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Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 1
5. Write the following numbers in standard form.
1. Underline the hundredths place.
a. 95.022 b. 15,002.811 c. 0.0076
2. Write down the place value of the digit 7 in the following numbers.
a. 127,000.223 b. 33,087.004 c. 1,630.007
3. Write the value of the underlined digit.
a. 3,229 b. 100,122,221 c. 3,009.09
4. Write each number in standard form.
a. Ten and two hundredths
b. Eighty-six one-thousandths
c. Three million, fifteen thousand, two hundred twenty-two.
a. 800,000 + 60,000 + 2,000 + 10 + 0.6 + 0.009
b. 1,000 + 90 + 3 + 0.6 + 0.09 + 0.002
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 2
6. Write the following numbers in expanded form.
7. Find the terms, constant/s and coefficient/s for each expression.
8. Write an algebraic expression for each verbal phrase.
a. 18,002.0321
b. 3,000.631
a. π + ππ + ππ = b. π + ππ + π = c. πππ + π =
πππ«π¦π¬: πππ«π’πππ₯ππ¬: ππ¨π§π¬πππ§π: ππ¨ππππ’ππ’ππ§ππ¬:
πππ«π¦π¬ πππ«π’πππ₯ππ¬: ππ¨π§π¬πππ§π: ππ¨ππππ’ππ’ππ§ππ¬:
πππ«π¦π¬: πππ«π’πππ₯π: ππ¨π§π¬πππ§π: ππ¨ππππ’ππ’ππ§π:
a. The sum of π and 20, divided by 9 b. 3 more than 2 times a number
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
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9. Evaluate each expression using the values given.
Find the value of each numerical expression. Follow the order of operations when finding each value.
a. π + ππ ππππ π = π πππ π = π
b. π β ππ ππππ π = ππ πππ π = π
10. πππ β (ππ β π) β (πππ β ππ) =
11. πππ Γ· (ππ Γ· π β ππ β πππ Γ· ππ)
12. (πππ Γ· π β π) β πππ Γ· ππ = 13. (πππ Γ· π + ππ) β (πππ Γ· ππ β π) =
14. πππ β (ππ β ππ) + (πππ Γ· π) =
15. π, πππ + (πππ β ππ β π)π =
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16. Write an algebraic expression for the word expression.
17. Write the word expression for each algebraic expression.
Evaluate each expression for the given values of the variable.
20. Write an integer to represent each situation.
a. The quotient of π and 30 b. The sum of 45 and the product of 8 and π
c. Twice a number increased by 89.
ππ + ππ
a. π β ππ b. π β π c. ππ + π
18.
ππ + π
π+ (ππ β π) =
π = ππ π = ππ
19. ππ + ππ β (π β π)π = π = ππ π = π
a. An increase of 78 points. b. A profit of 100 dollars. c. The stock market went down 600 points today.
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 5
21. Graph each integer or set of integers on a number line.
22. Find the opposite of each integer.
23. Graph each integer and its opposite on a number line.
24. Compare the following integers. Write <, = ππ >.
25. Find the absolute value of the following numbers.
a. {βπ, π}
b. {βπ, βπ, π}
a. Opposite of βπππ b. Opposite of βππ
c. Opposite of +ππ
a. βπ
b. π
a. π_____ β π b. βππ___ β ππ c. πππ_____|βπππ|
a. |βππ| = b. |βπππ| = c. |+ππ| =
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 6
Find the value of each numerical expression. Follow the order of operations when finding each value.
28. Find the sum of each expression below using the rules for adding integers.
29. Show the addition on the number line. Then write the sum.
30. Write the expression that each number line demonstrates. Then write the sum.
26. |βπππ| β π β |βππ| + ππ Γ· π = 27. ππ β |βππ| Γ· π β |+ππ| + ππ Γ· π =
a. βππ + (βππ) = b. ππ + (βππ) = c. βπππ + ππ =
π + (βπ) =
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 7
Solve each expression below.
34. Find the difference of each expression below.
35. Show the subtraction on the number line. Then write the difference.
31. βπππ + ππ + [βπππ + ππ]π = 32. ππ + (βπππ) + (βππ) + (βππ) =
33. At π a.m. the temperature was βπ Β°πͺ . At noon, the temperature rose ππΒ°πͺ. What was the temperature at noon?
a. βπ β (βππ) = b. π β (βππ) = c. βππ β ππ =
π β (βπ) =
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
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Unit 1 Algebraic Expressions and Integers Review Guide
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36. Write the expression that each number line demonstrates. Then write the difference.
