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Solved Examples
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fff Determine whether the set {0, 13, - 13} satisfies closure property with respective to multiplication. fff View Solution
fff Name the property illustrated by: (7x)(17x) = 1 fff View Solution
fff Simplify: | 4 | + | - 11 | + | 15 | + | - 7 |
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fff What is the value of |- 12 + (- 63)|? fff View Solution
fff Name the property of statement: 11 + 0 = 11
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fff Find the additive inverse of 5- 6.
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fff Find the multiplicative inverse of - 1312.
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fff Divide: - 180 ÷ (- 12) fff View Solution
fff Simplify: (| 5 | + | - 13 | - | 4 |) (5| 12 | - | - 13 |) (4| 7 - 12| - | 4 |) 3 fff View Solution
fff 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? fff View Solution
fff 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? fff View Solution
fff Name the subset(s) of the real numbers to which '- 11' belongs.
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fff Use the symbol < or > or =, to show the relationship between - 6, - 49 fff View Solution
fff Name the property of the statement: - 8 + 8 = 0
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fff 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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fff Find the property illustrated by the relation:
| 2.3l | + | 9k | = | 9k | + | 2.3l |
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fff Determine whether the following statement is true. If v, k, z are real numbers, then v (k - z) = vk - vz.
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fff Find the sum in clock arithmetic: 9 + 4 (on a 12-hour clock.)
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fff Find the sum in clock arithmetic: 2 + 1 (on a 12-hour clock.)
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fff Which of the following is an equivalent expression for (3 + 3) + 7?
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fff Which property is illustrated in the expression? 5.5 × (7.7 × 27.9) = (5.5 × 7.7) × 27.9
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fff Which of the following expressions is equivalent to 10 + ((- 10) + 55)?
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fff Name the property illustrated.
(2l + 9)(10 + 9l) =(2l + 9).(10) + (2l + 9).(9l)
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fff Simplify : 4 | - 2 | + 5 | 3 | - | - 7 |
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fff Simplify: | 7 - 9 |3 + | - 2 + 4 |4 + | 2 - 8 |3
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fff Determine whether the following statement is true. If a.h = b.h and h is non-zero, then a = b.
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fff What is the value of z, if the equation q × r × u = u × z illustrates the commutative property of multiplication?
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fff 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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fff Divide: - 40 ÷ (8)
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fff Simplify: 3 | 10 - 18 | fff View Solution
fff Simplify: |- 9| + |- 13|
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fff Add - 33 and (- 58).
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fff Find the multiplicative inverse of 3817.
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fff Find the additive inverse of 549.
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fff Simplify: | 14 - 4 |10 + | 12 - 15 |10 - | 15 + 12 |8
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fff Determine whether the statement | a + y | = | a | + | y | is true or false.
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fff Determine whether the statement | u | + | p | ≥ | u + p | is true or false.
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fff Which of the following is the absolute value of | 3 + 5 |?
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fff What is the value of | - 6 | + | - 5 |? fff View Solution
fff - 8 × - 8(- 7) = ____.
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fff Find the value of | 11 - 13 |.
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fff 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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fff What is the value of 45 - (- 7)? fff View Solution
fff What is the value of 45 - | - 6 |?
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fff What is the value of - 43 + (- 15)?
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fff The subtraction expression | - 92 | - | - 79 | can also be written as,
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fff What is the value of the expression? 91 + (- 58) + (- 95)
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fff Find the multiplicative inverse of (9 + 89).
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fff Name the property of the statement: 11 · (8 · 3) = (11 · 8) · 3
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fff 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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fff Perform the given operation: 5.82 yards($1617 yards) fff View Solution
fff The length of a wire is 1251 feet. Write the length of the wire in inches.
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fff Which property does "4 · 7 = 47 {real numbers}" illustrate?
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fff 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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fff Use the symbol < or > or =, to show the relationship between - 26, 26
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fff Use the symbol < or > or =, to show the relationship between 48, 7 fff View Solution
fff Perform the given operation: 136 feet4 seconds × 384 seconds3 hours× 9 miles1224 feet
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fff Write a comparison statement using <, =, or > .
0 __ - 0.438 fff
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fff Determine whether the following is true or false:
37.043 > 37.0043
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fff True or False?
