
8. -14 + 9 =
9. 16 + 37 =
10. 28 + (-10) =
11. -65 + (-18) =
12. -71 + 35 =
13. 84 + (-23) =
14. 47 + (-75) =
15. 62 + 14 =
16. -55 + (-55) =
17. 123 + (-60) =
18. -42 + 42=
19. -3 – 33 =
20. -43 – 71 =
21. -2 – (-56) =
22. 75 – (-83) =
23. -61 – 26 =
24. 36 – 72 =
25. -63 – (-79) =
26. -87 – (-31) =
27. 20 – (-41) =
28. -25 – 88 =
29. -36 – 78 =
30. 12 – 96 =
Name _________________________________________________________
Addition of Real Numbers Worksheet
Add the real numbers to find each sum.
1. 7 + 4
2. -5 + (-3)
3. 6 + (-2) + (-7)
4. -44 + 92 + (-84)
5. 19 + (-19)
6. 47 + (-95) + 12
7. -4.2 + 7.34 + 3
8. 7.15 + (-6.1)
9. 5.795 + (-5.871)
10. -16.17 + 38.143
11. 23.14 + (-12.78)
12. -15.4 + (-25.97)
1
13. − 5 +
16.
1
+
3
4
4
2
5
14. 3 + (− 8)
5
1
+ (− 4)
5
17.
1
2
+ (− 3)
11
4
7
15. −7 7 + (−3 8)
18.
1
2
3
+ (− 3) + (− 7)
2
19. You are picking up your friend and going to a concert. Your friend lives 3 miles
west of your house and the concert is 21 miles east of your friend’s house. When
you are at the concert, how far away from home are you?
20. The New England Patriots’ quarterback was sacked and lost 20 yards on first
down. On second down, a 25 yard pass was completed. On third down, the Patriots
rushed for 6 yards. Did the Pats get a first down (a gain of ten yards)? How many
net yards did they gain?
Name _________________________________________________________
Subtraction of Real Numbers Worksheet
Subtract the real numbers to find the difference.
1. -33 – 12
2. 45 – (-12)
3. -39 – (-45)
4. -2 – 7
5. 8 – (-3) - 2
6. 5 – (-5) - 7
7. 88.2 – (-30.4)
8. -18.14 – 3.7
9. 22.47 – (-17.38)
10. -75.4 – (-75.9)
11. -147.2 – (-56.8)
12. -136.7 – 67.3 + 4.5
13.
7
8
1
2
14. − 3 −
− (− 2)
4
4
1
15. −7 9 − 2 3
5
16. The highest temperature ever recorded in Hawaii is 100°F. The lowest
temperature ever recorded is 14°F. What is the range in temperatures?
17. Connor is a scuba diver at a depth of 52.8 feet below sea level. Thirty minutes
later, he is at a depth of 40 feet below sea level. What is his change in depth? Did
he go up or down?
18. The table shows the high temperatures for a week in May. Determine the
change in temperature each day. Find the total of these changes to discover the
net change in temperature.
Day
Temp.(°F)
Sun
76°
Mon
72°
Tues
80°
Wed
75°
Thurs
75°
Fri
74°
Sat
78°
Name ____________________________________________________
Matrices Worksheet
Determine the resulting matrix through addition.
3 7 1 2
1) 


1 4 5 3
 4 9  6   2  3 4 
2) 


2  2  3   1 2  1
 2 5  2   4 7 9 
3) 


3 6 2   3 2  1
 9 0  6  7
 5  4  2   1

4) 
 3 2  1  3

 
 1 6 7   0
Determine the resulting matrix through subtraction.
  4 2  3  1 
5) 


 5 1   5  7 
  1 6   4  2
6) 


 3  5  7 2 
0
9  4
7 5

8 1 
2
 4  3   1  3
7)  1
2    7
9 

 2 5   4 1 
 9 0  6  7
 5  4  2   1

8) 
 3 2  1  3

 
 1 6 7   0
4 2 
9. Calculate the following, given R = 8  1 and S =
0 3 
a) R + S
b) R – S
5
1
 3 5 


 4  3
c) S – R
2 3  1 5 
10. Calculate the following, given A = 
 and B =
 4 0 7  2
a) A + B
b) A – B
0
9  4
7 5

