Plaisi is solving 3 and 2/4 + 3 and 3/4

. What is the correct result?(1 point)

1 answer

To solve \( 3 \frac{2}{4} + 3 \frac{3}{4} \), we start by simplifying the fractions:

  1. Convert \( \frac{2}{4} \) to \( \frac{1}{2} \). So, \( 3 \frac{2}{4} = 3 \frac{1}{2} \).
  2. The second fraction \( 3 \frac{3}{4} \) remains the same.

Now we can rewrite the problem with improper fractions:

  • \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)
  • \( 3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \)

Now we need to add the two improper fractions:

  1. Find a common denominator. The least common multiple of 2 and 4 is 4.
  2. Convert \( \frac{7}{2} \) to a fraction with a denominator of 4: \[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]

Now, add \( \frac{14}{4} + \frac{15}{4} \):

\[ \frac{14}{4} + \frac{15}{4} = \frac{29}{4} \]

Now, convert \( \frac{29}{4} \) back to a mixed number:

  • \( 29 \div 4 = 7 \) remainder \( 1 \)
  • Therefore, \( \frac{29}{4} = 7 \frac{1}{4} \)

Thus, the final result of \( 3 \frac{2}{4} + 3 \frac{3}{4} \) is

\[ \boxed{7 \frac{1}{4}} \]