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Solved Examples
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eee Determine whether the set {0, 13, - 13} satisfies closure property with respective to multiplication. eee View Solution
eee Name the property illustrated by: (7x)(17x) = 1 eee View Solution
eee Simplify: | 4 | + | - 11 | + | 15 | + | - 7 |
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eee What is the value of |- 12 + (- 63)|? eee View Solution
eee Name the property of statement: 11 + 0 = 11
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eee Find the additive inverse of 5- 6.
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eee Find the multiplicative inverse of - 1312.
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eee Divide: - 180 ÷ (- 12) eee View Solution
eee Simplify: (| 5 | + | - 13 | - | 4 |) (5| 12 | - | - 13 |) (4| 7 - 12| - | 4 |) 3 eee View Solution
eee A cloth stores offers "25% off the sale price". A dress whose original price is $100 has a sales price that was 20% less than the original price. Then what percentage of the original price is the final price? eee View Solution
eee Name the subset(s) of the real numbers to which '- 11' belongs.
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eee Simplify : 4 | - 2 | + 5 | 3 | - | - 7 |
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eee Use the symbol < or > or =, to show the relationship between - 6, - 49 eee View Solution
eee A tradesman bought an article for $300. He wants a gain of 20% by allowing 5% discount on it. What price should the tradesman mark on the article? eee View Solution
eee Simplify: | 7 - 9 |3 + | - 2 + 4 |4 + | 2 - 8 |3
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eee Name the property of the statement: - 8 + 8 = 0
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eee Name the property illustrated.
(2l + 9)(10 + 9l) =(2l + 9).(10) + (2l + 9).(9l)
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eee Divide: - 40 ÷ (8)
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eee Determine whether the following statement is true. If a.h = b.h and h is non-zero, then a = b.
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eee Simplify: 3 | 10 - 18 | eee View Solution
eee Simplify: |- 9| + |- 13|
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eee Add - 33 and (- 58).
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eee Find the multiplicative inverse of 3817.
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eee Find the additive inverse of 549.
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eee Determine whether the following is true. If y, b, a are real numbers, and if y = b then y + a = b + a.
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eee Simplify: | 14 - 4 |10 + | 12 - 15 |10 - | 15 + 12 |8
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eee Determine whether the statement | a + y | = | a | + | y | is true or false.
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eee Determine whether the statement | u | + | p | ≥ | u + p | is true or false.
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eee Which of the following is the absolute value of | 3 + 5 |?
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eee What is the value of | - 6 | + | - 5 |? eee View Solution
eee - 8 × - 8(- 7) = ____.
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eee Find the value of | 11 - 13 |.
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eee Find the property illustrated by the relation:
| 2.3l | + | 9k | = | 9k | + | 2.3l |
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eee Determine whether the following statement is true. If v, k, z are real numbers, then v (k - z) = vk - vz.
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eee Find the sum in clock arithmetic: 9 + 4 (on a 12-hour clock.)
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eee Find the sum in clock arithmetic: 2 + 1 (on a 12-hour clock.)
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eee Which of the following is an equivalent expression for (3 + 3) + 7?
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eee Which property is illustrated in the expression? 5.5 × (7.7 × 27.9) = (5.5 × 7.7) × 27.9
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eee Which of the following expressions is equivalent to 10 + ((- 10) + 55)?
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eee What is the value of z, if the equation q × r × u = u × z illustrates the commutative property of multiplication?
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eee Which of the following is correct ?

I. 7 × 17 = 17 × 7 illustrates the associative property of addition.
II. 7 × (17 × 62) = (7 × 17) × 62 illustrates the associative property of multiplication.
III. 7 × (17 × 62) × 0 = 0 illustrates the associative property of addition.
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eee Which property does "4 · 7 = 47 {real numbers}" illustrate?
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eee On a particular day the temperature at sea level at a place was measured as 175° F. What would be the temperature at an altitude of 35000 feet if the temperature decreases about 5° F for every 1000 feet of altitude.
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eee What is the value of 45 - (- 7)? eee View Solution
eee What is the value of 45 - | - 6 |?
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eee What is the value of - 43 + (- 15)?
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eee The subtraction expression | - 92 | - | - 79 | can also be written as,
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eee What is the value of the expression? 91 + (- 58) + (- 95)
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eee Write a comparison statement using <, =, or > .
0 __ - 0.438 eee
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eee Find the multiplicative inverse of (9 + 89).
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eee Name the property of the statement: 11 · (8 · 3) = (11 · 8) · 3
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eee If a scooter travels 136 km on 4 liters of petrol, how many kilometers will it travel on 11 liters of petrol?
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eee Perform the given operation: 5.82 yards($1617 yards) eee View Solution
eee The length of a wire is 1251 feet. Write the length of the wire in inches.
