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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 Name the subset(s) of the real numbers to which '- 11' belongs.
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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 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 Divide: - 40 ÷ (8)
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DDD Name the property illustrated.
(2l + 9)(10 + 9l) =(2l + 9).(10) + (2l + 9).(9l)
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DDD Which of the following is an equivalent expression for (3 + 3) + 7?
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DDD Simplify: 3 | 10 - 18 | DDD View Solution
DDD Simplify: |- 9| + |- 13|
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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 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 Add - 33 and (- 58).
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DDD Which of the following expressions is equivalent to 10 + ((- 10) + 55)?
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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 Simplify: | 14 - 4 |10 + | 12 - 15 |10 - | 15 + 12 |8
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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 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: 9 | 18 - 29 | DDD View Solution
DDD Write a comparison statement using <, =, or > .
0 __ - 0.354 DDD
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DDD Simplify: | 13 - 4 |9 + | 11 - 14 |9 - | 14 + 11 |6
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DDD Determine whether the following true or false.
20 {real numbers}
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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 Simplify: |- 12| + |- 19|
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fff Determine whether the statement | x | - | y | ≤ | x - y | is true or false.
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fff Simplify : 6 | - 2 | + 11 | 9 | - | - 15 |
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fff Simplify: | 14 - 16 |4 + | - 4 + 11 |4 + | 7 - 15 |4
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fff What is the value of - 10 + (- 20)?
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fff The subtraction expression | - 84 | - | - 72 | can also be written as,
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fff What is the value of the expression? 76 + (- 98) + (- 85)
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fff Which property does "6 · 7 = 67 {real numbers}" illustrate?
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fff Find the value of | 2 - 4 |.
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fff Which of the following is the absolute value of | 2 + 6 |?
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fff What is the value of | - 3 | + | - 3 |? fff View Solution
fff - 5 × - 8(- 6) = ____.
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fff What is the value of |- 12 + (- 66)|? fff View Solution
fff What is the value of 44 - (- 9)? fff View Solution
fff Find the multiplicative inverse of (8 + 78).
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fff Find the opposite and the absolute value of - 34. fff View Solution
fff True or False?
4.595959............ {irrational numbers} fff
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fff Determine whether the following is true or false:
22.042 > 22.0042
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fff Find the property illustrated by the relation: 6.4(py) = (6.4p)y.
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fff Name the property illustrated by: (12c)(112c) = 1
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fff 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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fff Determine whether the following is true or false:
If a number is rational, then it is an integer.
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fff True or False?
0.464664410694... {irrational numbers}
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fff Use the symbol < or > or =, to show the relationship between - 7, - 64 fff View Solution
fff Name the property of the statement: - 11 + 11 = 0
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fff Name the subset(s) of the real numbers to which 511 belongs.
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fff Name the subset(s) of the real numbers to which 0.666666.... belongs.
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fff Name the subset(s) of the real numbers to which '- 27' belongs.
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fff Name the property illustrated.
0 + π = π. fff
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fff Name the subset(s) of the real numbers to which "π" belongs.
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fff Which of the following properties do not hold for the set of whole numbers? fff View Solution
fff Graph the number 312 fff View Solution
fff Give the coordinate that indicates the approximate location of point A. fff View Solution
fff Give the coordinate that indicates the approximate location of point A. fff View Solution
fff 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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fff 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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fff List the numbers in order from least to greatest - 0.015, - 0.0015, - 0.15, - 15.
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fff Find the property illustrated by the relation:
| 2.5w | + | 4t | = | 4t | + | 2.5w |
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fff Name the property of statement: 30 + 0 = 30
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fff Name the property of the statement: 14 · (10 · 6) = (14 · 10) · 6
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fff Name the property illustrated.
(2u + 7)(8 + 5u) =(2u + 7).(8) + (2u + 7).(5u)
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fff Determine whether the following statement is true. If g.d = i.d and d is non-zero, then g = i.
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fff Determine whether the associative property satisfied under the division operation.
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fff Determine whether the set of negative integers is closed under addition.
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fff Which one of the statements satisfies transitive property? fff View Solution
fff Determine whether the set of irrational numbers is closed under addition.
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fff Determine whether the following statement is true. If x = b - a then x + a = b; a, b are real numbers.
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fff Determine whether the set of irrational numbers is closed under multiplication. fff View Solution
fff Determine whether the following statement is true. If s, l, r are real numbers, then s (l - r) = sl - sr.
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fff Determine whether the set of whole numbers is closed under multiplication. fff View Solution
fff Determine which one of the sets does not satisfy closure property of addition.
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fff Find the sum in clock arithmetic: 9 + 8 (on a 12-hour clock.)
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fff Use the symbol < or > or =, to show the relationship between - 11, 11
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fff Find the sum in clock arithmetic: 6 + 3 (on a 12-hour clock.)
