Fractions Assessment worksheet with multiple-choice questions on equivalent fractions, comparisons, and ordering.

Fractions Assessment Solution and Explanation

#### Question 1: Use the diagram below to tell which fraction is equivalent to \( \frac{3}{4} \)?

The diagram shows:
- A rectangle divided into 8 equal parts, with 6 parts shaded.
- The fraction represented by the shaded part is \( \frac{6}{8} \).

We need to determine which fraction is equivalent to \( \frac{3}{4} \).

Step-by-Step Solution:
1. Simplify \( \frac{6}{8} \):
- Both the numerator (6) and the denominator (8) can be divided by their greatest common divisor (GCD), which is 2.
- \( \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \).

Thus, \( \frac{6}{8} \) is equivalent to \( \frac{3}{4} \).

Correct Answer:
\[ \boxed{C} \]

---

#### Question 2: Which of the following is NOT equivalent to \( \frac{3}{6} \)?

We need to identify which fraction is not equivalent to \( \frac{3}{6} \).

Step-by-Step Solution:
1. Simplify \( \frac{3}{6} \):
- Both the numerator (3) and the denominator (6) can be divided by their GCD, which is 3.
- \( \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \).
- Therefore, \( \frac{3}{6} = \frac{1}{2} \).

2. Check each option:
- A. \( \frac{1}{2} \): This is equivalent to \( \frac{3}{6} \).
- B. \( \frac{2}{4} \): Simplify \( \frac{2}{4} \):
- \( \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \).
- This is equivalent to \( \frac{3}{6} \).
- C. \( \frac{5}{8} \): This fraction cannot be simplified to \( \frac{1}{2} \). It is not equivalent to \( \frac{3}{6} \).
- D. \( \frac{5}{10} \): Simplify \( \frac{5}{10} \):
- \( \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \).
- This is equivalent to \( \frac{3}{6} \).

Correct Answer:
\[ \boxed{C} \]

---

#### Question 3: When comparing \( \frac{7}{9} \) and \( \frac{3}{4} \), which of the following shows the fractions written correctly and compared with common denominators?

We need to compare \( \frac{7}{9} \) and \( \frac{3}{4} \) using a common denominator.

Step-by-Step Solution:
1. Find the least common denominator (LCD) of 9 and 4:
- The LCD of 9 and 4 is 36.

2. Convert each fraction to have the denominator of 36:
- For \( \frac{7}{9} \):
- Multiply both the numerator and the denominator by 4: \( \frac{7 \times 4}{9 \times 4} = \frac{28}{36} \).
- For \( \frac{3}{4} \):
- Multiply both the numerator and the denominator by 9: \( \frac{3 \times 9}{4 \times 9} = \frac{27}{36} \).

3. Compare the fractions:
- \( \frac{28}{36} \) and \( \frac{27}{36} \).
- Since \( 28 > 27 \), \( \frac{28}{36} > \frac{27}{36} \).
- Therefore, \( \frac{7}{9} > \frac{3}{4} \).

Correct Answer:
\[ \boxed{A} \]

---

#### Question 4: Which of the following shows an accurate comparison?

We need to determine which comparison is correct.

Step-by-Step Solution:
1. Option A: \( \frac{1}{4} > \frac{1}{2} \):
- \( \frac{1}{4} \) is less than \( \frac{1}{2} \) because \( \frac{1}{4} = 0.25 \) and \( \frac{1}{2} = 0.5 \).
- This is incorrect.

2. Option B: \( \frac{5}{6} > \frac{2}{3} \):
- Convert \( \frac{2}{3} \) to have a denominator of 6: \( \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \).
- Compare \( \frac{5}{6} \) and \( \frac{4}{6} \):
- \( \frac{5}{6} > \frac{4}{6} \).
- This is correct.