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eee The following are the temperatures at various places: - 40° F, - 34° F, - 44° F, order the temperatures from highest to lowest.
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eee Use the symbol < or > or =, to show the relationship between - 26, 26
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eee Use the symbol < or > or =, to show the relationship between 48, 7 eee View Solution
eee Perform the given operation: 136 feet4 seconds × 384 seconds3 hours× 9 miles1224 feet
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eee Determine whether the following is true or false:
37.043 > 37.0043
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eee True or False?
0.25255227562... {irrational numbers}
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eee Name the subset(s) of the real numbers to which 72 belongs.
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eee Name the subset(s) of the real numbers to which 0.777777.... belongs.
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eee Write 0.201¯ as a quotient of two integers. eee View Solution
eee True or False?
7.373737............ {irrational numbers} eee
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eee Determine whether the following true or false.
12 {real numbers}
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eee List the numbers in order from least to greatest - 0.017, - 0.0017, - 0.17, - 17.
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eee Write 0.26 as a quotient of two integers.
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eee Write 2.4 as a quotient of two integers.
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eee List the numbers in order from least to greatest 6, 5, 4, 18.
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eee List the numbers in order from least to greatest 534, 5116, 513, 5748
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eee Write the repeating decimal 0.43629¯ as a ratio of two integers.
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eee Write the repeating decimal 0.707¯ as a quotient of two integers.
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eee True or false? If a < b, then a2 < b2.
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eee Determine whether the statement is true or false.
If b2 > y2, then b > y.
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eee True or False? If h > i, then hc > ic.
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eee Determine whether the statement is true or false.
If x > c, then x + z > c + z, for any real number z. eee
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eee Determine whether the statement is true or false.
If b2 = x2, then b =x.
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cc  Use a real number to represent 90 meters below sea level.  cc View Solution
cc  Use a real number to represent a debit of $2900.  cc View Solution
cc  The length of a wire is 1474 feet. Write the length of the wire in inches.
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cc  Identify whether 224 is a rational or an irrational number.
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cc  The length of river Nile is 6670 kilo meters. Express its length in miles.
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cc  On a particular day the temperature at sea level at a place was measured as 64° F. What would be the temperature at an altitude of 16000 feet if the temperature decreases about 4° F for every 1000 feet of altitude.
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cc  Identify whether 258 is a rational or an irrational number.  cc View Solution
cc  Determine if the set of natural numbers and the operation of multiplication form a field.
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cc  Find the property illustrated by the relation: 10.6(pw) = (10.6p)w.
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cc  Name the property illustrated by: (11x)(111x) = 1  cc View Solution
cc  Which property does (- 8) + [- (- 8)] = 0 illustrate?  cc View Solution
cc  What number (on a 12-hour clock) in clock arithmetic serves as the additive identity?
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cc  Simplify: | 9 | + | - 35 | + | 44 | + | - 32 |
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cc  What is the value of 16 - | - 9 |?
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cc  Graph the real numbers - 2.1, 2 and 73
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cc  Perform the given operation: 4.99 yards($333 yards)  cc View Solution
cc  Write a comparison statement using <, =, or > .
0 __ - 0.354  cc
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cc  Determine whether the following true or false.
20 {real numbers}
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cc  Determine whether the product of an irrational number and a positive integer other than '0' will be an irrational number.
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cc  Simplify: 9 | 18 - 29 |  cc View Solution
cc  Simplify: |- 12| + |- 19|
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cc  Simplify : 6 | - 2 | + 11 | 9 | - | - 15 |
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cc  Add - 20 and (- 48).
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cc  Simplify: | 14 - 16 |4 + | - 4 + 11 |4 + | 7 - 15 |4
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cc  Divide: - 6 ÷ (2)
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cc  Find the multiplicative inverse of 345.
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cc  Find the property illustrated by the relation: 6.4(py) = (6.4p)y.
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cc  Find the additive inverse of 6511.
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cc  Name the property illustrated by: (12c)(112c) = 1
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cc  Simplify: | 13 - 4 |9 + | 11 - 14 |9 - | 14 + 11 |6
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cc  Determine whether the statement | z + a | = | z | + | a | is true or false.
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cc  Determine whether the statement | k | + | w | ≥ | k + w | is true or false.
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cc  Determine whether the statement | x | - | y | ≤ | x - y | is true or false.
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cc  Name the property illustrated.
0 + π = π.  cc
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cc  Which of the following properties do not hold for the set of whole numbers?  cc View Solution
cc  Determine whether the following is true. If b, z, a are real numbers, and if b = z then b + a = z + a.
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cc  Find the property illustrated by the relation:
| 2.5w | + | 4t | = | 4t | + | 2.5w |
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cc  Name the property illustrated.
