Question

you and your friend are talking about adding the fractions below:

\\\frac{3}{5} + \frac{1}{4}\\

your friends says this:

\\\frac{3}{5} + \frac{1}{4} = \frac{4}{9}\\

you disagree.

answer the questions below.

select option a or option b.

row 1

which model represents adding these two fractions by finding common denominators?

Explanation:

Identify the target fractions and their common denominator

The problem asks to represent adding \(\frac{3}{5} + \frac{1}{4}\) using a common denominator model.
The least common denominator for denominators \(5\) and \(4\) is \(20\).

$$ \frac{3}{5} = \frac{12}{20}, \quad \frac{1}{4} = \frac{5}{20} $$

Analyze the visual options

• Option A: Shows two circles, each divided into \(20\) equal sectors.
• The first circle has \(12\) out of \(20\) sectors shaded, representing \(\frac{12}{20}\) (which is \(\frac{3}{5}\)).
• The second circle has \(5\) out of \(20\) sectors shaded, representing \(\frac{5}{20}\) (which is \(\frac{1}{4}\)).
• Option B: Shows circles divided into \(5\) and \(4\) sectors respectively, representing the original fractions without finding a common denominator.

Select the correct option

Option A represents the addition by converting both fractions to have the common denominator of \(20\).

Answer:

• Option A (Correct answer)
• Option B