By LearningExpress Editors
Updated on Mar 23, 2011
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 d. For the order of operations, addition and subtraction are done left to right. First subtract 5 from 10, and then add 2 to get a result of 7.
 c. Division is done before subtraction for the order of operations. First, divide 40 by 4, and then subtract this number from 32.
 c. Using the order of operations, solve inside the parentheses first: 7 + (56) × (7). Now, multiply: 7 + 392. The answer is 399, but the question asks you to estimate the answer to the nearest 10. 399 is between 390 and 400, but it is closer to 400.
 e. All of the choices show examples of factors that produce 60, but choice e is the only factorization showing all prime numbers.
 e. 10 × 2 = 20, and 10 × 3 = 30, so the greatest common factor is 10. Also, using prime factorization, 20 = 2 × 2 × 5, and 30 = 2 × 3 × 5. Two and 5 are prime factors of both 20 and 30, so the greatest common factor is 2 × 5, which is 10.
 d. List the multiples of 40 and 50 until one is found in common. Multiples of 50 are 50, 100, 150, 200, 250,… , and multiples of 40 are 40, 80, 120, 160, 200, 240,… A common multiple is found, namely 200.
 b. The distributive property states that multiplication distributes over addition or subtraction. An illustration of this is choice b.
 a. The absolute value symbol serves as a grouping symbol, and grouping symbols are evaluated first. –5 × 3 = 15 (the absolute value is always positive). Now divide 5 into 100 to get 20. Finally, add 20 + 15 = 35.
 b. Choice b shows an example of the associative property, which states that when all operations in an expression are addition (or multiplication), you can change the grouping symbols to get the same result.
 c. The commutative property states that when all operations are multiplication (or addition) you can change the order of the operands to get the same result.
 d. To solve this problem, you do not need to solve each expression. Rather, remember the rules for adding or multiplying odd and even numbers. Only odd plus odd (7 + 5) results in an even number.
 e. 3 × –7 = –21, because a positive times a negative always equals a negative. However, the absolute value of –21 is 21.
 d. Multiplication is done before addition in the order of operations. First multiply 15 by 3 and then add 25 to get the result of 45 + 25 = 70.
 c. For the order of operations, you must perform division first. This subresult is 5. 5 subtracted from 8 results in positive 3.
 b. Expressions within parentheses are evaluated first. 6 + 19 = 25. Now perform multiplication, and 5 × 25 = 125.
 a. First, evaluate parentheses to get 8 + 4 = 12. Now division is performed before addition: 144 ÷ 12 = 12. The final step is to add 12 + 12 = 24.
 c. Multiplication and division are done left to right, so first evaluate 120 divided by 5, which is 24. To evaluate multiplication, remember that a positive times a negative is a negative result, and 24 times –2 is –48.
 c. All of the choices show examples of factors that produce 90, but choice c is the only factorization showing all prime numbers.
 b. The distributive property states that multiplication distributes over addition or subtraction. An illustration of this is choice b.
 e. First find the prime factorization of both 48 and 120, and then look for all common prime factors. 48 = 2 × 2 × 2 × 2 × 3 and 120 = 2 × 2 × 2 × 3 × 5. The common prime factors are 2 × 2 × 2 × 3 = 24. The greatest common factor is 24.
 d. With these numbers, it is easy to just list the multiples of 20 and 30 to find the first one in common. Multiples of 20 are 20, 40, 60, 80,… and multiples of 30 are 30, 60, 90,… The least common multiple is 60.
 d. Addition and subtraction are done left to right. Subtraction must be evaluated first. 35 – 5 = 30. 30 + 7 = 37. Now find the nearest ten: 37 is between 30 and 40, but closer to 40.
 e. Remember odd + even always results in an odd number.
 c. First, do the operations within the absolute symbols: 9 – 4 = 5. 5 times what number equals –25? 5 × –5 = –25.
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