Solve each expression below.
39. Round the number to the nearestβ¦β¦..
37. βπππ + πππ β [ππ β ππ]π = 38. πππ β (βπ) β (βπ) + (βπ) β ππ =
a. ππ, πππ Nearest thousand
b. π, πππ Nearest hundred
c. πππ Nearest ten
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
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Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 9
40. Round the number to the nearestβ¦β¦.. (USE NUMBER LINE)
Estimate the answer using rounding method.
Estimate the answer using front end estimation.
π, πππ Nearest hundred
41. πππ + π, πππ =
42. ππ, πππ β π, πππ =
43. π, πππ + πππ =
44. πππ β πππ =
1,300 1,350
1,400
1,450
1,500
4
1,250 1,200 1,150 1,100 1,550
1,600
1,050 1,000
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 10
Estimate the answer using cluster estimation.
Write a rule for each number pattern, and find the next number.
Find one counterexample to show that each conjecture is false.
Fill in the missing numbers.
45. πππ + πππ + ππ + πππ =
46. ππ β ππ β ππ β ππ =
47. π, π, ππ, ππ β¦ β¦ β¦ ..
48. The difference ππ β ππ is equal to (π β π)π
49. All numbers that are divisible by 3 are also divisible by 6.
50. The rule for the pattern shown is +π. π, ______, ππ, ππ, ππ, _______, β¦ β¦ β¦ β¦ β¦ ..
51. The rule for the pattern shown is βππ. ππ, ______, ππ, ππ, ______, ππ, β¦ β¦ β¦ β¦ β¦ ..
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Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 11
52. Find the quotient of each expression below using the rules for dividing integers.
Solve each expression below.
Graph each point on a coordinate plane and find the line segment lengths.
a. βπππ Γ· (βπ) = b. πππ Γ· (βπ) = c. βπππ
ππ=
53. ππ β (βππ) + [βπππ Γ· π]π = 54. [ππ Γ· (βπ)]π β [π β (βπ)]π + ππ =
55. π¨ (βπ, π) πππ π΅ (βπ, βπ) 56. π» (βπ, π) πππ πΉ (π, π)
π
π
π
π
0 1 2 3 4 5 -5 -4 -3 -2 -1
-2
-3
-4
-5
1
2
3 4 5
0 1 2 3 4 5 -5 -4 -3 -2 -1
-2
-4 -5
1
2 3 4 5
-3
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Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 12
ANSWERS
5. Write the following numbers in standard form.
1. Underline the hundredths place.
a. 95.022 b. 15,002.811 c. 0.0076
95.022 15,002.811 0.0076
2. Write down the place value of the digit 7 in the following numbers.
a. 127,000.223 b. 33,087.004 c. 1,630.007
One-thousands Ones One-thousandths
3. Write the value of the underlined digit.
a. 3,229 b. 100,122,221 c. 3,009.09
Tens 20
Hundred-millions 100,000,000
Hundredths 0.09
4. Write each number in standard form.
a. Ten and two hundredths
10.02
b. Eighty-six one-thousandths
0.086
c. Three million, fifteen thousand, two hundred twenty-two.
3, 015,222
a. 800,000 + 60,000 + 2,000 + 10 + 0.6 + 0.009
862,010.609
b. 1,000 + 90 + 3 + 0.6 + 0.09 + 0.002
1,093.692
Name: _________________________________________________ Period: ___________ Date: ________________
