Question

Express the fractions 3/4, 7/16, and 5/8 with the LCD.
Question 3 options:

A)

12/16, 7/16, 10/16

B)

9/16, 49/16, 36/16

C)

3/4, 2/4, 3/4

D)

24/32, 14/32, 24/32

Answer 1

To find the least common denominator (LCD) for the fractions 3/4, 7/16, and 5/8, we first need to find the denominators: 4, 16, and 8.

- The least common multiple of 4, 16, and 8 is 16 because:
- 4 can be expressed as 16/4 = 4.
- 16 remains as 16/16 = 1.
- 5/8 can be converted to a denominator of 16 by multiplying the numerator and the denominator by 2: (5 × 2)/(8 × 2) = 10/16.

Now, we can express all fractions with a denominator of 16:

1. For \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}
\]

2. For \( \frac{7}{16} \):
\[
\frac{7}{16} \text{ is already in terms of 16.}
\]

3. For \( \frac{5}{8} \):
\[
\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16}
\]

Thus, the fractions expressed with a denominator of 16 are:

- \( \frac{3}{4} = \frac{12}{16} \)
- \( \frac{7}{16} = \frac{7}{16} \)
- \( \frac{5}{8} = \frac{10}{16} \)

Therefore, the answer is:

**A) 12/16, 7/16, 10/16**