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