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Solved Examples
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BB  Determine whether the set {0, 13, - 13} satisfies closure property with respective to multiplication.  BB View Solution
BB  Name the property illustrated by: (7x)(17x) = 1  BB View Solution
BB  Simplify: | 4 | + | - 11 | + | 15 | + | - 7 |
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BB  What is the value of |- 12 + (- 63)|?  BB View Solution
BB  Name the property of statement: 11 + 0 = 11
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BB  Find the additive inverse of 5- 6.
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BB  Find the multiplicative inverse of - 1312.
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BB  Divide: - 180 ÷ (- 12)  BB View Solution
BB  Simplify: (| 5 | + | - 13 | - | 4 |) (5| 12 | - | - 13 |) (4| 7 - 12| - | 4 |) 3  BB View Solution
BB  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?  BB View Solution
BB  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?  BB View Solution
BB  Use the symbol < or > or =, to show the relationship between - 6, - 49  BB View Solution
BB  Name the subset(s) of the real numbers to which '- 11' belongs.
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BB  Name the property of the statement: - 8 + 8 = 0
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BB  Simplify : 4 | - 2 | + 5 | 3 | - | - 7 |
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BB  Simplify: | 7 - 9 |3 + | - 2 + 4 |4 + | 2 - 8 |3
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BB  Name the property illustrated.
(2l + 9)(10 + 9l) =(2l + 9).(10) + (2l + 9).(9l)
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BB  Determine whether the following statement is true. If a.h = b.h and h is non-zero, then a = b.
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BB  Divide: - 40 ÷ (8)
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BB  Simplify: 3 | 10 - 18 |  BB View Solution
BB  Simplify: |- 9| + |- 13|
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BB  Add - 33 and (- 58).
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BB  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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BB  Find the property illustrated by the relation:
| 2.3l | + | 9k | = | 9k | + | 2.3l |
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BB  Find the multiplicative inverse of 3817.
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BB  Determine whether the following statement is true. If v, k, z are real numbers, then v (k - z) = vk - vz.
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BB  Find the additive inverse of 549.
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BB  Find the sum in clock arithmetic: 9 + 4 (on a 12-hour clock.)
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BB  Simplify: | 14 - 4 |10 + | 12 - 15 |10 - | 15 + 12 |8
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BB  Find the sum in clock arithmetic: 2 + 1 (on a 12-hour clock.)
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BB  Determine whether the statement | a + y | = | a | + | y | is true or false.
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BB  Determine whether the statement | u | + | p | ≥ | u + p | is true or false.
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BB  Which of the following is the absolute value of | 3 + 5 |?
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BB  What is the value of | - 6 | + | - 5 |?  BB View Solution
BB  - 8 × - 8(- 7) = ____.
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BB  Which of the following is an equivalent expression for (3 + 3) + 7?
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BB  Which property is illustrated in the expression? 5.5 × (7.7 × 27.9) = (5.5 × 7.7) × 27.9
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BB  Which of the following expressions is equivalent to 10 + ((- 10) + 55)?
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BB  Find the value of | 11 - 13 |.
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BB  What is the value of z, if the equation q × r × u = u × z illustrates the commutative property of multiplication?
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BB  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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BB  Which property does "4 · 7 = 47 {real numbers}" illustrate?
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BB  Write a comparison statement using <, =, or > .
0 __ - 0.438  BB
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BB  Determine whether the following is true or false:
37.043 > 37.0043
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BB  True or False?
0.25255227562... {irrational numbers}
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BB  Name the subset(s) of the real numbers to which 72 belongs.
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BB  Name the subset(s) of the real numbers to which 0.777777.... belongs.
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BB  Write 0.201¯ as a quotient of two integers.  BB View Solution
BB  True or False?
7.373737............ {irrational numbers}  BB
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BB  Determine whether the following true or false.
12 {real numbers}
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BB  List the numbers in order from least to greatest - 0.017, - 0.0017, - 0.17, - 17.
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BB  Write 0.26 as a quotient of two integers.
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BB  Write 2.4 as a quotient of two integers.
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BB  List the numbers in order from least to greatest 6, 5, 4, 18.
