Calculate 6.1 6x 3- 1000 $$ 6.3(16+21) imes 100 $$ $$ 6.553 imes 20 \div 1000 $$ Which is smaller. $$ \frac{3}{5} $$ OR $$ \frac{7}{35} $$ Simphily, without the use of a calculithor: $$ 8.1 \frac{5}{8}+\frac{2}{4} $$ $$ 33 \quad 2 \frac{1}{5}-\frac{3}{5} $$ 8. $$ \frac{2}{7} imes \frac{3}{5} $$ $$ 14+\frac{2}{5} \div \frac{1}{4} $$

Question

Calculate 6.1 6x 3- 1000 $$ 6.3(16+21) 	imes 100 $$ $$ 6.553 	imes 20 \div 1000 $$ Which is smaller. $$ \frac{3}{5} $$ OR $$ \frac{7}{35} $$ Simphily, without the use of a calculithor: $$ 8.1 \frac{5}{8}+\frac{2}{4} $$ $$ 33 \quad 2 \frac{1}{5}-\frac{3}{5} $$ 8. $$ \frac{2}{7} 	imes \frac{3}{5} $$ $$ 14+\frac{2}{5} \div \frac{1}{4} $$

UpStudy AI · Accepted Answer

Certainly! Let's go through each of your calculations step by step.

---

### 1. $$ 6.1 \times 6 \times 3 - 1000 $$

**Step-by-Step Calculation:**
1. **Multiply 6.1 by 6:**
   $$
   6.1 \times 6 = 36.6
   $$
2. **Multiply the result by 3:**
   $$
   36.6 \times 3 = 109.8
   $$
3. **Subtract 1000:**
   $$
   109.8 - 1000 = -890.2
   $$

**Final Answer:** $$-890.2$$

---

### 2. $$ 6.3(16 + 21) \times 100 $$

**Step-by-Step Calculation:**
1. **Add inside the parentheses:**
   $$
   16 + 21 = 37
   $$
2. **Multiply by 6.3:**
   $$
   6.3 \times 37 = 233.1
   $$
3. **Multiply by 100:**
   $$
   233.1 \times 100 = 23,310
   $$

**Final Answer:** $$23,310$$

---

### 3. $$ 6.553 \times 20 \div 1000 $$

**Step-by-Step Calculation:**
1. **Multiply 6.553 by 20:**
   $$
   6.553 \times 20 = 131.06
   $$
2. **Divide by 1000:**
   $$
   131.06 \div 1000 = 0.13106
   $$

**Final Answer:** $$0.13106$$

---

### 4. Which is Smaller: $$ \frac{3}{5} $$ or $$ \frac{7}{35} $$

**Step-by-Step Comparison:**
1. **Simplify $$ \frac{7}{35} $$:**
   $$
   \frac{7}{35} = \frac{1}{5}
   $$
2. **Compare the two fractions:**
   $$
   \frac{3}{5} \quad \text{vs} \quad \frac{1}{5}
   $$
   $$\frac{1}{5}$$ is smaller than $$\frac{3}{5}$$.

**Final Answer:** $$ \frac{7}{35} $$ (which simplifies to $$ \frac{1}{5} $$) is smaller.

---

### 5. $$ 8 \frac{5}{8} + \frac{2}{4} $$

**Step-by-Step Calculation:**
1. **Simplify $$ \frac{2}{4} $$:**
   $$
   \frac{2}{4} = \frac{1}{2}
   $$
2. **Convert mixed numbers to fractions:**
   $$
   8 \frac{5}{8} = 8 + \frac{5}{8} = \frac{69}{8}
   $$
3. **Add the fractions:**
   $$
   \frac{69}{8} + \frac{1}{2} = \frac{69}{8} + \frac{4}{8} = \frac{73}{8} = 9 \frac{1}{8}
   $$

**Final Answer:** $$9 \frac{1}{8}$$

---

### 6. $$ 33 + 2 \frac{1}{5} - \frac{3}{5} $$

**Step-by-Step Calculation:**
1. **Convert mixed number to improper fraction:**
   $$
   2 \frac{1}{5} = \frac{11}{5}
   $$
2. **Subtract the fractions:**
   $$
   \frac{11}{5} - \frac{3}{5} = \frac{8}{5} = 1 \frac{3}{5}
   $$
3. **Add to 33:**
   $$
   33 + 1 \frac{3}{5} = 34 \frac{3}{5}
   $$

**Final Answer:** $$34 \frac{3}{5}$$

---

### 7. $$ \frac{2}{7} \times \frac{3}{5} $$

**Step-by-Step Calculation:**
1. **Multiply the numerators and denominators:**
   $$
   \frac{2 \times 3}{7 \times 5} = \frac{6}{35}
   $$

**Final Answer:** $$ \frac{6}{35} $$

---

### 8. $$ 14 + \frac{2}{5} \div \frac{1}{4} $$

**Step-by-Step Calculation:**
1. **Divide the fractions:**
   $$
   \frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1} = \frac{8}{5} = 1 \frac{3}{5}
   $$
2. **Add to 14:**
   $$
   14 + 1 \frac{3}{5} = 15 \frac{3}{5}
   $$

**Final Answer:** $$15 \frac{3}{5}$$

---

Feel free to ask if you have any more questions or need further clarification on any of these problems!
-890.2, 23,310, 0.13106, $$ \frac{7}{35} $$ is smaller, $$9 \frac{1}{8}$$, $$34 \frac{3}{5}$$, $$ \frac{6}{35} $$, $$15 \frac{3}{5}$$.

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