3. Option C: \( \frac{3}{10} > \frac{7}{8} \):
- \( \frac{3}{10} = 0.3 \) and \( \frac{7}{8} = 0.875 \).
- \( \frac{3}{10} \) is less than \( \frac{7}{8} \).
- This is incorrect.

4. Option D: \( \frac{3}{8} > \frac{2}{3} \):
- Convert \( \frac{2}{3} \) to have a denominator of 24: \( \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \).
- Convert \( \frac{3}{8} \) to have a denominator of 24: \( \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \).
- Compare \( \frac{9}{24} \) and \( \frac{16}{24} \):
- \( \frac{9}{24} < \frac{16}{24} \).
- This is incorrect.

Correct Answer:
\[ \boxed{B} \]

---

#### Question 5: Which of the following sets of fractions is in order from least to greatest?

We need to determine which set of fractions is ordered correctly from least to greatest.

Step-by-Step Solution:
1. Option A: \( \frac{5}{6}, \frac{2}{3}, \frac{1}{4}, \frac{1}{2} \):
- Convert all fractions to decimals:
- \( \frac{5}{6} \approx 0.833 \)
- \( \frac{2}{3} \approx 0.667 \)
- \( \frac{1}{4} = 0.25 \)
- \( \frac{1}{2} = 0.5 \)
- Order: \( 0.25, 0.5, 0.667, 0.833 \).
- Correct order: \( \frac{1}{4}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6} \).
- This is incorrect.

2. Option B: \( \frac{2}{3}, \frac{1}{4}, \frac{1}{2}, \frac{5}{6} \):
- Using the same decimal values as above:
- Order: \( 0.667, 0.25, 0.5, 0.833 \).
- This is incorrect.

3. Option C: \( \frac{1}{2}, \frac{1}{4}, \frac{5}{6}, \frac{2}{3} \):
- Using the same decimal values as above:
- Order: \( 0.5, 0.25, 0.833, 0.667 \).
- This is incorrect.

4. Option D: \( \frac{1}{4}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6} \):
- Using the same decimal values as above:
- Order: \( 0.25, 0.5, 0.667, 0.833 \).
- This is correct.

Correct Answer:
\[ \boxed{D} \]

---

#### Question 6: Which of the following sets of fractions is in order from greatest to least?

We need to determine which set of fractions is ordered correctly from greatest to least.

Step-by-Step Solution:
1. Option A: \( \frac{5}{8}, \frac{5}{10}, \frac{9}{12}, \frac{2}{6} \):
- Convert all fractions to decimals:
- \( \frac{5}{8} = 0.625 \)
- \( \frac{5}{10} = 0.5 \)
- \( \frac{9}{12} = 0.75 \)
- \( \frac{2}{6} = \frac{1}{3} \approx 0.333 \)
- Order: \( 0.75, 0.625, 0.5, 0.333 \).
- Correct order: \( \frac{9}{12}, \frac{5}{8}, \frac{5}{10}, \frac{2}{6} \).
- This is incorrect.

2. Option B: \( \frac{5}{10}, \frac{2}{6}, \frac{5}{8}, \frac{9}{12} \):
- Using the same decimal values as above:
- Order: \( 0.5, 0.333, 0.625, 0.75 \).
- This is incorrect.

3. Option C: \( \frac{2}{6}, \frac{5}{8}, \frac{9}{12}, \frac{5}{10} \):
- Using the same decimal values as above:
- Order: \( 0.333, 0.625, 0.75, 0.5 \).
- This is incorrect.

4. Option D: \( \frac{2}{6}, \frac{5}{10}, \frac{9}{12}, \frac{5}{8} \):
- Using the same decimal values as above:
- Order: \( 0.333, 0.5, 0.75, 0.625 \).
- This is incorrect.

Correct Answer:
\[ \boxed{C} \]

---

Final Answers:

1. \( \boxed{C} \)
2. \( \boxed{C} \)
3. \( \boxed{A} \)
4. \( \boxed{B} \)
5. \( \boxed{D} \)
6. \( \boxed{C} \)