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BB  List the numbers in order from least to greatest 534, 5116, 513, 5748
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BB  Write the repeating decimal 0.43629¯ as a ratio of two integers.
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BB  Write the repeating decimal 0.707¯ as a quotient of two integers.
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BB  True or false? If a < b, then a2 < b2.
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BB  Determine whether the statement is true or false.
If b2 > y2, then b > y.
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BB  True or False? If h > i, then hc > ic.
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BB  Determine whether the statement is true or false.
If x > c, then x + z > c + z, for any real number z.  BB
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BB  Determine whether the statement is true or false.
If b2 = x2, then b =x.
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BB  Use a real number to represent 90 meters below sea level.  BB View Solution
BB  Use a real number to represent a debit of $2900.  BB View Solution
BB  Identify whether 224 is a rational or an irrational number.
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BB  Identify whether 258 is a rational or an irrational number.  BB View Solution
BB  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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BB  What is the value of 45 - (- 7)?  BB View Solution
BB  What is the value of 45 - | - 6 |?
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BB  What is the value of - 43 + (- 15)?
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BB  The subtraction expression | - 92 | - | - 79 | can also be written as,
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BB  What is the value of the expression? 91 + (- 58) + (- 95)
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BB  Find the multiplicative inverse of (9 + 89).
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BB  Name the property of the statement: 11 · (8 · 3) = (11 · 8) · 3
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BB  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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BB  Perform the given operation: 5.82 yards($1617 yards)  BB View Solution
BB  The length of a wire is 1251 feet. Write the length of the wire in inches.
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BB  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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BB  Use the symbol < or > or =, to show the relationship between - 26, 26
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BB  Use the symbol < or > or =, to show the relationship between 48, 7  BB View Solution
BB  Perform the given operation: 136 feet4 seconds × 384 seconds3 hours× 9 miles1224 feet
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BB  The length of a wire is 1474 feet. Write the length of the wire in inches.
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BB  The length of river Nile is 6670 kilo meters. Express its length in miles.
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BB  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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BB  Determine if the set of natural numbers and the operation of multiplication form a field.
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BB  Find the property illustrated by the relation: 10.6(pw) = (10.6p)w.
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BB  Name the property illustrated by: (11x)(111x) = 1  BB View Solution
BB  Which property does (- 8) + [- (- 8)] = 0 illustrate?  BB View Solution
BB  What number (on a 12-hour clock) in clock arithmetic serves as the additive identity?
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BB  Simplify: | 9 | + | - 35 | + | 44 | + | - 32 |
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BB  What is the value of 16 - | - 9 |?
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BB  Graph the real numbers - 2.1, 2 and 73
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BB  Perform the given operation: 4.99 yards($333 yards)  BB View Solution
BB  Determine whether the product of an irrational number and a positive integer other than '0' will be an irrational number.
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BB  Add - 20 and (- 48).
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BB  Divide: - 6 ÷ (2)
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BB  Find the multiplicative inverse of 345.
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BB  Find the additive inverse of 6511.
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BB  Simplify: | 13 - 4 |9 + | 11 - 14 |9 - | 14 + 11 |6
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BB  Simplify: 9 | 18 - 29 |  BB View Solution
BB  Simplify: |- 12| + |- 19|
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BB  Determine whether the statement | z + a | = | z | + | a | is true or false.
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BB  Simplify : 6 | - 2 | + 11 | 9 | - | - 15 |
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BB  Determine whether the statement | k | + | w | ≥ | k + w | is true or false.
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BB  Simplify: | 14 - 16 |4 + | - 4 + 11 |4 + | 7 - 15 |4
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BB  Determine whether the statement | x | - | y | ≤ | x - y | is true or false.
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BB  Write a comparison statement using <, =, or > .
0 __ - 0.354  BB
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BB  Determine whether the following true or false.
20 {real numbers}
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BB  Find the property illustrated by the relation: 6.4(py) = (6.4p)y.
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BB  Name the property illustrated by: (12c)(112c) = 1
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BB  Name the property illustrated.
