At the beginning of the day, Xavier has 20 apples. At lunch, he meets his sister Emma and gives her half of his apples. After lunch, he stops by his neighbor Jim's house and gives him 6 of his apples. He then uses 3/4 of his remaining apples to make an apple pie for dessert at dinner. At the end of the day, how many apples does Xavier have left?

Correct Answer: D

Rationale: Xavier gives away half of his 20 apples (10), then gives 6 more apples, leaving him with 4 apples. He uses 3/4 of the remaining 4 apples (3) for the pie, leaving him with 1 apple at the end of the day. Therefore, the correct answer is 1. Choices A, B, and C are incorrect because they do not accurately reflect the calculations of apples given away and used for the pie, resulting in the remaining amount of 1 apple.

Correct Answer: D

Rationale: To find the sum of fractions, they need to have a common denominator. In this case, the common denominator is 8. So, 3/4 = 6/8. Adding 6/8 and 5/8 gives 11/8, which simplifies to 1 3/8. Therefore, the correct answer is 1 3/8, which corresponds to choice A. Choices B, C, and D are incorrect as they do not represent the correct sum of 3/4 and 5/8.

Correct Answer: C

Rationale: To add 7/8 and 5/8, we combine the numerators while keeping the denominator the same: 7/8 + 5/8 = (7+5)/8 = 12/8. To simplify this fraction, we divide both the numerator and the denominator by their greatest common factor, which is 4. This yields 12/8 = 3/2. Therefore, the reduced form of 7/8 + 5/8 is 3/2, which is also equivalent to 1.5 as a mixed number. However, the question specifically asks for the answer in reduced form, making choice C, 3/2 or 31/36 after further simplification, the correct answer. Choices A, B, and D are incorrect because they do not represent the correct result of adding 7/8 and 5/8 in reduced form.

Correct Answer: A

Rationale: In the given problem, we are asked to divide 52 by 27 and 51 by 27. To divide 52 by 27, we perform the division and get 1 with a remainder of 25. So, 52 divided by 27 is 1 and 25/27. This can also be expressed as 1.925 or 1 25/27 in mixed number form. To divide 51 by 27, we perform the division and get 1 with a remainder of 24. So, 51 divided by 27 is 1 and 24/27. This can also be expressed as 1.888 or 1 24/27 in mixed number form. The correct answer is A) 52/27 because it represents the accurate result of dividing 52 by 27. Option B) 51/27 is incorrect as it represents the result of dividing 51 by 27, not 52 by 27. Options C) and D) are also incorrect as they are not the results of the division operations specified in the question. In an educational context, understanding division helps in solving real-life problems involving sharing, grouping, or finding equal parts. Being able to interpret and simplify division expressions accurately is crucial for mathematical proficiency. This question enhances students' division skills and reinforces the concept of dividing numbers to obtain quotients and remainders.

Correct Answer: A

Rationale: To express 18/5 as a reduced mixed number, we need to perform long division. 18 divided by 5 equals 3 with a remainder of 3. This means that our mixed number will be 3 whole units and 3/5 of another unit. Hence, the correct answer is A) 3 3/5. Option B) 3 1/15, is incorrect because 18 cannot be evenly divided by 15 without a remainder. Option C) 3 1/18 is incorrect because 18 is the numerator, not the denominator, in the original fraction. Option D) 3 1/54 is incorrect because 54 is not a factor of 18. In an educational context, understanding how to convert improper fractions to mixed numbers is essential for working with fractions in real-life situations, such as measurements or recipes. It helps students grasp the concept of wholes and parts and builds a foundation for more advanced fraction operations. Practicing these skills through questions like this one helps reinforce the concept and improves overall math proficiency.