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Complete the equation. Write the sum as a mixed number.

2(2)/(3)+(4)/(5)=(40)/(◻)+(12)/(◻)=◻(◻)/(◻)

Complete the equation. Write the sum as a mixed number. $\newline$ $2 \frac{2}{3}+\frac{4}{5}=\frac{40}{\square}+\frac{12}{\square}=\square \frac{\square}{\square}$

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Multiplication with rational exponents

Full solution

Q. Complete the equation. Write the sum as a mixed number.

\newline

2 \frac{2}{3}+\frac{4}{5}=\frac{40}{\square}+\frac{12}{\square}=\square \frac{\square}{\square}

Convert to Improper Fraction: Convert the mixed number to an improper fraction: $\newline$ $2\left(\frac{2}{3}\right) = \left(2\times 3 + 2\right)/3 = \frac{8}{3}$
Find Common Denominator: Find a common denominator for $\frac{8}{3}$ and $\frac{4}{5}$ : $\newline$ The least common denominator (LCD) of $3$ and $5$ is $15$ .
Convert to Common Denominator: Convert each fraction to have the common denominator: $\newline$ $\frac{8}{3} = \frac{(8\times5)}{(3\times5)} = \frac{40}{15}$ $\newline$ $\frac{4}{5} = \frac{(4\times3)}{(5\times3)} = \frac{12}{15}$
Add Fractions: Add the fractions: $\newline$ $\frac{40}{15} + \frac{12}{15} = \frac{40 + 12}{15} = \frac{52}{15}$
Convert to Mixed Number: Convert the improper fraction back to a mixed number: $\frac{52}{15} = 3$ remainder $7$ , so it's $3\left(\frac{7}{15}\right)$

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