0 + π = π.  BB
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BB  Which of the following properties do not hold for the set of whole numbers?  BB View Solution
BB  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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BB  Find the property illustrated by the relation:
| 2.5w | + | 4t | = | 4t | + | 2.5w |
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BB  Name the property illustrated.
(2u + 7)(8 + 5u) =(2u + 7).(8) + (2u + 7).(5u)
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BB  Determine whether the following statement is true. If g.d = i.d and d is non-zero, then g = i.
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BB  Which one of the statements satisfies transitive property?  BB View Solution
BB  Determine whether the following statement is true. If x = b - a then x + a = b; a, b are real numbers.
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BB  Determine whether the following statement is true. If s, l, r are real numbers, then s (l - r) = sl - sr.
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BB  Determine which one of the sets does not satisfy closure property of addition.
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BB  Find the sum in clock arithmetic: 9 + 8 (on a 12-hour clock.)
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BB  Find the sum in clock arithmetic: 6 + 3 (on a 12-hour clock.)
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BB  What is the value of - 10 + (- 20)?
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BB  The subtraction expression | - 84 | - | - 72 | can also be written as,
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BB  What is the value of the expression? 76 + (- 98) + (- 85)
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BB  Find the value of | 2 - 4 |.
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BB  Which of the following is the absolute value of | 2 + 6 |?
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BB  What is the value of | - 3 | + | - 3 |?  BB View Solution
BB  - 5 × - 8(- 6) = ____.
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BB  What is the value of |- 12 + (- 66)|?  BB View Solution
BB  What is the value of 44 - (- 9)?  BB View Solution
BB  Find the multiplicative inverse of (8 + 78).
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BB  Find the opposite and the absolute value of - 34.  BB View Solution
BB  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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BB  Use the symbol < or > or =, to show the relationship between - 7, - 64  BB View Solution
eee Name the property of the statement: - 11 + 11 = 0
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eee Which of the expressions does not illustrate the identity property of addition?
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eee Which of the following equation represents identity property of multiplication?
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eee What is the value of k, if the equation l × v × n = n × k illustrates the commutative property of multiplication?
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eee Which of the following expressions represents the commutative property of addition? eee View Solution
eee 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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eee Which of the following is an equivalent expression for (2 + 3) + 6?
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eee Name the property of statement: 30 + 0 = 30
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eee Which property is illustrated in the expression? 3.3 × (6.6 × 33.7) = (3.3 × 6.6) × 33.7
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eee Name the property of the statement: 14 · (10 · 6) = (14 · 10) · 6
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eee Determine whether the associative property satisfied under the division operation.
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eee Determine whether the set of negative integers is closed under addition.
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eee What is commutative property of addition? eee View Solution
eee Which of the following expressions illustrates the commutative property of addition? eee View Solution
eee What is the number that should be added to a number so that the sum is the number itself?
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eee Which of the following expressions is equivalent to 12 + ((- 11) + 98)?
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eee 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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eee Which property does "6 · 7 = 67 {real numbers}" illustrate?
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eee Determine whether the set of irrational numbers is closed under addition.
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eee Determine whether the set of irrational numbers is closed under multiplication. eee View Solution
eee Determine whether the set of whole numbers is closed under multiplication. eee View Solution
eee True or False?
4.595959............ {irrational numbers} eee
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eee Use the symbol < or > or =, to show the relationship between - 11, 11
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eee Use the symbol < or > or =, to show the relationship between 63, 8 eee View Solution
eee Write the numbers in increasing order: - 13, 1, - 94, - 2
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eee Determine whether the following is true or false:
22.042 > 22.0042
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eee Write the numbers in increasing order: 0.5, 10, - 2.1, - 6 eee View Solution
eee Determine whether the following is true or false:
If a number is rational, then it is an integer.
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eee Determine whether the statement is true for all real numbers a, b and c: (a - b) - c = a - (b - c)
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eee True or False?
0.464664410694... {irrational numbers}
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eee Name the subset(s) of the real numbers to which 511 belongs.
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eee 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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eee Use a real number to represent a credit of $6000.
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eee Identify whether 10064 is a rational or an irrational number. eee View Solution
eee Name the subset(s) of the real numbers to which 0.666666.... belongs.