Unit 1 Algebraic Expressions and Integers Review Guide
Copyright Β© PreAlgebraCoach.com 13
6. Write the following numbers in expanded form.
7. Find the terms, constant/s and coefficient/s for each expression.
8. Write an algebraic expression for each verbal phrase.
a. 18,002.0321
Value of 1 = 1 * 10,000 = 10,000 Value of 8 = 8 * 1,000 = 8,000 Value of 2 = 2 * 1 = 2 Value of 3 = 3 * 0.01 = 0.03 Value of 2 = 2 * 0.001 = 0.002 Value of 1 = 1 * 0.0001 = 0.0001 18,002.0321= 10,000+ 8,000+ 2 + 0.03+ 0.002+ 0.0001
b. 3,000.631
Value of 3 = 3 * 1,000 = 3,000 Value of 6 = 6 * 0.1 = 0.6 Value of 3 = 3 * 0.01 = 0.03 Value of 1 = 1 * 0.001 = 0.001 3,000.631= 3,000 + 0.6 + 0.03 + 0.001
a. π + ππ + ππ = b. π + ππ + π = c. πππ + π =
πππ«π¦π¬: π, ππ, ππ πππ«π’πππ₯ππ¬: π, π ππ¨π§π¬πππ§π: ππ ππ¨ππππ’ππ’ππ§ππ¬: π, π
πππ«π¦π¬: π, ππ , π πππ«π’πππ₯ππ¬: π, π ππ¨π§π¬πππ§π: π ππ¨ππππ’ππ’ππ§ππ¬: π, π
πππ«π¦π¬: πππ , π πππ«π’πππ₯π: π ππ¨π§π¬πππ§π: πππ ππ¨ππππ’ππ’ππ§π: π
a. The sum of π and 20, divided by 9 b. 3 more than 2 times a number
(π + ππ) Γ· π π + ππ
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9. Evaluate each expression using the values given.
Find the value of each numerical expression. Follow the order of operations when finding each value.
a. π + ππ ππππ π = π πππ π = π
π + ππ = π + π β π = = π + ππ = = ππ
b. π β ππ ππππ π = ππ πππ π = π
π β ππ = = ππ β π β π = = ππ β ππ = = π
10. πππ β (ππ β π) β (πππ β ππ) =
11. πππ Γ· (ππ Γ· π β ππ β πππ Γ· ππ)
πππ β (ππ β π) β (πππ β ππ) = = πππ β ππ β ππ = = πππ β ππ = = πππ
πππ Γ· (ππ Γ· π β ππ β πππ Γ· ππ) = πππ Γ· (ππ β ππ β π) = = πππ Γ· (ππ β π) = = πππ Γ· ππ = = ππ
12. (πππ Γ· π β π) β πππ Γ· ππ = 13. (πππ Γ· π + ππ) β (πππ Γ· ππ β π) =
(πππ Γ· π β π) β πππ Γ· ππ = = (πππ β π) β πππ Γ· ππ = = πππ β πππ Γ· ππ = = πππ β ππ = = πππ
(πππ Γ· π + ππ) β (πππ Γ· ππ β π) = = (ππ + ππ) β (π β π) = = ππ β π = = ππ
14. πππ β (ππ β ππ) + (πππ Γ· π) =
15. π, πππ + (πππ β ππ β π)π =
πππ β (ππ β ππ) + (πππ Γ· π) = = πππ β (ππ β ππ) + ππ = = πππ β π + ππ = = ππ + ππ = = πππ
π, πππ + (πππ β ππ β π)π = = π, πππ + (πππ β ππ β π)π = = π, πππ + (πππ β ππ)π = = π, πππ + (ππ)π = = π, πππ + πππ = = π, πππ
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16. Write an algebraic expression for the word expression.
17. Write the word expression for each algebraic expression.
Evaluate each expression for the given values of the variable.
20. Write an integer to represent each situation.
a. The quotient of π and 30 b. The sum of 45 and the product of 8 and π
c. Twice a number increased by 89.
π
ππ ππ π Γ· ππ
ππ + ππ ππ + ππ
a. π β ππ b. π β π c. ππ + π
The difference of a number π and 13
A number π take away 9 π cubed increased by 8
18.
ππ + π
π+ (ππ β π) =
π = ππ π = ππ
19. ππ + ππ β (π β π)π = π = ππ π = π
ππ + π
π+ (ππ β π) =
=π β ππ + ππ
π+ (π β ππ β ππ) =
=ππ + ππ
π+ (ππ β ππ) =
=ππ
π+ ππ =
= ππ + ππ = = ππ
ππ + ππ β (π β π)π = = π β ππ + π β π β (ππ β π)π = = ππ + ππ β (π)π = = ππ + ππ β ππ = = ππ β ππ = = ππ
a. An increase of 78 points. b. A profit of 100 dollars. c. The stock market went down 600 points today.
+ππ +πππ βπππ
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21. Graph each integer or set of integers on a number line.
22. Find the opposite of each integer.
23. Graph each integer and its opposite on a number line.
24. Compare the following integers. Write <, = ππ >.
25. Find the absolute value of the following numbers.
a. {βπ, π} {βπ, π}
b. {βπ, βπ, π} {βπ, βπ, π}
a. Opposite of βπππ b. Opposite of βππ
c. Opposite of +ππ
+πππ
+ππ βππ
a. βπ +π
b. π
βπ
a. π_____ β π b. βππ___ β ππ c. πππ_____|βπππ|
π > βπ βππ > βππ πππ = |βπππ|
a. |βππ| = b. |βπππ| = c. |+ππ| =
|βππ| = ππ |βπππ| = πππ |+ππ| = ππ
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
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Find the value of each numerical expression. Follow the order of operations when finding each value.