0.25255227562... {irrational numbers}
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fff Name the subset(s) of the real numbers to which 72 belongs.
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fff Name the subset(s) of the real numbers to which 0.777777.... belongs.
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fff Write 0.201¯ as a quotient of two integers. fff View Solution
fff True or False?
7.373737............ {irrational numbers} fff
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fff Determine whether the following true or false.
12 {real numbers}
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fff List the numbers in order from least to greatest - 0.017, - 0.0017, - 0.17, - 17.
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fff Write 0.26 as a quotient of two integers.
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fff Write 2.4 as a quotient of two integers.
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fff List the numbers in order from least to greatest 6, 5, 4, 18.
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fff List the numbers in order from least to greatest 534, 5116, 513, 5748
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fff Write the repeating decimal 0.43629¯ as a ratio of two integers.
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fff Write the repeating decimal 0.707¯ as a quotient of two integers.
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fff True or false? If a < b, then a2 < b2.
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fff Determine whether the statement is true or false.
If b2 > y2, then b > y.
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fff True or False? If h > i, then hc > ic.
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fff Determine whether the statement is true or false.
If x > c, then x + z > c + z, for any real number z. fff
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fff Determine whether the statement is true or false.
If b2 = x2, then b =x.
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fff Use a real number to represent 90 meters below sea level. fff View Solution
fff Use a real number to represent a debit of $2900. fff View Solution
fff Identify whether 224 is a rational or an irrational number.
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fff Identify whether 258 is a rational or an irrational number. fff View Solution
fff The length of a wire is 1474 feet. Write the length of the wire in inches.
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fff The length of river Nile is 6670 kilo meters. Express its length in miles.
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fff 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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fff Determine if the set of natural numbers and the operation of multiplication form a field.
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fff Find the property illustrated by the relation: 10.6(pw) = (10.6p)w.
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fff Name the property illustrated by: (11x)(111x) = 1 fff View Solution
fff Which property does (- 8) + [- (- 8)] = 0 illustrate? fff View Solution
fff What number (on a 12-hour clock) in clock arithmetic serves as the additive identity?
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fff Simplify: | 9 | + | - 35 | + | 44 | + | - 32 |
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fff What is the value of 16 - | - 9 |?
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fff Graph the real numbers - 2.1, 2 and 73
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fff Perform the given operation: 4.99 yards($333 yards) fff View Solution
fff Determine whether the product of an irrational number and a positive integer other than '0' will be an irrational number.
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fff Simplify: 9 | 18 - 29 | fff View Solution
fff Simplify: |- 12| + |- 19|
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fff Simplify : 6 | - 2 | + 11 | 9 | - | - 15 |
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B   Simplify: | 14 - 16 |4 + | - 4 + 11 |4 + | 7 - 15 |4
   B
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B   Add - 20 and (- 48).
   B
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B   Divide: - 6 ÷ (2)
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B   Find the multiplicative inverse of 345.
   B
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B   Find the additive inverse of 6511.
   B
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B   Simplify: | 13 - 4 |9 + | 11 - 14 |9 - | 14 + 11 |6
   B
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B   Write a comparison statement using <, =, or > .
0 __ - 0.354   B
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B   Determine whether the statement | z + a | = | z | + | a | is true or false.
   B
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B   Determine whether the statement | k | + | w | ≥ | k + w | is true or false.
   B
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B   Determine whether the following true or false.
20 {real numbers}
   B
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B   Determine whether the statement | x | - | y | ≤ | x - y | is true or false.
   B
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B   Which property does "6 · 7 = 67 {real numbers}" illustrate?
   B
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B   What is the value of - 10 + (- 20)?
   B
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B   The subtraction expression | - 84 | - | - 72 | can also be written as,
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B   What is the value of the expression? 76 + (- 98) + (- 85)
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B   Find the value of | 2 - 4 |.
   B
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B   Which of the following is the absolute value of | 2 + 6 |?
   B
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B   True or False?
4.595959............ {irrational numbers}   B
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B   Determine whether the following is true or false:
22.042 > 22.0042
   B
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B   Determine whether the following is true or false:
If a number is rational, then it is an integer.
   B
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B   True or False?
0.464664410694... {irrational numbers}
   B
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B   Name the subset(s) of the real numbers to which 511 belongs.
