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