Questions: Add the fractions and write the answer in simplest form. 6. 3/4 + 2/5

$Add the fractions and write the answer in simplest form. 6. 3/4 + 2/5$

Transcript text: Add the fractions and write the answer in simplest form. 6. $\frac{3}{4}+\frac{2}{5}$

Solution

Solution Steps

Step 1: Find a Common Denominator

To add the fractions $\frac{3}{4}$ and $\frac{2}{5}$, we first need to find a common denominator. The denominators are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.

Step 2: Convert Fractions to Have the Common Denominator

Convert each fraction to an equivalent fraction with a denominator of 20.

\[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]

\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]

Step 3: Add the Fractions

Now that both fractions have the same denominator, add the numerators:

\[ \frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20} \]

Final Answer

The sum of $\frac{3}{4}$ and $\frac{2}{5}$ in simplest form is:

\[ \boxed{\frac{23}{20}} \]

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