28. Find the sum of each expression below using the rules for adding integers.
29. Show the addition on the number line. Then write the sum.
30. Write the expression that each number line demonstrates. Then write the sum.
26. |βπππ| β π β |βππ| + ππ Γ· π = 27. ππ β |βππ| Γ· π β |+ππ| + ππ Γ· π =
|βπππ| β π β |βππ| + ππ Γ· π = = πππ β π β ππ + ππ Γ· π = = πππ β ππ + π = = ππ + π = = ππ
ππ β |βππ| Γ· π β |+ππ| + ππ Γ· π = = ππ β ππ Γ· π β ππ + ππ Γ· π = = ππ β ππ β ππ + ππ = = ππ β ππ + ππ = = ππ + ππ = = ππ
a. βππ + (βππ) = b. ππ + (βππ) = c. βπππ + ππ =
βππ + (βππ) = βππ ππ + (βππ) = βππ βπππ + ππ = βππ
π + (βπ) =
βπ
+π
π + (βπ) = π
βππ
+π
π + (βππ) = βπ
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
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Copyright Β© PreAlgebraCoach.com 18
Solve each expression below.
34. Find the difference of each expression below.
35. Show the subtraction on the number line. Then write the difference.
31. βπππ + ππ + [βπππ + ππ]π = 32. ππ + (βπππ) + (βππ) + (βππ) =
βπππ + ππ + [βπππ + ππ]π = = βπππ + ππ + [βπππ]π = = βπππ + ππ + ππ, πππ = = βπππ + ππ, πππ = = π, πππ
ππ + (βπππ) + (βππ) + (βππ) = = βπππ + (βππ) + (βππ) = = βπππ + (βππ) = = βπππ
33. At π a.m. the temperature was βπ Β°πͺ . At noon, the temperature rose ππΒ°πͺ. What was the temperature at noon?
Temperature in π a.m. βπ Β°πͺ = βπ β¦ . rose ππΒ°πͺ = +ππ βπ + ππ = π The temperature at noon was πΒ°πͺ.
a. βπ β (βππ) = b. π β (βππ) = c. βππ β ππ =
βπ β (βππ) = = βπ + ππ = = ππ
π β (βππ) = = π + ππ = = ππ
βππ β ππ = = βππ + (βππ) = = βππ
π β (βπ) =
+π + π
π β (βπ) = = π + π = = π
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
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36. Write the expression that each number line demonstrates. Then write the difference.
Solve each expression below.
39. Round the number to the nearestβ¦β¦..
+π
βπ
βπ β (βπ) = = βπ + π = = π
37. βπππ + πππ β [ππ β ππ]π = 38. πππ β (βπ) β (βπ) + (βπ) β ππ =
βπππ + πππ β [ππ β ππ]π = = βπππ + πππ β [ππ + (βππ)]π = = βπππ + πππ β [βπ]π = βπππ + πππ β ππ = βππ β ππ = = βππ + (βππ) = = βππ
πππ β (βπ) β (βπ) + (βπ) β ππ = = πππ + π β (βπ) + (βπ) β ππ = = πππ β (βπ) + (βπ) β ππ = = πππ + π + (βπ) β ππ = = πππ + (βπ) β ππ = = πππ β ππ = = πππ + (βππ) = = ππ
a. ππ, πππ Nearest thousand
b. π, πππ Nearest hundred
c. πππ Nearest ten
ππ, π ππ β ππ, πππ
π, π π π β π, πππ
ππ π β πππ
0 1 2 3 4 -1 -2 -3 -4 5 6 -5 -6
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40. Round the number to the nearestβ¦β¦.. (USE NUMBER LINE)
Estimate the answer using rounding method.
Estimate the answer using front end estimation.