(2u + 7)(8 + 5u) =(2u + 7).(8) + (2u + 7).(5u)
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cc  Determine whether the following statement is true. If g.d = i.d and d is non-zero, then g = i.
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cc  Which one of the statements satisfies transitive property?  cc View Solution
cc  Determine whether the following statement is true. If x = b - a then x + a = b; a, b are real numbers.
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cc  Determine whether the following statement is true. If s, l, r are real numbers, then s (l - r) = sl - sr.
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cc  Determine which one of the sets does not satisfy closure property of addition.
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cc  Find the sum in clock arithmetic: 9 + 8 (on a 12-hour clock.)
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cc  Find the sum in clock arithmetic: 6 + 3 (on a 12-hour clock.)
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cc  Which of the expressions does not illustrate the identity property of addition?
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cc  Which of the following equation represents identity property of multiplication?
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cc  What is the value of k, if the equation l × v × n = n × k illustrates the commutative property of multiplication?
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cc  Which of the following expressions represents the commutative property of addition?  cc View Solution
cc  Which of the following is an equivalent expression for (2 + 3) + 6?
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cc  Which property is illustrated in the expression? 3.3 × (6.6 × 33.7) = (3.3 × 6.6) × 33.7
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cc  What is commutative property of addition?  cc View Solution
cc  Which of the following expressions illustrates the commutative property of addition?  cc View Solution
cc  What is the number that should be added to a number so that the sum is the number itself?
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cc  Which of the following expressions is equivalent to 12 + ((- 11) + 98)?
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cc  Which of the following is correct ?

I. 6 × 16 = 16 × 6 illustrates the associative property of addition.
II. 6 × (16 × 59) = (6 × 16) × 59 illustrates the associative property of multiplication.
III. 6 × (16 × 59) × 0 = 0 illustrates the associative property of addition.
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cc  What is the value of - 10 + (- 20)?
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cc  The subtraction expression | - 84 | - | - 72 | can also be written as,
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cc  What is the value of the expression? 76 + (- 98) + (- 85)
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cc  Which property does "6 · 7 = 67 {real numbers}" illustrate?
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cc  Find the value of | 2 - 4 |.
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cc  Which of the following is the absolute value of | 2 + 6 |?
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cc  What is the value of | - 3 | + | - 3 |?  cc View Solution
cc  - 5 × - 8(- 6) = ____.
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cc  What is the value of |- 12 + (- 66)|?  cc View Solution
cc  What is the value of 44 - (- 9)?  cc View Solution
cc  Find the multiplicative inverse of (8 + 78).
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cc  Find the opposite and the absolute value of - 34.  cc View Solution
cc  If a scooter travels 64 km on 2 liters of petrol, how many kilometers will it travel on 4 liters of petrol?
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cc  Use the symbol < or > or =, to show the relationship between - 7, - 64  cc View Solution
cc  Name the property of the statement: - 11 + 11 = 0
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cc  The following are the temperatures at various places: - 41° F, - 35° F, - 48° F, order the temperatures from highest to lowest.
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cc  Name the property of statement: 30 + 0 = 30
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cc  True or False?
4.595959............ {irrational numbers}  cc
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cc  Determine whether the following is true or false:
22.042 > 22.0042
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cc  Determine whether the following is true or false:
If a number is rational, then it is an integer.
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cc  True or False?
0.464664410694... {irrational numbers}
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cc  Name the subset(s) of the real numbers to which 511 belongs.
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cc  Name the subset(s) of the real numbers to which 0.666666.... belongs.
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cc  Name the subset(s) of the real numbers to which '- 27' belongs.
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cc  Name the subset(s) of the real numbers to which "π" belongs.
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cc  Graph the number 312  cc View Solution
cc  Give the coordinate that indicates the approximate location of point A.  cc View Solution
cc  Give the coordinate that indicates the approximate location of point A.  cc View Solution
cc  List the numbers in order from least to greatest - 0.015, - 0.0015, - 0.15, - 15.
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cc  True or False?The difference of two whole numbers is a whole number.
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cc  Determine whether the statement is true or false.
The product of two irrational numbers is an irrational number.  cc
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cc  True or False?
The product of two irrational numbers is a rational number.  cc
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cc  Determine whether the statement is true or false.
The sum of two irrational numbers is an irrational number.
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cc  Use a real number to represent 85 meters below sea level.  cc View Solution
cc  Use a real number to represent a debit of $1900.  cc View Solution
cc  Name the property of the statement: 14 · (10 · 6) = (14 · 10) · 6
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cc  Write 0.165¯ as a quotient of two integers.  cc View Solution
cc  Write 0.48 as a quotient of two integers.
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cc  Identify whether 368 is a rational or an irrational number.
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cc  Determine whether the associative property satisfied under the division operation.