   B
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B   Name the subset(s) of the real numbers to which 0.666666.... belongs.
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B   Name the subset(s) of the real numbers to which '- 27' belongs.
   B
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B   Name the subset(s) of the real numbers to which "π" belongs.
   B
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B   Graph the number 312   B View Solution
B   Give the coordinate that indicates the approximate location of point A.   B View Solution
B   Give the coordinate that indicates the approximate location of point A.   B View Solution
B   List the numbers in order from least to greatest - 0.015, - 0.0015, - 0.15, - 15.
   B
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B   True or False?The difference of two whole numbers is a whole number.
   B
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B   Determine whether the statement is true or false.
The product of two irrational numbers is an irrational number.   B
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B   True or False?
The product of two irrational numbers is a rational number.   B
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B   Determine whether the statement is true or false.
The sum of two irrational numbers is an irrational number.
   B
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B   Use a real number to represent 85 meters below sea level.   B View Solution
B   Use a real number to represent a debit of $1900.   B View Solution
B   Write 0.165¯ as a quotient of two integers.   B View Solution
B   Write 0.48 as a quotient of two integers.
   B
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B   Identify whether 368 is a rational or an irrational number.
   B
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B   Mark point A so that AC = CB.
   B
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B   Identify whether 224 is a rational or an irrational number.   B View Solution
B   Write 7.2 as a quotient of two integers.
   B
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B   List the numbers in order from least to greatest 8, 6, 5, 26.
   B
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B   List the numbers in order from least to greatest 345, 3125, 314, 39100
   B
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B   Find the property illustrated by the relation: 6.4(py) = (6.4p)y.
   B
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B   Name the property illustrated by: (12c)(112c) = 1
   B
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B   Write the repeating decimal 0.23424¯ as a ratio of two integers.
   B
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B   Write the repeating decimal 0.794¯ as a quotient of two integers.
   B
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B   True or false? If y < x, then y2 < x2.
   B
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B   Determine whether the statement is true or false.
If y2 > c2, then y > c.
   B
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B   True or False? If b > e, then bd > ed.
   B
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B   Determine whether the statement is true or false.
If a > x, then a + z > x + z, for any real number z.   B
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B   Determine whether the statement is true or false.
If c2 = a2, then c =a.
   B
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B   Name the property illustrated.
0 + π = π.   B
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B   Which of the following properties do not hold for the set of whole numbers?   B View Solution
B   Determine whether the following is true. If b, z, a are real numbers, and if b = z then b + a = z + a.
   B
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B   Find the property illustrated by the relation:
| 2.5w | + | 4t | = | 4t | + | 2.5w |
   B
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B   Name the property illustrated.
(2u + 7)(8 + 5u) =(2u + 7).(8) + (2u + 7).(5u)
   B
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B   Determine whether the following statement is true. If g.d = i.d and d is non-zero, then g = i.
   B
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B   Which one of the statements satisfies transitive property?   B View Solution
B   Determine whether the following statement is true. If x = b - a then x + a = b; a, b are real numbers.
   B
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B   Determine whether the following statement is true. If s, l, r are real numbers, then s (l - r) = sl - sr.
   B
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B   Determine which one of the sets does not satisfy closure property of addition.
   B
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B   Find the sum in clock arithmetic: 9 + 8 (on a 12-hour clock.)
   B
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B   Find the sum in clock arithmetic: 6 + 3 (on a 12-hour clock.)
   B
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B   Which of the expressions does not illustrate the identity property of addition?
   B
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B   Which of the following equation represents identity property of multiplication?
   B
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B   What is the value of k, if the equation l × v × n = n × k illustrates the commutative property of multiplication?
   B
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B   Which of the following expressions represents the commutative property of addition?   B View Solution
B   Which of the following is an equivalent expression for (2 + 3) + 6?
   B
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B   Which property is illustrated in the expression? 3.3 × (6.6 × 33.7) = (3.3 × 6.6) × 33.7
   B
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B   What is commutative property of addition?   B View Solution
B   Which of the following expressions illustrates the commutative property of addition?   B View Solution
B   What is the number that should be added to a number so that the sum is the number itself?
   B
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B   What is the value of | - 3 | + | - 3 |?   B View Solution
B   - 5 × - 8(- 6) = ____.
