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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.
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Compare the relationships of these numbers: 0.045 is ______ to 0.054.
- A. less than
- B. greater than
- C. equal to
- D. not comparable
Correct Answer: A
Rationale: When comparing decimal numbers like 0.045 and 0.054, we look at their values. In this case, 0.045 is smaller than 0.054 because in decimal numbers, a larger number signifies a greater value. Therefore, the correct relationship between 0.045 and 0.054 is 'less than'. In this context, 'less than' accurately describes the relationship between the two numbers, with 0.045 being smaller than 0.054.
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.
Subtract: 12 1/8 - 9 1/2 =
- A. 2 5/8
- B. 2 1/8
- C. 3 3/8
- D. 3 5/8
Correct Answer: A
Rationale: To solve this problem, first convert the mixed numbers to improper fractions. 12 1/8 can be written as 97/8, and 9 1/2 can be written as 19/2. Ensure a common denominator (8) by rewriting 19/2 as 76/8. Now, subtract the fractions: 97/8 - 76/8 = 21/8 = 2 5/8. Therefore, the correct answer is 2 5/8.
An artist sells paintings at $5.50 each. She has 7 stands in town and pays $35 per stand. What was her profit if she sold an average of 11 paintings per stand?
- A. $245
- B. $178.50
- C. $175
- D. $423.50
Correct Answer: B
Rationale: To calculate the profit per stand, we first find the total revenue per stand by multiplying the number of paintings sold (11) by the price per painting ($5.50), which equals $60.50. Then, we subtract the stand cost ($35) from the total revenue to find the profit per stand: $60.50 - $35 = $25.50. Since the artist has 7 stands, the total profit is $25.50 * 7 = $178.50. Therefore, the correct answer is $178.50. The profit per stand is determined by subtracting the stand cost from the total revenue generated from selling paintings. Multiplying this profit per stand by the number of stands gives the total profit. In this scenario, the artist's profit from selling an average of 11 paintings per stand would amount to $178.50.
After spending $75.64 at one store and $22.43 at the next store, how much money does a shopper who started with $100.00 have left?
- A. $1.93
- B. $5.00
- C. $0.72
- D. $20.13
Correct Answer: A
Rationale: To determine the remaining amount of money the shopper has, subtract the total spent ($75.64 + $22.43) from the initial amount of $100.00: $100.00 - $75.64 - $22.43 = $1.93. Therefore, the correct answer is A, $1.93, which represents the money left after the shopper's purchases. This calculation ensures that the shopper's expenses are subtracted accurately from the starting amount, providing the correct remaining balance.