f. $$ \quad 3 \frac{1}{4}+2 \frac{1}{6}-2 \frac{3}{8}= $$ h. $$ 8 \frac{1}{6}-2 \frac{8}{9}+1 \frac{1}{2}= $$ j. $$ \quad 8 \frac{3}{10}+\left(2 \frac{5}{6}-1 \frac{4}{5}\right)= $$

Question

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$8+\frac{1}{6}-2-\frac{8}{9}+1+\frac{1}{2}$$
- step1: Calculate:
  $$7+\frac{1}{6}-\frac{8}{9}+\frac{1}{2}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{7\times 6\times 3}{6\times 3}+\frac{3}{6\times 3}-\frac{8\times 2}{9\times 2}+\frac{9}{2\times 9}$$
- step3: Multiply the numbers:
  $$\frac{7\times 6\times 3}{18}+\frac{3}{6\times 3}-\frac{8\times 2}{9\times 2}+\frac{9}{2\times 9}$$
- step4: Multiply the numbers:
  $$\frac{7\times 6\times 3}{18}+\frac{3}{18}-\frac{8\times 2}{9\times 2}+\frac{9}{2\times 9}$$
- step5: Multiply the numbers:
  $$\frac{7\times 6\times 3}{18}+\frac{3}{18}-\frac{8\times 2}{18}+\frac{9}{2\times 9}$$
- step6: Multiply the numbers:
  $$\frac{7\times 6\times 3}{18}+\frac{3}{18}-\frac{8\times 2}{18}+\frac{9}{18}$$
- step7: Transform the expression:
  $$\frac{7\times 6\times 3+3-8\times 2+9}{18}$$
- step8: Multiply the terms:
  $$\frac{126+3-8\times 2+9}{18}$$
- step9: Multiply the numbers:
  $$\frac{126+3-16+9}{18}$$
- step10: Calculate:
  $$\frac{122}{18}$$
- step11: Reduce the fraction:
  $$\frac{61}{9}$$
Calculate or simplify the expression $$ 3 + 1/4 + 2 - 1/6 - 2 - 3/8 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3+\frac{1}{4}+2-\frac{1}{6}-2-\frac{3}{8}$$
- step1: Simplify:
  $$3+\frac{1}{4}-\frac{1}{6}-\frac{3}{8}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{3\times 4\times 3\times 2}{4\times 3\times 2}+\frac{3\times 2}{4\times 3\times 2}-\frac{2\times 2}{6\times 2\times 2}-\frac{3\times 3}{8\times 3}$$
- step3: Multiply the terms:
  $$\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{4\times 3\times 2}-\frac{2\times 2}{6\times 2\times 2}-\frac{3\times 3}{8\times 3}$$
- step4: Multiply the terms:
  $$\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{24}-\frac{2\times 2}{6\times 2\times 2}-\frac{3\times 3}{8\times 3}$$
- step5: Multiply the terms:
  $$\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{24}-\frac{2\times 2}{24}-\frac{3\times 3}{8\times 3}$$
- step6: Multiply the numbers:
  $$\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{24}-\frac{2\times 2}{24}-\frac{3\times 3}{24}$$
- step7: Transform the expression:
  $$\frac{3\times 4\times 3\times 2+3\times 2-2\times 2-3\times 3}{24}$$
- step8: Multiply the terms:
  $$\frac{72+3\times 2-2\times 2-3\times 3}{24}$$
- step9: Multiply the numbers:
  $$\frac{72+6-2\times 2-3\times 3}{24}$$
- step10: Multiply the numbers:
  $$\frac{72+6-4-3\times 3}{24}$$
- step11: Multiply the numbers:
  $$\frac{72+6-4-9}{24}$$
- step12: Calculate:
  $$\frac{65}{24}$$
Calculate or simplify the expression $$ 8 + 3/10 + (2 + 5/6 - 1 - 4/5) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$8+\frac{3}{10}+\left(2+\frac{5}{6}-1-\frac{4}{5}\right)$$
- step1: Calculate:
  $$8+\frac{3}{10}+\frac{31}{30}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{8\times 10\times 3}{10\times 3}+\frac{3\times 3}{10\times 3}+\frac{31}{30}$$
- step3: Multiply the numbers:
  $$\frac{8\times 10\times 3}{30}+\frac{3\times 3}{10\times 3}+\frac{31}{30}$$
- step4: Multiply the numbers:
  $$\frac{8\times 10\times 3}{30}+\frac{3\times 3}{30}+\frac{31}{30}$$
- step5: Transform the expression:
  $$\frac{8\times 10\times 3+3\times 3+31}{30}$$
- step6: Multiply the terms:
  $$\frac{240+3\times 3+31}{30}$$
- step7: Multiply the numbers:
  $$\frac{240+9+31}{30}$$
- step8: Add the numbers:
  $$\frac{280}{30}$$
- step9: Reduce the fraction:
  $$\frac{28}{3}$$
Let's solve each of the expressions step by step.