   B
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B   What is the value of |- 12 + (- 66)|?   B View Solution
B   What is the value of 44 - (- 9)?   B View Solution
B   Which of the following expressions is equivalent to 12 + ((- 11) + 98)?
   B
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B   Find the multiplicative inverse of (8 + 78).
   B
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B   Find the opposite and the absolute value of - 34.   B View Solution
B   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.
   B
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B   If a scooter travels 64 km on 2 liters of petrol, how many kilometers will it travel on 4 liters of petrol?
   B
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B   Use the symbol < or > or =, to show the relationship between - 7, - 64   B View Solution
B   Name the property of the statement: - 11 + 11 = 0
   B
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B   The following are the temperatures at various places: - 41° F, - 35° F, - 48° F, order the temperatures from highest to lowest.
   B
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B   Name the property of statement: 30 + 0 = 30
   B
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B   Name the property of the statement: 14 · (10 · 6) = (14 · 10) · 6
   B
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B   Determine whether the associative property satisfied under the division operation.
   B
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B   Determine whether the set of negative integers is closed under addition.
   B
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B   Write a comparison statement using <, =, or > :
63 __ 63
   B
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B   Determine whether the set of irrational numbers is closed under addition.
   B
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B   Write a comparison statement using <, =, or >.
47 __ 99
   B
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B   Write 0.45¯ as a quotient of two integers.   B View Solution
B   Find the property illustrated by the relation.
|2.3q| + |7r| = |7r| + |2.3q|
   B
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B   Name the property illustrated.
(5m + 2)(3 + 3m) = (5m + 2).(3) + (5m + 2).(3m).
   B
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B   What is the value of r, if the equation w × p × x = x × r illustrates the commutative property of multiplication?
   B
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B   Find the property illustrated by the relation:
|3.6p| + |9s| = |9s| + |3.6p|   B
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B   Find the property illustrated by the relation:
|5.8x| + |13z| = |13z| + |5.8x|
   B
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B   Determine whether the following statement is true or false.
"If t2 = w2, then t = w."   B
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B   Find the property illustrated by the relation:
|2.5a| + |6a| = |6a| + |2.5a|
   B
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B   Find the property illustrated by the relation:
|2.6a| + |10a| = |10a| + |2.6a|   B
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B   Find the property illustrated by the relation.
|5.6r| + |13r| = |13r| + |5.6r|
   B
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B   Find the property illustrated by the relation.
|3.6s| + |6s| = |6s| + |3.6s|
   B
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B   Find the property illustrated by the relation:
|5.8b| + |14b| = |14b| + |5.8b|
   B
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B   Find the property illustrated by the relation:
|3.5s| + |11s| = |11s| + |3.5s|
   B
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B   Find the property illustrated by the relation:
|2.6b| + |4b| = |4b| + |2.6b|   B
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B   Find the property illustrated by the relation.
|4.5r| + |6r| = |6r| + |4.5r|   B
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B   Find the property illustrated by the relation:
|3.7s| + |8s| = |8s| + |3.7s|   B
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B   Find the property illustrated by the relation:
|3.6s| + |8s| = |8s| + |3.6s|
   B
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B   Use a real number to represent a credit of $6000.
   B
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B   Identify whether 10064 is a rational or an irrational number.   B View Solution
B   Determine whether the set of irrational numbers is closed under multiplication.   B View Solution
B   Determine whether the set of whole numbers is closed under multiplication.   B View Solution
B   Use the symbol < or > or =, to show the relationship between - 11, 11
   B
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B   Use the symbol < or > or =, to show the relationship between 63, 8   B View Solution
B   Write the numbers in increasing order: - 13, 1, - 94, - 2
   B
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B   Write the numbers in increasing order: 0.5, 10, - 2.1, - 6   B View Solution
B   Determine whether the statement is true for all real numbers a, b and c: (a - b) - c = a - (b - c)
   B
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B   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
   B
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B   Perform the given operation: 52 feet4 seconds × 608 seconds4 hours× 9 miles468 feet
   B
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B   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.
   B
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B   Which property does (- 13) + [- (- 13)] = 0 illustrate?   B View Solution
B   Find the property illustrated by the relation: 7.2(xt) = (7.2x)t.   B View Solution