8  1
2
c) B – A
4 6 5 1 
 3  2 1 4


Name _________________________________________________________
Multiplying and Dividing Integers Worksheet
Multiply to find the product.
1. 8 * 9
2. -8 * (-9)
3. 27 * (-5)
4. -14 • 10
5. -45 • (-12)
6. 100 • (-10)
7. (-16)(7)
8. (-25)(5)
9. -2(2)
10. (-1)(-2)(-3)
11. 5 • (-4) • (-6)
12. 10 * (-7) * (-8)
Divide to find the quotient.
13. -18/(-9)
14. -40/(-5)
1
5. -256/(-16)
16. -1000 ÷ 125
17. -105 ÷ 5
18. -81 ÷ (-9)
19. -51/17
20. 63 ÷ (-7)
21. -80/5
22. -36/3/2
23. -36 ÷ (-9) ÷ (-1)
24. -56 ÷ 7 ÷ (-2)
Name__________________________________________________________
Multiplication of Real Numbers Worksheet
Find the product.
1. -4 * -12
2. 7(-2)(-3)
3. (-4)(-3)(-9)(3)
4. -6 * 8 * 2 * -1
5. -4.02 * 3.1
6. (-7.6)(-2.1)(-2)
2
7. − 3 ∗
4
5
1
7
8. −3 5 ∗ (−2 8)
3
6
9. − 4 (−1)(− 7)(−2)
Simplify the variable expressions.
10. 5 (-x)
11. (-4)(-x)(-x)
12. 6(-r)(-r)(-r)
13. (-3)(z2)(z)
15. (-y)2(y)2
1
16. (2)(−2𝑥)
14. -7(-d)3
5
7
17. − 7 (− 5 𝑥)
3
18. (− 4)(−𝑘)(−4𝑘)
Evaluate the expression.
19. -4x when x = 3
20. -5(t)(-t) when t = -4
21. x3+2 when x = -2
22. 2y3 – 3 when y = -3
23. –x2- 5x + 7 when x = -2
24. -2(│y -5│) when y = 3
25. 2x2 - 3x + 1 when x = 2
26. 4m + m2 when m = -5
Name _________________________________________________________
Division of Real Numbers Worksheet
Find the quotient.
1. -8 / 4
2. 18 ÷ (-3)
4. -18 ÷ 36
5. −80 ÷ (− 5)
7.
3. -48 ÷ (-4)
4
−24
8.
6
−
7
1
6. −13 ÷ 2
36
2
9. −33 ÷ 3 3
9
−
10
Simplify the variable expressions.
10. -15x/3
11. -6y ÷ (-3)
13.
𝑐
8
14.
÷4
6
16. −12𝑦 ÷ − 11
Evaluate the expression.
𝑥+2
19. 𝑦 when x = 8 and y = 2
21.
4𝑥−3
𝑦
when x = 3 and y = -3
3𝑏
4
12. 48x ÷ (-6)
3
5
15. −20𝑘 ÷ 6
÷4
12
𝑥
17. 60𝑎 ÷ (− 7 )
7
18. − 4 ÷ 16
20.
𝑥−𝑦
22.
5𝑥+2
4
𝑦
when x = 17 and y = 1
when x = -2 and y = -4
Name__________________________________________________________
More Practice Multiplying and Dividing Real Numbers
Simplify the variable expression.
1. (14)(−𝑥)
2. (−2)(−𝑦)(−𝑦)
3. (−3)3 (−𝑡)2
4. −(−𝑦)2 (𝑦)2
3
5. (− 4)(−𝑘)(−16𝑘)
2
7. −16𝑥 2 ÷ (− 3)
9. −
3𝑏
8
1
÷ (−4 2)
6. (−13)(−6𝑦)
36𝑎
9𝑎
8. − 40𝑏 ÷ −10
3
10. −15 ÷ − 5 𝑦
Evaluate the expression for the given values of the variable(s).
11.
4+𝑥 2
𝑦
, 𝑤ℎ𝑒𝑛 𝑥 = −4 𝑎𝑛𝑑 𝑦 = 2
13. 2𝑦 2 − 3 𝑤ℎ𝑒𝑛 𝑥 = −3
12.
4𝑥 2 −3
−𝑦
, 𝑤ℎ𝑒𝑛 𝑥 = 3 𝑎𝑛𝑑 𝑦 = −3
14. −𝑥 3 + 𝑥 2 𝑤ℎ𝑒𝑛 𝑥 = −2
Name _________________________________________________________
Combining Like Terms Worksheet
Simplify by combining the like terms.
1) 6k + 7k
