Write the sum or difference. 11(1)/(5)-6(2)/(3)=5

Convert to Improper Fractions: Convert mixed numbers to improper fractions. 11(1)/(5) can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator: (11 * 5) + 1 = 55 + 1 = 56. So, 11(1)/(5) becomes 56/5. 6(2)/(3) can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator: (6 * 3) + 2 = 18 + 2 = 20. So, 6(2)/(3) becomes 20/3.Perform Subtraction with Common Denominator: Perform the subtraction of the two improper fractions. To subtract the fractions, we need a common denominator. The least common multiple (LCM) of 5 and 3 is 15. We will convert both fractions to have a denominator of 15. 56/5 = (56 * 3) / (5 * 3) = 168/15 20/3 = (20 * 5) / (3 * 5) = 100/15 Now we can subtract the two fractions: 168/15 - 100/15.Subtract Numerators with Common Denominator: Subtract the numerators and keep the common denominator. 168/15 - 100/15 = (168 - 100) / 15 = 68/15Convert Back to Mixed Number: Convert the improper fraction back to a mixed number if necessary. 68/15 is an improper fraction. To convert it to a mixed number, we divide the numerator by the denominator: 68 ÷ 15 = 4 with a remainder of 8. So, 68/15 as a mixed number is 4(8)/(15).

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Algebra 2

Roots of rational numbers

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Q. Write the sum or difference.

\newline

\begin{array}{r}11 \frac{1}{5} \\ -\quad 6 \frac{2}{3} \\ \hline \end{array}

Convert to Improper Fractions: Convert mixed numbers to improper fractions. $\newline$ $11\frac{1}{5}$ can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator: $(11 \times 5) + 1 = 55 + 1 = 56$ . So, $11\frac{1}{5}$ becomes $\frac{56}{5}$ . $\newline$ $6\frac{2}{3}$ can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator: $(6 \times 3) + 2 = 18 + 2 = 20$ . So, $6\frac{2}{3}$ becomes $\frac{20}{3}$ .
Perform Subtraction with Common Denominator: Perform the subtraction of the two improper fractions. $\newline$ To subtract the fractions, we need a common denominator. The least common multiple (LCM) of $5$ and $3$ is $15$ . We will convert both fractions to have a denominator of $15$ . $\newline$ $\frac{56}{5} = \left(\frac{56 \times 3}{5 \times 3}\right) = \frac{168}{15}$ $\newline$ $\frac{20}{3} = \left(\frac{20 \times 5}{3 \times 5}\right) = \frac{100}{15}$ $\newline$ Now we can subtract the two fractions: $\frac{168}{15} - \frac{100}{15}$ .
Subtract Numerators with Common Denominator: Subtract the numerators and keep the common denominator. $\frac{168}{15} - \frac{100}{15} = \frac{(168 - 100)}{15} = \frac{68}{15}$
Convert Back to Mixed Number: Convert the improper fraction back to a mixed number if necessary. $\newline$ $\frac{68}{15}$ is an improper fraction. To convert it to a mixed number, we divide the numerator by the denominator: $68 \div 15 = 4$ with a remainder of $8$ . So, $\frac{68}{15}$ as a mixed number is $4\left(\frac{8}{15}\right)$ .