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