By LearningExpress Editors

Updated on Jul 15, 2011

More practice problems can be found at:

- Miscellaneous Math Practice Problems Set 1
- Miscellaneous Math Practice Problems Set 2
- Miscellaneous Math Practice Problems Set 3
- Miscellaneous Math Practice Problems Set 4
*You are here* - Miscellaneous Math Practice Problems Set 5
- Miscellaneous Math Practice Problems Set 6
- Miscellaneous Math Practice Problems Set 7
- Miscellaneous Math Practice Problems Set 8
- Miscellaneous Math Practice Problems Set 9
- Miscellaneous Math Practice Problems Set 10

### Problems

- What is the estimated product when 157 and 817 are rounded to the nearest hundred and multiplied?
- 160,000
- 180,000
- 16,000
- 80,000

- (–19) + 6 =
- –25
- –13
- 0
- 13

- –4 × (–9) =
- 13
- –13
- 36
- –36

- –6 + (–6) =
- –12
- 12
- 36
- –36

- 7 + (–15) =
- 22
- –22
- –8
- 8

- 75 + (–75) =
- 0
- 150
- –75
- 1

- Which of the following choices is equivalent to 6 × 6 × 6?
- 3 × 6
- 12 × 6
- 6
^{3} - 3
^{6}

- Which of the following choices is equivalent to 2
^{5}?- 7
- 10
- 16
- 32

- Which of the following represents a composite number?
- 11
- 29
- 41
- 91

- 19
^{2}=- 38
- 76
- 152
- 361

- 10
^{5}÷ 10^{2}=- 1
^{3} - 10
^{3} - 10
^{7} - 10
^{10}

- 1
- –4
^{2}=- –8
- 8
- –16
- 16

- –5
^{3}=- –15
- 15
- 125
- –125

- –11
^{2}=- 121
- –121
- –22
- 22

- What is the square root of 64?
- 8
- 32
- 128
- 4,096

- Which of these equations is incorrect?
- Neither is incorrect.
- Both are incorrect.

### Answers

**a.**The number 157 is rounded to 200, and 817 is rounded to 800; 200 × 800 = 160,000.**b.**When*adding*negative numbers, follow this rule: If both numbers have**different signs**, subtract the smaller from the larger. The sum takes the sign of the larger number. In this equation the correct answer is –13.**c.**When multiplying integers, begin by multiplying the numbers: 4 × 9 = 36. If there is an*odd*number of negative signs, the answer is negative. If there is an*even*number of negative signs, the answer is positive. In this equation, there are two negative signs; therefore, the correct answer is 36.**a.**When adding negative numbers, simply add the numbers and carry the negative sign into the answer. The correct answer to this equation is –12.**c.**When adding a negative number to a positive number, subtract the smaller from the larger and carry the sign of the larger number into the answer. The correct answer to this equation is –8.**a.**When adding two numbers that are the same, but have opposite signs, you will always get zero as your answer.**c.**The meaning of 6^{3}is 6 to the power of 3, or 6 used as a factor 3 times: 6 × 6 × 6 = 6^{3}.**d.**In this problem, 2 is the base and 5 is the exponent.*Two raised to the power of 5*means to use 2 as a factor five times: 2 × 2 × 2 × 2 × 2 = 32.**d.**A composite number is a whole number greater than 1 that has other factors besides 1 and itself; in other words, it is not prime. Each of the answer choices are prime numbers except 91, which has factors of 1, 7, 13, and 91.**d.**When squaring a number, simply multiply it by itself: 19 × 19 = 361.**b.**To solve this division problem, subtract the exponents only: 5 –2 = 3, so the answer is 10^{3}.**c.**–4^{2}means the opposite of the result of 4 raised to the second power. Think of it as –1 × 4^{2}. As in the order of operations, evaluate the exponent first, and then multiply: –1 × 16 = –16.**d.**–5^{3}means the opposite of the result of 5 raised to the third power. Think of it as –1 × 5^{3}. As in the order of operations, evaluate the exponent first, and then multiply: –1 × (5 × 5 × 5) = –1 × 125 = –125.**a.**Since there are parentheses, the base in this question is –11; (–11)^{2}means –11 × –11, which is equal to 121. Because there is an even number of negatives, the answer is positive.**a.**To find the square root of a number, ask the question, "What number times itself equals 64?" The answer is 8.**a.**Square roots can be multiplied and divided, but they cannot be added or subtracted.

More practice problems can be found at:

- Miscellaneous Math Practice Problems Set 1
- Miscellaneous Math Practice Problems Set 2
- Miscellaneous Math Practice Problems Set 3
- Miscellaneous Math Practice Problems Set 5
- Miscellaneous Math Practice Problems Set 6
- Miscellaneous Math Practice Problems Set 7
- Miscellaneous Math Practice Problems Set 8
- Miscellaneous Math Practice Problems Set 9
- Miscellaneous Math Practice Problems Set 10

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