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