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cc  Mark point A so that AC = CB.
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cc  Determine whether the set of negative integers is closed under addition.
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cc  Identify whether 224 is a rational or an irrational number.  cc View Solution
cc  Determine whether the set of irrational numbers is closed under addition.
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cc  Determine whether the set of irrational numbers is closed under multiplication.  cc View Solution
cc  Write 7.2 as a quotient of two integers.
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cc  List the numbers in order from least to greatest 8, 6, 5, 26.
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cc  List the numbers in order from least to greatest 345, 3125, 314, 39100
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cc  Write the repeating decimal 0.23424¯ as a ratio of two integers.
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cc  Write the repeating decimal 0.794¯ as a quotient of two integers.
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cc  True or false? If y < x, then y2 < x2.
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cc  Determine whether the statement is true or false.
If y2 > c2, then y > c.
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cc  True or False? If b > e, then bd > ed.
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cc  Determine whether the statement is true or false.
If a > x, then a + z > x + z, for any real number z.  cc
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cc  Determine whether the statement is true or false.
If c2 = a2, then c =a.
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cc  Determine whether the set of whole numbers is closed under multiplication.  cc View Solution
cc  Use the symbol < or > or =, to show the relationship between - 11, 11
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cc  Use the symbol < or > or =, to show the relationship between 63, 8  cc View Solution
cc  Write the numbers in increasing order: - 13, 1, - 94, - 2
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cc  Write the numbers in increasing order: 0.5, 10, - 2.1, - 6  cc View Solution
cc  Determine whether the statement is true for all real numbers a, b and c: (a - b) - c = a - (b - c)
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cc  The record of low temperatures for six states are given below, find which states have record of low temperatures below - 45° F?
StatesTemperatures
Michigan- 34° F
New Mexico- 46° F
New York- 32° F
North Carolina- 52° F
Pennsylvania- 44° F
Virginia- 50° F
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cc  Perform the given operation: 52 feet4 seconds × 608 seconds4 hours× 9 miles468 feet
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cc  ICCC stands for International Credit Card Code which is a 12-digit number. The twelth digit of an ICCC is called its prime digit. The prime digit of an ICCC can be obtained by performing the following operations on the first eleven digits.
(i). Add the digits in the odd positions and multiply by 3.
(ii). Add the digits in the even positions.
(iii). Add the results of first two steps.
(iv). Subtract the total sum from the next highest multiple of 10.
Determine the prime digit of an ICCC whose first eleven digits are 01522514658.
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cc  Find the property illustrated by the relation.
|2.3q| + |7r| = |7r| + |2.3q|
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cc  Name the property illustrated.
(5m + 2)(3 + 3m) = (5m + 2).(3) + (5m + 2).(3m).
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cc  What is the value of r, if the equation w × p × x = x × r illustrates the commutative property of multiplication?
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cc  Find the property illustrated by the relation:
|3.6p| + |9s| = |9s| + |3.6p|  cc
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cc  Find the property illustrated by the relation:
|5.8x| + |13z| = |13z| + |5.8x|
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cc  Find the property illustrated by the relation:
|2.5a| + |6a| = |6a| + |2.5a|
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cc  Find the property illustrated by the relation:
|2.6a| + |10a| = |10a| + |2.6a|  cc
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cc  Find the property illustrated by the relation.
|5.6r| + |13r| = |13r| + |5.6r|
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cc  Find the property illustrated by the relation.
|3.6s| + |6s| = |6s| + |3.6s|
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cc  Find the property illustrated by the relation:
|5.8b| + |14b| = |14b| + |5.8b|
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cc  Use a real number to represent a credit of $6000.
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cc  Identify whether 10064 is a rational or an irrational number.  cc View Solution
cc  Write a comparison statement using <, =, or > :
63 __ 63
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cc  Write a comparison statement using <, =, or >.
47 __ 99
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cc  Write 0.45¯ as a quotient of two integers.  cc View Solution
cc  Find the property illustrated by the relation:
|3.5s| + |11s| = |11s| + |3.5s|
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cc  Determine whether the following statement is true or false.
"If t2 = w2, then t = w."  cc
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cc  Find the property illustrated by the relation:
|2.6b| + |4b| = |4b| + |2.6b|  cc
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cc  Find the property illustrated by the relation.
|4.5r| + |6r| = |6r| + |4.5r|  cc
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cc  Find the property illustrated by the relation:
|3.7s| + |8s| = |8s| + |3.7s|  cc
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cc  Find the property illustrated by the relation:
|3.6s| + |8s| = |8s| + |3.6s|
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cc  Which property does (- 13) + [- (- 13)] = 0 illustrate?  cc View Solution
cc  Find the property illustrated by the relation: 7.2(xt) = (7.2x)t.  cc View Solution