(2) $$ 5 \frac{1}{2}-n+3 $$ for $$ n=3 \frac{1}{3} $$ (3) $$ \left(\frac{3}{4}-a ight) imes 4 $$ for $$ a=\frac{1}{5} $$

Question

(2) $$ 5 \frac{1}{2}-n+3 $$ for $$ n=3 \frac{1}{3} $$ (3) $$ \left(\frac{3}{4}-aight) 	imes 4 $$ for $$ a=\frac{1}{5} $$

UpStudy AI · Accepted Answer

Evaluate the expression by following steps:
- step0: Evaluate:
  $$\left(\frac{3}{4}-a\right)\times 4$$
- step1: Substitute:
  $$\left(\frac{3}{4}-\frac{1}{5}\right)\times 4$$
- step2: Subtract the numbers:
  $$\frac{11}{20}\times 4$$
- step3: Reduce the numbers:
  $$\frac{11}{5}\times 1$$
- step4: Multiply:
  $$\frac{11}{5}$$
Substitute $$ n=3 \frac{1}{3} $$ into the expression $$ 5 \frac{1}{2}-n+3 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$5\frac{1}{2}-n+3$$
- step1: Substitute:
  $$5\frac{1}{2}-3\frac{1}{3}+3$$
- step2: Convert the expressions:
  $$\frac{11}{2}-\frac{10}{3}+3$$
- step3: Reduce fractions to a common denominator:
  $$\frac{11\times 3}{2\times 3}-\frac{10\times 2}{3\times 2}+\frac{3\times 2\times 3}{2\times 3}$$
- step4: Multiply the numbers:
  $$\frac{11\times 3}{6}-\frac{10\times 2}{3\times 2}+\frac{3\times 2\times 3}{2\times 3}$$
- step5: Multiply the numbers:
  $$\frac{11\times 3}{6}-\frac{10\times 2}{6}+\frac{3\times 2\times 3}{2\times 3}$$
- step6: Multiply the numbers:
  $$\frac{11\times 3}{6}-\frac{10\times 2}{6}+\frac{3\times 2\times 3}{6}$$
- step7: Transform the expression:
  $$\frac{11\times 3-10\times 2+3\times 2\times 3}{6}$$
- step8: Multiply the numbers:
  $$\frac{33-10\times 2+3\times 2\times 3}{6}$$
- step9: Multiply the numbers:
  $$\frac{33-20+3\times 2\times 3}{6}$$
- step10: Multiply the terms:
  $$\frac{33-20+18}{6}$$
- step11: Calculate:
  $$\frac{31}{6}$$
Let's solve each expression step by step.

### Problem (2): Evaluate $$ 5 \frac{1}{2} - n + 3 $$ for $$ n = 3 \frac{1}{3} $$

1. **Convert Mixed Numbers to Improper Fractions:**
   - $$ 5 \frac{1}{2} = \frac{11}{2} $$
   - $$ 3 \frac{1}{3} = \frac{10}{3} $$

2. **Substitute $$ n $$ into the expression:**
   $$
   5 \frac{1}{2} - n + 3 = \frac{11}{2} - \frac{10}{3} + 3
   $$

3. **Convert 3 to a fraction:**
   $$
   3 = \frac{6}{2}
   $$

4. **Combine the fractions:**
   $$
   \frac{11}{2} - \frac{10}{3} + \frac{6}{2} = \frac{11 + 6}{2} - \frac{10}{3} = \frac{17}{2} - \frac{10}{3}
   $$

5. **Find a common denominator (which is 6):**
   $$
   \frac{17}{2} = \frac{51}{6}, \quad \frac{10}{3} = \frac{20}{6}
   $$

6. **Subtract the fractions:**
   $$
   \frac{51}{6} - \frac{20}{6} = \frac{31}{6}
   $$

Thus, the result for Problem (2) is:
$$
\frac{31}{6} \quad \text{or} \quad 5 \frac{1}{6} \quad \text{or} \quad 5.1\dot{6}
$$

### Problem (3): Evaluate $$ \left(\frac{3}{4} - a\right) \times 4 $$ for $$ a = \frac{1}{5} $$

1. **Substitute $$ a $$ into the expression:**
   $$
   \left(\frac{3}{4} - a\right) \times 4 = \left(\frac{3}{4} - \frac{1}{5}\right) \times 4
   $$

2. **Find a common denominator (which is 20):**
   $$
   \frac{3}{4} = \frac{15}{20}, \quad \frac{1}{5} = \frac{4}{20}
   $$

3. **Subtract the fractions:**
   $$
   \frac{15}{20} - \frac{4}{20} = \frac{11}{20}
   $$

4. **Multiply by 4:**
   $$
   \frac{11}{20} \times 4 = \frac{44}{20} = \frac{11}{5}
   $$

Thus, the result for Problem (3) is:
$$
\frac{11}{5} \quad \text{or} \quad 2 \frac{1}{5} \quad \text{or} \quad 2.2
$$

### Final Results:
- For Problem (2): $$ \frac{31}{6} $$ or $$ 5 \frac{1}{6} $$ or $$ 5.1\dot{6} $$
- For Problem (3): $$ \frac{11}{5} $$ or $$ 2 \frac{1}{5} $$ or $$ 2.2 $$
For Problem (2), the result is $$ \frac{31}{6} $$ or $$ 5 \frac{1}{6} $$ or $$ 5.1\dot{6} $$. For Problem (3), the result is $$ \frac{11}{5} $$ or $$ 2 \frac{1}{5} $$ or $$ 2.2 $$.

(2) \( 5 \frac{1}{2}-n+3 \) for \( n=3 \frac{1}{3} \) (3) \( \left(\frac{3}{4}-a\right) \times 4 \) for \( a=\frac{1}{5} \)

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