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