π, πππ Nearest hundred
π, π π π
π, π π π β π, πππ
41. πππ + π, πππ =
42. ππ, πππ β π, πππ =
πππ + π, πππ = Round to nearest ten
ππ π β πππ
π, ππ π β π, πππ πππ + π, πππ = π, πππ
ππ, πππ β π, πππ = Round to nearest thousand
ππ, π ππ β ππ, πππ
π, π ππ β π, πππ ππ, πππ β π, πππ = ππ, πππ
43. π, πππ + πππ =
44. πππ β πππ =
π, πππ + πππ =
π, π ππ β π, πππ
π π π β πππ π, πππ + πππ = π, πππ
πππ β πππ =
π π π β π, πππ
π π π β πππ π, πππ β πππ = πππ
1,300 1,350
1,400
1,450
1,500
4
1,250 1,200 1,150 1,100 1,550
1,600
1,050 1,000
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Copyright Β© PreAlgebraCoach.com 21
Estimate the answer using cluster estimation.
Write a rule for each number pattern, and find the next number.
Find one counterexample to show that each conjecture is false.
Fill in the missing numbers.
45. πππ + πππ + ππ + πππ =
46. ππ β ππ β ππ β ππ =
πππ + πππ + ππ + πππ = Notice that they all cluster around πππ. πππ + πππ + πππ + πππ = π β πππ = πππ Real answer: πππ + πππ + ππ + πππ = πππ
ππ β ππ β ππ β ππ = Notice that they all cluster around ππ. ππ β ππ β ππ β ππ = ππ, πππ Real answer: ππ β ππ β ππ β ππ = ππ, πππ
47. π, π, ππ, ππ β¦ β¦ β¦ ..
Start with 3 , each number is 3 times the previous number. π β π = π π β π = ππ ππ β π = ππ ππ β π = πππ The next number is πππ
48. The difference ππ β ππ is equal to (π β π)π
49. All numbers that are divisible by 3 are also divisible by 6.
ππ β ππ = (π β π)π ππ β ππ = ππ β ππ = ππ
(π β π)π = ππ = π ππ β π
9 is divisible by 3 but no divisible by 6.
50. The rule for the pattern shown is +π. π, ______, ππ, ππ, ππ, _______, β¦ β¦ β¦ β¦ β¦ ..
51. The rule for the pattern shown is βππ. ππ, ______, ππ, ππ, ______, ππ, β¦ β¦ β¦ β¦ β¦ ..
π + π = π π + π = ππ ππ + π = ππ ππ + π = ππ ππ + π = ππ π, π, ππ, ππ, ππ, ππ, β¦ β¦ β¦ β¦ β¦.
ππ β ππ = ππ ππ β ππ = ππ ππ β ππ = ππ ππ β ππ = ππ ππ β ππ = ππ ππ, ππ, ππ, ππ, ππ, ππ β¦ β¦ β¦ β¦ β¦ ..
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52. Find the quotient of each expression below using the rules for dividing integers.
Solve each expression below.
Graph each point on a coordinate plane and find the line segment lengths.
a. βπππ Γ· (βπ) = b. πππ Γ· (βπ) = c. βπππ
ππ=
βπππ Γ· (βπ) = πππ πππ Γ· (βπ) = βππ βπππ
ππ= βπ
53. ππ β (βππ) + [βπππ Γ· π]π = 54. [ππ Γ· (βπ)]π β [π β (βπ)]π + ππ =
ππ β (βππ) + [βπππ Γ· π]π = = ππ β (βππ) + [βππ]π = = ππ β (βππ) + π, πππ = = βπππ + π, πππ = = π, πππ
[ππ Γ· (βπ)]π β [π β (βπ)]π + ππ = = [βπ]π β [βππ]π + ππ = = ππ β πππ + ππ = = ππ + (βπππ) + ππ = = βπππ + ππ = = βπππ
55. π¨ (βπ, π) πππ π΅ (βπ, βπ) 56. π» (βπ, π) πππ πΉ (π, π)
π
π¨
π
π΅
π π» πΉ
π
π¨π΅Μ Μ Μ Μ is vertical π¨π΅Μ Μ Μ Μ = |π πππππππππ ππ π β πππππ ππππππ| π¨π΅Μ Μ Μ Μ = |π β (βπ)| = |π + π| = π π¨π΅Μ Μ Μ Μ = π πππππ
π»πΉΜ Μ Μ Μ is horizontal π»πΉΜ Μ Μ Μ = |π πππππππππ ππ π β πππππ ππππππ| π»πΉΜ Μ Μ Μ = |π β (βπ)| = |π + π| = π π»πΉΜ Μ Μ Μ = π πππππ
0 1 2 3 4 5 -5 -4 -3 -2 -1
-2
-3
-4
-5
1
2
3 4 5
0 1 2 3 4 5 -5 -4 -3 -2 -1
-2
1
2 3 4 5
-3 -4 -5
