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What is the result of adding 23.5 + 7.025?
- A. 30.525
- B. 30.5
- C. 30.025
- D. 16.475
Correct Answer: A
Rationale: To find the sum of 23.5 and 7.025, align the decimals and add the numbers: 23.5 + 7.025 = 30.525. The correct answer is choice A, which is 30.525. When adding decimal numbers, it's essential to align the decimal points properly and perform the addition as usual. Careful attention to decimal arithmetic ensures accuracy in the final result, making choice A the correct answer.
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What is the result of dividing 5 & 3/4 by 1/2, reduced to the simplest form?
- A. 5 & 1/2
- B. 2 & 3/8
- C. 11 & 1/2
- D. 18
Correct Answer: C
Rationale: To divide a mixed number by a fraction, you first convert the mixed number to an improper fraction. 5 & 3/4 as an improper fraction is 23/4. Dividing 23/4 by 1/2 is equivalent to multiplying 23/4 by 2/1, resulting in 46/4. When simplified back to a mixed number, 46/4 is 11 & 1/2.
What is the sum of 23.5 + 7.025?
- A. 30.525
- B. 30.5
- C. 30.025
- D. 16.475
Correct Answer: A
Rationale: To find the sum of 23.5 and 7.025, align the decimal points and add the numbers as if they were whole numbers. 23.5 + 7.025 equals 30.525. Therefore, the correct answer is A, which is 30.525. When adding decimal numbers, it is essential to maintain the alignment of decimal points and add the numbers accordingly. In this case, adding 23.5 and 7.025 results in 30.525, with the decimal point staying in the same position as the numbers being added.
Which number system is commonly used in the United States?
- A. Tertiary
- B. Decimal
- C. Napoleonic
- D. Binary
Correct Answer: B
Rationale: The correct answer is B: Decimal. The decimal number system, based on powers of 10, is the most commonly used number system in the United States and many other parts of the world. It employs 10 digits (0-9) and is used for everyday calculations, commerce, and representation of numbers in various contexts. The use of the decimal system simplifies arithmetic operations and aligns with the way people count using their ten fingers, making it intuitive and widely adopted.
Subtract 3/5 - 2/7 =
- A. 1/2
- B. 3/35
- C. -1/2
- D. 11/35
Correct Answer: D
Rationale: To subtract fractions, you need a common denominator. In this case, the common denominator of 5 and 7 is 35. Rewrite the fractions with the common denominator: 3/5 = 21/35 and 2/7 = 10/35. Subtract: 21/35 - 10/35 = 11/35. Therefore, the correct answer is D, 11/35. Remember, when subtracting fractions, always ensure to find a common denominator to perform the operation accurately.
Evaluate ab^2-ac if a=c, b=-4, and c=-5
- A. 56
- B. 105
- C. -23
- D. -5
Correct Answer: B
Rationale: To evaluate the expression "ab^2 - ac", substitute the values into the expression. Thus, "ab^2 - ac" becomes "(-5)(-4)^2 - (-5)(-5)", which simplifies to "(-5)(16) - 25 = -80 - 25 = -105". Therefore, the evaluated expression is -105.