### f. $$ 3 \frac{1}{4} + 2 \frac{1}{6} - 2 \frac{3}{8} $$

1. Convert mixed numbers to improper fractions:
   - $$ 3 \frac{1}{4} = \frac{13}{4} $$
   - $$ 2 \frac{1}{6} = \frac{13}{6} $$
   - $$ 2 \frac{3}{8} = \frac{19}{8} $$

2. Find a common denominator for $$ \frac{13}{4} $$, $$ \frac{13}{6} $$, and $$ \frac{19}{8} $$. The least common multiple of 4, 6, and 8 is 24.

3. Convert each fraction:
   - $$ \frac{13}{4} = \frac{78}{24} $$
   - $$ \frac{13}{6} = \frac{52}{24} $$
   - $$ \frac{19}{8} = \frac{57}{24} $$

4. Now substitute back into the expression:
   $$
   \frac{78}{24} + \frac{52}{24} - \frac{57}{24} = \frac{78 + 52 - 57}{24} = \frac{73}{24}
   $$

5. Convert to a mixed number:
   $$
   \frac{73}{24} = 3 \frac{1}{24}
   $$

### h. $$ 8 \frac{1}{6} - 2 \frac{8}{9} + 1 \frac{1}{2} $$

1. Convert mixed numbers to improper fractions:
   - $$ 8 \frac{1}{6} = \frac{49}{6} $$
   - $$ 2 \frac{8}{9} = \frac{26}{9} $$
   - $$ 1 \frac{1}{2} = \frac{3}{2} $$

2. Find a common denominator for $$ \frac{49}{6} $$, $$ \frac{26}{9} $$, and $$ \frac{3}{2} $$. The least common multiple of 6, 9, and 2 is 18.

3. Convert each fraction:
   - $$ \frac{49}{6} = \frac{147}{18} $$
   - $$ \frac{26}{9} = \frac{52}{18} $$
   - $$ \frac{3}{2} = \frac{27}{18} $$

4. Now substitute back into the expression:
   $$
   \frac{147}{18} - \frac{52}{18} + \frac{27}{18} = \frac{147 - 52 + 27}{18} = \frac{122}{18}
   $$

5. Simplify:
   $$
   \frac{122}{18} = 6 \frac{7}{9}
   $$

### j. $$ 8 \frac{3}{10} + \left(2 \frac{5}{6} - 1 \frac{4}{5}\right) $$

1. Convert mixed numbers to improper fractions:
   - $$ 8 \frac{3}{10} = \frac{83}{10} $$
   - $$ 2 \frac{5}{6} = \frac{17}{6} $$
   - $$ 1 \frac{4}{5} = \frac{9}{5} $$

2. Find a common denominator for $$ \frac{17}{6} $$ and $$ \frac{9}{5} $$. The least common multiple of 6 and 5 is 30.

3. Convert each fraction:
   - $$ \frac{17}{6} = \frac{85}{30} $$
   - $$ \frac{9}{5} = \frac{54}{30} $$

4. Now substitute back into the expression:
   $$
   8 \frac{3}{10} + \left(\frac{85}{30} - \frac{54}{30}\right) = \frac{83}{10} + \frac{31}{30}
   $$

5. Convert $$ \frac{83}{10} $$ to have a common denominator of 30:
   $$
   \frac{83}{10} = \frac{249}{30}
   $$

6. Now combine:
   $$
   \frac{249}{30} + \frac{31}{30} = \frac{280}{30} = 9 \frac{1}{3}
   $$

### Final Answers:
- f. $$ 3 \frac{1}{24} $$
- h. $$ 6 \frac{7}{9} $$
- j. $$ 9 \frac{1}{3} $$
f. $$ 3 \frac{1}{24} $$ h. $$ 6 \frac{7}{9} $$ j. $$ 9 \frac{1}{3} $$

f. \( \quad 3 \frac{1}{4}+2 \frac{1}{6}-2 \frac{3}{8}= \) h. \( 8 \frac{1}{6}-2 \frac{8}{9}+1 \frac{1}{2}= \) j. \( \quad 8 \frac{3}{10}+\left(2 \frac{5}{6}-1 \frac{4}{5}\right)= \)

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