Activity 8 Divide $$ \begin{array}{ll} ext { First estimate and then calculate. Check yo } \ ext { (1) } 157 \div 6 & ext { 2 } 1140 \div 8\end{array} $$

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Activity 8 Divide $$ \begin{array}{ll}	ext { First estimate and then calculate. Check yo } \ 	ext { (1) } 157 \div 6 & 	ext { 2 } 1140 \div 8\end{array} $$

UpStudy AI · Accepted Answer

**Problem (1): $$157 \div 6$$**

1. **Estimate the quotient:**

- Since $$6 \times 20 = 120$$ and $$6 \times 30 = 180$$, we know that $$157$$ lies between these products.
   - A closer estimate: $$6 \times 26 = 156$$ which is very near $$157$$.

2. **Calculate exactly:**

- Multiply $$6$$ by $$26$$:  
     $$
     6 \times 26 = 156
     $$
   - Subtract the product from $$157$$ to find the remainder:  
     $$
     157 - 156 = 1
     $$

3. **Express the result:**

- The division gives a quotient of $$26$$ with a remainder of $$1$$.  
   - In mixed number form, the answer can be written as:  
     $$
     26\frac{1}{6}
     $$
   - In decimal form (if needed), since $$\frac{1}{6} \approx 0.1667$$, the answer is approximately:  
     $$
     26.1667
     $$

---

**Problem (2): $$1140 \div 8$$**

1. **Estimate the quotient:**

- Since $$8 \times 100 = 800$$ and $$8 \times 150 = 1200$$, the answer will be somewhere between $$100$$ and $$150$$.
   - A closer estimate: $$8 \times 142 = 1136$$ which is near $$1140$$.

2. **Calculate exactly:**

- Multiply $$8$$ by $$142$$:  
     $$
     8 \times 142 = 1136
     $$
   - Subtract the product from $$1140$$ to find the remainder:  
     $$
     1140 - 1136 = 4
     $$

3. **Express the result:**

- The division gives a quotient of $$142$$ with a remainder of $$4$$.
   - The remainder as a fraction is:  
     $$
     \frac{4}{8}=\frac{1}{2}
     $$
   - In mixed number form, the answer is:  
     $$
     142\frac{1}{2}
     $$
   - In decimal form, the answer is:  
     $$
     142.5
     $$

---

**Summary of Answers:**

1. $$157 \div 6 = 26\frac{1}{6} \approx 26.1667$$
2. $$1140 \div 8 = 142\frac{1}{2} = 142.5$$
**Problem (1): $$157 \div 6$$** - **Estimate:** Approximately $$26$$ - **Exact Calculation:** $$26$$ with a remainder of $$1$$, or $$26\frac{1}{6}$$ or $$26.1667$$ **Problem (2): $$1140 \div 8$$** - **Estimate:** Approximately $$142$$ - **Exact Calculation:** $$142$$ with a remainder of $$4$$, or $$142\frac{1}{2}$$ or $$142.5$$ **Summary:** 1. $$157 \div 6 = 26\frac{1}{6} \approx 26.1667$$ 2. $$1140 \div 8 = 142\frac{1}{2} = 142.5$$

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