Use properties of rational numbers to simplify the expression. 2/5 + 7/15 + 1/5

Question

A.1/2
B. 2/3
C. 4/5
D. 1 1/15

Answer 1

To simplify the expression \( \frac{2}{5} + \frac{7}{15} + \frac{1}{5} \), we first need to find a common denominator for the fractions involved.

The denominators are 5 and 15. The least common multiple of 5 and 15 is 15.

Now, we can express each fraction with a denominator of 15:

1. Convert \( \frac{2}{5} \): \[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \]

2. The second fraction remains \( \frac{7}{15} \).

3. Convert \( \frac{1}{5} \): \[ \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \]

Now we can rewrite the expression: \[ \frac{6}{15} + \frac{7}{15} + \frac{3}{15} \] Now, we can add the fractions: \[ \frac{6 + 7 + 3}{15} = \frac{16}{15} \]

Next, we can convert \( \frac{16}{15} \) to a mixed number: \[ \frac{16}{15} = 1 \frac{1}{15} \]

Thus, the simplified result of the expression is:

D. \( 1 \frac{1}{15} \)