Convert to Improper Fractions: Convert mixed numbers to improper fractions. To add fractions, they need to be in improper form. 2(1)/(2) can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 2 * 2 + 1 = 5, so the fraction becomes 5/2. 4(1)/(5) can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 4 * 5 + 1 = 21, so the fraction becomes 21/5.Add Improper Fractions: Add the improper fractions. To add fractions, they must have a common denominator. In this case, the denominators are different (2 and 5), so we need to find a common denominator. The least common denominator (LCD) for 2 and 5 is 10. Now, convert each fraction to an equivalent fraction with a denominator of 10. For 5/2, multiply both the numerator and denominator by 5 to get (5*5)/(2*5) = 25/10. For 21/5, multiply both the numerator and denominator by 2 to get (21*2)/(5*2) = 42/10.Find Common Denominator: Now that we have equivalent fractions with a common denominator, we can add them. 25/10 + 42/10 = (25 + 42)/10 = 67/10Add Fractions: Convert the improper fraction back to a mixed number if necessary. 67/10 is an improper fraction. To convert it to a mixed number, divide the numerator by the denominator. 67 ÷ 10 = 6 with a remainder of 7. So, 67/10 as a mixed number is 6(7)/(10).

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$2 \frac{1}{2}+4 \frac{1}{5}$

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Algebra 1

Multiplication with rational exponents

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2 \frac{1}{2}+4 \frac{1}{5}

Convert to Improper Fractions: Convert mixed numbers to improper fractions. $\newline$ To add fractions, they need to be in improper form. $\newline$ $2\frac{1}{2}$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $2 \times 2 + 1 = 5$ , so the fraction becomes $\frac{5}{2}$ . $\newline$ $4\frac{1}{5}$ can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: $4 \times 5 + 1 = 21$ , so the fraction becomes $\frac{21}{5}$ .
Add Improper Fractions: Add the improper fractions. $\newline$ To add fractions, they must have a common denominator. In this case, the denominators are different $2$ and $5$ , so we need to find a common denominator. $\newline$ The least common denominator (LCD) for $2$ and $5$ is $10$ . $\newline$ Now, convert each fraction to an equivalent fraction with a denominator of $10$ . $\newline$ For $\frac{5}{2}$ , multiply both the numerator and denominator by $5$ to get $\left(5\times5\right)\div\left(2\times5\right) = \frac{25}{10}$ . $\newline$ For $\frac{21}{5}$ , multiply both the numerator and denominator by $2$ to get $5$ $1$ .
Find Common Denominator: Now that we have equivalent fractions with a common denominator, we can add them. $\frac{25}{10} + \frac{42}{10} = \frac{25 + 42}{10}$ $= \frac{67}{10}$
Add Fractions: Convert the improper fraction back to a mixed number if necessary. $\newline$ $\frac{67}{10}$ is an improper fraction. To convert it to a mixed number, divide the numerator by the denominator. $\newline$ $67 \div 10 = 6$ with a remainder of $7$ . $\newline$ So, $\frac{67}{10}$ as a mixed number is $6\left(\frac{7}{10}\right)$ .