An illustration shows 2 rectangles. The first rectangle is divided vertically into 6 equal parts, and 1 part is shaded. The second rectangle is divided vertically into 5 equal parts, and 4 parts are shaded.

Question

Add the fractions from the picture provided.

(1 point)

Answer 1

To add the fractions from the description of the rectangles:

1. The first rectangle is divided into 6 equal parts, with 1 part shaded. This can be represented as the fraction \( \frac{1}{6} \).

2. The second rectangle is divided into 5 equal parts, with 4 parts shaded. This can be represented as the fraction \( \frac{4}{5} \).

To add these fractions, we need a common denominator. The least common multiple (LCM) of 6 and 5 is 30.

Now, we can convert each fraction:

• For \( \frac{1}{6} \): \[ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \]

• For \( \frac{4}{5} \): \[ \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \]

Now, we can add the two fractions: \[ \frac{5}{30} + \frac{24}{30} = \frac{5 + 24}{30} = \frac{29}{30} \]

So, the sum of the fractions is \( \frac{29}{30} \).