5 $$ 4.5 .3 \quad 24 \div 6+2 imes 9 $$ $$ \qquad $$ $$ \qquad $$ (2) $$ 4.5 .40,4 imes 0,02 $$ $$ \qquad $$ $$ \qquad $$ (1) [13] QUESTION 5 Calculate the following without the use of a calculator: $$ 5.1-8^{2} \div(-2)^{3} $$ (1) $$ 5.2 \quad 2 \frac{1}{2}+1 \frac{1}{3} $$ $$ \qquad $$ $$ \qquad $$ (1) $$ 5.3 \quad 2 \frac{2}{3} \div 1 \frac{1}{9} $$ $$ \qquad $$ $$ \qquad $$ (1) $$ 5.4 \sqrt[3]{-\frac{1}{8}}-\sqrt{2 \frac{1}{4}} $$ $$ \qquad $$ (1)

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5 $$ 4.5 .3 \quad 24 \div 6+2 	imes 9 $$ $$ \qquad $$ $$ \qquad $$ (2) $$ 4.5 .40,4 	imes 0,02 $$ $$ \qquad $$ $$ \qquad $$ (1) [13] QUESTION 5 Calculate the following without the use of a calculator: $$ 5.1-8^{2} \div(-2)^{3} $$ (1) $$ 5.2 \quad 2 \frac{1}{2}+1 \frac{1}{3} $$ $$ \qquad $$ $$ \qquad $$ (1) $$ 5.3 \quad 2 \frac{2}{3} \div 1 \frac{1}{9} $$ $$ \qquad $$ $$ \qquad $$ (1) $$ 5.4 \sqrt[3]{-\frac{1}{8}}-\sqrt{2 \frac{1}{4}} $$ $$ \qquad $$ (1)

UpStudy AI · Accepted Answer

Let's solve each part of the problem step by step.

### 5.1 Calculate $$ 5.1 - 8^{2} \div (-2)^{3} $$

1. **Calculate $$ 8^{2} $$**:
   $$
   8^{2} = 64
   $$

2. **Calculate $$ (-2)^{3} $$**:
   $$
   (-2)^{3} = -8
   $$

3. **Now perform the division**:
   $$
   64 \div (-8) = -8
   $$

4. **Finally, subtract from 5.1**:
   $$
   5.1 - (-8) = 5.1 + 8 = 13.1
   $$

So, the answer for 5.1 is $$ 13.1 $$.

### 5.2 Calculate $$ 2 \frac{1}{2} + 1 \frac{1}{3} $$

1. **Convert mixed numbers to improper fractions**:
   $$
   2 \frac{1}{2} = \frac{5}{2}, \quad 1 \frac{1}{3} = \frac{4}{3}
   $$

2. **Find a common denominator** (which is 6):
   $$
   \frac{5}{2} = \frac{15}{6}, \quad \frac{4}{3} = \frac{8}{6}
   $$

3. **Add the fractions**:
   $$
   \frac{15}{6} + \frac{8}{6} = \frac{23}{6}
   $$

So, the answer for 5.2 is $$ \frac{23}{6} $$ or $$ 3 \frac{5}{6} $$.

### 5.3 Calculate $$ 2 \frac{2}{3} \div 1 \frac{1}{9} $$

1. **Convert mixed numbers to improper fractions**:
   $$
   2 \frac{2}{3} = \frac{8}{3}, \quad 1 \frac{1}{9} = \frac{10}{9}
   $$

2. **Perform the division** (which is the same as multiplying by the reciprocal):
   $$
   \frac{8}{3} \div \frac{10}{9} = \frac{8}{3} \times \frac{9}{10} = \frac{72}{30}
   $$

3. **Simplify the fraction**:
   $$
   \frac{72}{30} = \frac{12}{5}
   $$

So, the answer for 5.3 is $$ \frac{12}{5} $$ or $$ 2 \frac{2}{5} $$.

### 5.4 Calculate $$ \sqrt[3]{-\frac{1}{8}} - \sqrt{2 \frac{1}{4}} $$

1. **Calculate $$ \sqrt[3]{-\frac{1}{8}} $$**:
   $$
   \sqrt[3]{-\frac{1}{8}} = -\frac{1}{2}
   $$

2. **Convert $$ 2 \frac{1}{4} $$ to an improper fraction**:
   $$
   2 \frac{1}{4} = \frac{9}{4}
   $$

3. **Calculate $$ \sqrt{\frac{9}{4}} $$**:
   $$
   \sqrt{\frac{9}{4}} = \frac{3}{2}
   $$

4. **Now perform the subtraction**:
   $$
   -\frac{1}{2} - \frac{3}{2} = -\frac{4}{2} = -2
   $$

So, the answer for 5.4 is $$ -2 $$.

### Summary of Answers:
- **5.1**: $$ 13.1 $$
- **5.2**: $$ \frac{23}{6} $$ or $$ 3 \frac{5}{6} $$
- **5.3**: $$ \frac{12}{5} $$ or $$ 2 \frac{2}{5} $$
- **5.4**: $$ -2 $$
- **5.1**: 13.1 - **5.2**: 3 5⁄6 - **5.3**: 2 2⁄5 - **5.4**: -2

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