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eee Perform the given operation: 52 feet4 seconds × 608 seconds4 hours× 9 miles468 feet
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eee Name the subset(s) of the real numbers to which '- 27' belongs.
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eee Name the subset(s) of the real numbers to which "π" belongs.
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eee Graph the number 312 eee View Solution
eee Give the coordinate that indicates the approximate location of point A. eee View Solution
eee Give the coordinate that indicates the approximate location of point A. eee View Solution
eee List the numbers in order from least to greatest - 0.015, - 0.0015, - 0.15, - 15.
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eee True or False?The difference of two whole numbers is a whole number.
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eee Determine whether the statement is true or false.
The product of two irrational numbers is an irrational number. eee
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eee True or False?
The product of two irrational numbers is a rational number. eee
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eee Determine whether the statement is true or false.
The sum of two irrational numbers is an irrational number.
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eee Use a real number to represent 85 meters below sea level. eee View Solution
eee Use a real number to represent a debit of $1900. eee View Solution
eee Write 0.165¯ as a quotient of two integers. eee View Solution
eee Write 0.48 as a quotient of two integers.
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eee Identify whether 368 is a rational or an irrational number.
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eee Mark point A so that AC = CB.
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eee Identify whether 224 is a rational or an irrational number. eee View Solution
eee Write 7.2 as a quotient of two integers.
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eee List the numbers in order from least to greatest 8, 6, 5, 26.
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eee 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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eee List the numbers in order from least to greatest 345, 3125, 314, 39100
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eee Write the repeating decimal 0.23424¯ as a ratio of two integers.
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eee Write the repeating decimal 0.794¯ as a quotient of two integers.
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eee True or false? If y < x, then y2 < x2.
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eee Determine whether the statement is true or false.
If y2 > c2, then y > c.
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eee True or False? If b > e, then bd > ed.
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eee Write a comparison statement using <, =, or > :
63 __ 63
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eee Write a comparison statement using <, =, or >.
47 __ 99
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eee Write 0.45¯ as a quotient of two integers. eee View Solution
eee Find the property illustrated by the relation.
|2.3q| + |7r| = |7r| + |2.3q|
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eee Name the property illustrated.
(5m + 2)(3 + 3m) = (5m + 2).(3) + (5m + 2).(3m).
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eee What is the value of r, if the equation w × p × x = x × r illustrates the commutative property of multiplication?
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eee Find the property illustrated by the relation:
|3.6p| + |9s| = |9s| + |3.6p| eee
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eee Find the property illustrated by the relation:
|5.8x| + |13z| = |13z| + |5.8x|
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eee Determine whether the following statement is true or false.
"If t2 = w2, then t = w." eee
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eee Find the property illustrated by the relation:
|2.5a| + |6a| = |6a| + |2.5a|
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eee Find the property illustrated by the relation:
|2.6a| + |10a| = |10a| + |2.6a| eee
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eee Determine whether the statement is true or false.
If a > x, then a + z > x + z, for any real number z. eee
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eee Find the property illustrated by the relation.
|5.6r| + |13r| = |13r| + |5.6r|
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eee Find the property illustrated by the relation.
|3.6s| + |6s| = |6s| + |3.6s|
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eee Determine whether the statement is true or false.
If c2 = a2, then c =a.
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eee Find the property illustrated by the relation:
|5.8b| + |14b| = |14b| + |5.8b|
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eee Find the property illustrated by the relation:
|3.5s| + |11s| = |11s| + |3.5s|
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eee Find the property illustrated by the relation:
|2.6b| + |4b| = |4b| + |2.6b| eee
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eee Find the property illustrated by the relation.
|4.5r| + |6r| = |6r| + |4.5r| eee
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eee Find the property illustrated by the relation:
|3.7s| + |8s| = |8s| + |3.7s| eee
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eee Find the property illustrated by the relation:
|3.6s| + |8s| = |8s| + |3.6s|
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eee Which property does (- 13) + [- (- 13)] = 0 illustrate? eee View Solution
eee Find the property illustrated by the relation: 7.2(xt) = (7.2x)t. eee View Solution