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fff Use the symbol < or > or =, to show the relationship between 63, 8 fff View Solution
fff Which of the expressions does not illustrate the identity property of addition?
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fff Write the numbers in increasing order: - 13, 1, - 94, - 2
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fff Which of the following equation represents identity property of multiplication?
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fff True or False?The difference of two whole numbers is a whole number.
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fff Write the numbers in increasing order: 0.5, 10, - 2.1, - 6 fff View Solution
fff What is the value of k, if the equation l × v × n = n × k illustrates the commutative property of multiplication?
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fff Determine whether the statement is true or false.
The product of two irrational numbers is an irrational number. fff
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fff Determine whether the statement is true for all real numbers a, b and c: (a - b) - c = a - (b - c)
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fff Which of the following expressions represents the commutative property of addition? fff View Solution
fff True or False?
The product of two irrational numbers is a rational number. fff
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fff 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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fff Which of the following is an equivalent expression for (2 + 3) + 6?
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fff Determine whether the statement is true or false.
The sum of two irrational numbers is an irrational number.
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fff Perform the given operation: 52 feet4 seconds × 608 seconds4 hours× 9 miles468 feet
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fff Use a real number to represent 85 meters below sea level. fff View Solution
fff 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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fff Which property is illustrated in the expression? 3.3 × (6.6 × 33.7) = (3.3 × 6.6) × 33.7
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fff What is commutative property of addition? fff View Solution
fff Which of the following expressions illustrates the commutative property of addition? fff View Solution
fff What is the number that should be added to a number so that the sum is the number itself?
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fff Which of the following expressions is equivalent to 12 + ((- 11) + 98)?
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fff Use a real number to represent a debit of $1900. fff View Solution
fff 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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fff Write 0.165¯ as a quotient of two integers. fff View Solution
fff Write 0.48 as a quotient of two integers.
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fff Identify whether 368 is a rational or an irrational number.
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fff Mark point A so that AC = CB.
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fff Identify whether 224 is a rational or an irrational number. fff View Solution
fff Write 7.2 as a quotient of two integers.
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fff List the numbers in order from least to greatest 8, 6, 5, 26.
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fff Find the property illustrated by the relation.
|2.3q| + |7r| = |7r| + |2.3q|
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fff List the numbers in order from least to greatest 345, 3125, 314, 39100
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fff Write a comparison statement using <, =, or > :
63 __ 63
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fff Write the repeating decimal 0.23424¯ as a ratio of two integers.
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fff Name the property illustrated.
(5m + 2)(3 + 3m) = (5m + 2).(3) + (5m + 2).(3m).
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fff Write the repeating decimal 0.794¯ as a quotient of two integers.
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fff Write a comparison statement using <, =, or >.
47 __ 99
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fff True or false? If y < x, then y2 < x2.
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fff Determine whether the statement is true or false.
If y2 > c2, then y > c.
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fff True or False? If b > e, then bd > ed.
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fff Determine whether the statement is true or false.
If a > x, then a + z > x + z, for any real number z. fff
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fff Write 0.45¯ as a quotient of two integers. fff View Solution
fff Determine whether the statement is true or false.
If c2 = a2, then c =a.
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fff Determine whether the following statement is true or false.
"If t2 = w2, then t = w." fff
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fff What is the value of r, if the equation w × p × x = x × r illustrates the commutative property of multiplication?
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fff Find the property illustrated by the relation:
|3.6p| + |9s| = |9s| + |3.6p| fff
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fff Find the property illustrated by the relation:
|5.8x| + |13z| = |13z| + |5.8x|
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fff Use a real number to represent a credit of $6000.
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fff Identify whether 10064 is a rational or an irrational number. fff View Solution
fff Find the property illustrated by the relation:
|2.5a| + |6a| = |6a| + |2.5a|
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fff Find the property illustrated by the relation:
|2.6a| + |10a| = |10a| + |2.6a| fff
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fff Find the property illustrated by the relation.
|5.6r| + |13r| = |13r| + |5.6r|
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fff Find the property illustrated by the relation.
|3.6s| + |6s| = |6s| + |3.6s|
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fff Find the property illustrated by the relation:
|5.8b| + |14b| = |14b| + |5.8b|
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fff Find the property illustrated by the relation:
|3.5s| + |11s| = |11s| + |3.5s|
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fff Find the property illustrated by the relation:
|2.6b| + |4b| = |4b| + |2.6b| fff
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fff Find the property illustrated by the relation.
|4.5r| + |6r| = |6r| + |4.5r| fff
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fff Find the property illustrated by the relation:
|3.7s| + |8s| = |8s| + |3.7s| fff
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fff Find the property illustrated by the relation:
|3.6s| + |8s| = |8s| + |3.6s|
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fff Which property does (- 13) + [- (- 13)] = 0 illustrate? fff View Solution
fff Find the property illustrated by the relation: 7.2(xt) = (7.2x)t. fff View Solution