Find the sum. $$ \begin{array}{ll} ext { 1. } \frac{1}{2}+\frac{2}{3}= & ext { 2. } \frac{8}{12}+\frac{8}{11}= \ ext { 3. } \frac{2}{7}+\frac{6}{10}= & ext { 4. } \frac{1}{6}+\frac{6}{11}= \ \frac{5}{9}+\frac{1}{2}= & ext { 6. } \frac{9}{12}+\frac{2}{12}= \ \frac{2}{7}+\frac{1}{4}= & ext { 8. } \frac{1}{4}+\frac{6}{8}=\end{array} $$

Question

Find the sum. $$ \begin{array}{ll}	ext { 1. } \frac{1}{2}+\frac{2}{3}= & 	ext { 2. } \frac{8}{12}+\frac{8}{11}= \ 	ext { 3. } \frac{2}{7}+\frac{6}{10}= & 	ext { 4. } \frac{1}{6}+\frac{6}{11}= \ \frac{5}{9}+\frac{1}{2}= & 	ext { 6. } \frac{9}{12}+\frac{2}{12}= \ \frac{2}{7}+\frac{1}{4}= & 	ext { 8. } \frac{1}{4}+\frac{6}{8}=\end{array} $$

UpStudy AI · Accepted Answer

1. We have
$$
\frac{1}{2} + \frac{2}{3} = \frac{1\times3}{2\times3} + \frac{2\times2}{3\times2} = \frac{3}{6} + \frac{4}{6} = \frac{3+4}{6} = \frac{7}{6}.
$$

2. We compute
$$
\frac{8}{12} + \frac{8}{11}.
$$
The common denominator is $$12\times11=132$$:
$$
\frac{8}{12}=\frac{8\times11}{132}=\frac{88}{132},\quad \frac{8}{11}=\frac{8\times12}{132}=\frac{96}{132}.
$$
Thus,
$$
\frac{88}{132} + \frac{96}{132} = \frac{184}{132}.
$$
Dividing numerator and denominator by $$4$$ (since $$\gcd(184,132)=4$$):
$$
\frac{184\div4}{132\div4} = \frac{46}{33}.
$$

3. We evaluate
$$
\frac{2}{7} + \frac{6}{10}.
$$
The common denominator is $$70$$:
$$
\frac{2}{7}=\frac{2\times10}{70}=\frac{20}{70},\quad \frac{6}{10}=\frac{6\times7}{70}=\frac{42}{70}.
$$
Then,
$$
\frac{20}{70} + \frac{42}{70} = \frac{62}{70}.
$$
Dividing numerator and denominator by $$2$$:
$$
\frac{62\div2}{70\div2}=\frac{31}{35}.
$$

4. We calculate
$$
\frac{1}{6} + \frac{6}{11}.
$$
The common denominator is $$6\times11=66$$:
$$
\frac{1}{6}=\frac{1\times11}{66}=\frac{11}{66},\quad \frac{6}{11}=\frac{6\times6}{66}=\frac{36}{66}.
$$
So,
$$
\frac{11}{66} + \frac{36}{66} = \frac{47}{66}.
$$

5. Next, we have
$$
\frac{5}{9}+\frac{1}{2}.
$$
The common denominator is $$9\times2=18$$:
$$
\frac{5}{9}=\frac{5\times2}{18}=\frac{10}{18},\quad \frac{1}{2}=\frac{1\times9}{18}=\frac{9}{18}.
$$
Thus,
$$
\frac{10}{18}+\frac{9}{18}=\frac{19}{18}.
$$

6. Then,
$$
\frac{9}{12}+\frac{2}{12}.
$$
Since the denominators are the same,
$$
\frac{9+2}{12}=\frac{11}{12}.
$$

7. We compute
$$
\frac{2}{7}+\frac{1}{4}.
$$
The common denominator is $$7\times4=28$$:
$$
\frac{2}{7}=\frac{2\times4}{28}=\frac{8}{28},\quad \frac{1}{4}=\frac{1\times7}{28}=\frac{7}{28}.
$$
Thus,
$$
\frac{8}{28}+\frac{7}{28}=\frac{15}{28}.
$$

8. Finally, we have
$$
\frac{1}{4}+\frac{6}{8}.
$$
First simplify $$\frac{6}{8}$$ to $$\frac{3}{4}$$:
$$
\frac{1}{4}+\frac{3}{4}=\frac{1+3}{4}=\frac{4}{4}=1.
$$
1. $$ \frac{7}{6} $$ 2. $$ \frac{46}{33} $$ 3. $$ \frac{31}{35} $$ 4. $$ \frac{47}{66} $$ 5. $$ \frac{19}{18} $$ 6. $$ \frac{11}{12} $$ 7. $$ \frac{15}{28} $$ 8. $$ 1 $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Arithmetic Questions