3/4 as sum of unit fractions?
- A. 1/8 + 1/8 + 1/8 + 1/4 + 1/4
- B. 2/8 + 1/4 + 4/16
- C. 5/8 + 2/16
- D. 1/2 + 1/4
Correct Answer & Rationale
Correct Answer: D
To express \( \frac{3}{4} \) as a sum of unit fractions, each option must be evaluated for its total. Option A totals \( \frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \), which exceeds \( \frac{3}{4} \). Option B simplifies to \( \frac{2}{8} + \frac{2}{8} + \frac{1}{4} = \frac{2}{8} + \frac{2}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \), but includes non-unit fractions. Option C simplifies to \( \frac{5}{8} + \frac{1}{4} = \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \), again exceeding \( \frac{3}{4} \). Option D correctly adds \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \) using unit fractions only.
To express \( \frac{3}{4} \) as a sum of unit fractions, each option must be evaluated for its total. Option A totals \( \frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \), which exceeds \( \frac{3}{4} \). Option B simplifies to \( \frac{2}{8} + \frac{2}{8} + \frac{1}{4} = \frac{2}{8} + \frac{2}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4} \), but includes non-unit fractions. Option C simplifies to \( \frac{5}{8} + \frac{1}{4} = \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \), again exceeding \( \frac{3}{4} \). Option D correctly adds \( \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \) using unit fractions only.
Other Related Questions
Yellow binders?
- A. 20
- B. 40
- C. 200
- D. 400
Correct Answer & Rationale
Correct Answer: D
The option D, 400, represents the total number of yellow binders available, reflecting a larger quantity that may be required for extensive documentation or organizational needs. Option A, 20, is too low for most standard uses, suggesting insufficient resources. Option B, 40, while more adequate than A, still may not meet the demands of larger projects or groups. Option C, 200, although a significant number, does not fulfill the potential requirement for comprehensive organization, especially in larger settings. Thus, option D ensures ample supply for diverse needs.
The option D, 400, represents the total number of yellow binders available, reflecting a larger quantity that may be required for extensive documentation or organizational needs. Option A, 20, is too low for most standard uses, suggesting insufficient resources. Option B, 40, while more adequate than A, still may not meet the demands of larger projects or groups. Option C, 200, although a significant number, does not fulfill the potential requirement for comprehensive organization, especially in larger settings. Thus, option D ensures ample supply for diverse needs.
p=5n, questions n, points p. True?
- A. Points dependent
- B. Questions dependent
- C. 5 points dependent
- D. 1/5 question dependent
Correct Answer & Rationale
Correct Answer: A
In the equation \( p = 5n \), points \( p \) are directly calculated based on the number of questions \( n \). This indicates that points are dependent on the number of questions asked, making option A accurate. Option B incorrectly suggests that questions are dependent on points, which is the reverse of the relationship defined. Option C is misleading as it implies a fixed point value per question without considering the variable nature of \( n \). Option D suggests an inverse relationship, indicating fewer questions yield more points, which contradicts the original equation. Thus, option A accurately reflects the dependency of points on the number of questions.
In the equation \( p = 5n \), points \( p \) are directly calculated based on the number of questions \( n \). This indicates that points are dependent on the number of questions asked, making option A accurate. Option B incorrectly suggests that questions are dependent on points, which is the reverse of the relationship defined. Option C is misleading as it implies a fixed point value per question without considering the variable nature of \( n \). Option D suggests an inverse relationship, indicating fewer questions yield more points, which contradicts the original equation. Thus, option A accurately reflects the dependency of points on the number of questions.
Shaded region shows?
- A. 3/4 x 1/2
- B. 3/4 x 3/4
- C. 3/4 x 3/2
- D. 3/4 x 3
Correct Answer & Rationale
Correct Answer: A
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
Order 0.68, 1/12, 1(1/5), 3/5 least to greatest?
- A. 1(1/5), 0.68, 3/5, 1/12
- B. 1/12, 3/5, 0.68, 1(1/5)
- C. 1/12, 0.68, 3/5, 1(1/5)
- D. 0.68, 1/12, 3/5, 1(1/5)
Correct Answer & Rationale
Correct Answer: B
To compare the values, first convert them to a common format. - 1(1/5) equals 1.2. - 0.68 remains as is. - 3/5 converts to 0.6. - 1/12 is approximately 0.0833. Ordering these from least to greatest gives: 1/12 (0.0833), 3/5 (0.6), 0.68, and 1(1/5) (1.2). Option A incorrectly places 1(1/5) first, while C misplaces 3/5 and 0.68. Option D also misorders the values by placing 0.68 before 1/12. Thus, B accurately reflects the correct sequence of values.
To compare the values, first convert them to a common format. - 1(1/5) equals 1.2. - 0.68 remains as is. - 3/5 converts to 0.6. - 1/12 is approximately 0.0833. Ordering these from least to greatest gives: 1/12 (0.0833), 3/5 (0.6), 0.68, and 1(1/5) (1.2). Option A incorrectly places 1(1/5) first, while C misplaces 3/5 and 0.68. Option D also misorders the values by placing 0.68 before 1/12. Thus, B accurately reflects the correct sequence of values.