2) 12r − 8 − 12
3) n - 10 + 9n − 3
4) -4x + 10x
5) r + 10r
6) 2x + 11 - 6x
7) 11r − 7r
8) v + 8 + 12v
9) 8x + 3 + 11x + 4
10) n + 14 - 9 + 5n
11) -12r + 5 + 3r − 5
12) 5n + 18 + 12n
13) 9y + 60y + 10
14) 4x3 + 2x2 + 8x3 + 1
15) 4c + 7c2 – 2c
16) 10xy + 8x + 3y – 5xy
17) 12abc – 4abc + 2
18) 2x3 – 4 + 5x3 + 7
Name _________________________________________________________
The Distributive Property
Simplify.
1. 8(3m + 4)
2. 7(2x2 – 6y)
3. ½ (8r – 12)
4. (16 + 13p)10
5. (54g + 10g2)5
6. 2 (12x + 16)
7. 4(13v – 9)
8. 3(1 + k)
Factor.
9. 8x + 8
10. 20n – 15
11. 12a + 16
12. 24g – 9
13. 20 – 5r
14. 26p - 18
Name _________________________________________________________
Combining Like Terms and Distributive Property Worksheet
Combine the like terms to simplify.
1. 5x + 16y - 2x – 20y
2. 16m + 7 + (– 4m)
3. 9.2x + 7.1x – 12
4. -2r + 4r2 + 7r – 18r2
5.
7
8
𝑥+
5
9
2
𝑥+3
4
6. − 5 𝑝 −
1
2
+
1
3
𝑝+
3
4
Use the distributive property to simplify.
7. 8(x + 5)
8. 4(y – 7)
9. -6(r -1)
10. -12(3 + m)
11. y2(2 – 3y)
12. -3x(-x - 5)
13. –a(a + 2)
14. –(4t – 8)
Use the distributive property and combine like terms to simplify.
15. 2(x + 1) + x
16. 2(3a – 5) + 2a
17. -4(5m + 2) + 3m
18. 2t + (3+ 5t)4
19. 2x(x + 4) + 5x2
20. -2m(m – 5) + (-5m2)
21. 5 + 2(a + 8)
22. 4 - 3(y + 8)
23. 7c - 2c(c + 3)
24. 9p – 8(p – 6)
Name _________________________________________________________
Chapter 2 Practice Test
Find the value of the expression.
1. |-7.2|- 16.4
2. -1.8 + |-7.4 - 3.1|
3. 16.23 - (-14.2) + (-9.3)
1
3
4.  7  4
3
7
Write the numbers in increasing order.
5
2
1
5. 4 , 1.5,  2.35,  2 ,  2
9
5
9
Find the value.
6. A company has a loss of $213.15 in January, a loss of $57.11 in February, and a
profit of $121.55 in March. What was the company’s net profit or loss over the
three month period?
Evaluate the expression for the given value of the variable.
7. 7 + x + (-11) + (-3) when x = 2
8. -3x3 – 5 when x = -2
9. 2|4x - 6| when x = -4
10. 6x2 + 1 when x =
1
3
Add or subtract the matrices.
 8 .7
11.  2.8
 3.4
3
1
 4 1 4

12. 
 4  3

5

5 .6 
 6.4

 12.9 +  10.5

14.12 
 5.1
6
2
2
3

 7


6


-
 1.9
3.76 
7.1 
2
3


1
3

2

1
4
3
10
1
1  3 
2


1
5 
4

Find the product or quotient.
13. (-5)(-4)(2)(-3)
15. 8y(-y)(-y)(-y)
17. (-5)3(-h)5
14. -12 ÷ 
16.
42
7

8
2
3
Simplify the expression.
18. 21x2 + 27x + 36x2 + 9
19. -7.6p + 14.5p
20. (-8c2)(2c2-3c)
21. -9(2q + 3)
22. 4k + 6(3 – 7k)
23. 4y + 5(2 + y)
24. 12r – (3r + 9)
25. 4m – 5(2f - 8)