Find the quotient in (a) and check it in (b) using multiplication. $$ \begin{array}{ll} ext { (a) } 6 . 3 \longdiv { 1 7 . 6 4 } & ext { (b) Check with multiplication: }\end{array} $$

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Find the quotient in (a) and check it in (b) using multiplication. $$ \begin{array}{ll}	ext { (a) } 6 . 3 \longdiv { 1 7 . 6 4 } & 	ext { (b) Check with multiplication: }\end{array} $$

UpStudy AI · Accepted Answer

Certainly! Let's solve the division problem step-by-step and then verify the result through multiplication.

### **(a) Division: $$ \frac{17.64}{6.3} $$**

1. **Understand the Problem:**
   
   We need to find how many times **6.3** fits into **17.64**.

2. **Simplify the Division:**
   
   To make the division easier, we can eliminate the decimals by multiplying both the dividend and the divisor by 10:
   
   $$
   \frac{17.64 \times 10}{6.3 \times 10} = \frac{176.4}{63}
   $$
   
3. **Perform the Division:**
   
   - **Find how many times 63 fits into 176.4:**
     
     - **63 × 2 = 126**
     - **63 × 3 = 189** (This is too large since 189 > 176.4)
     
     So, it fits **2 times** with a remainder:
     
     $$
     176.4 - 126 = 50.4
     $$
   
   - **Now, find how many times 63 fits into 50.4:**
     
     Since 63 is larger than 50.4, we'll consider decimal places.
     
     - **63 × 0.8 = 50.4**
     
     So, it fits **0.8 times**.
   
   - **Combine the two parts:**
     
     $$
     2 + 0.8 = 2.8
     $$
   
4. **Final Quotient:**
   
   $$
   \frac{17.64}{6.3} = 2.8
   $$

### **(b) Check with Multiplication: $$ 6.3 \times 2.8 $$**

To ensure our division result is correct, we'll multiply the divisor by the quotient and see if we get back the original dividend.

1. **Multiply the Numbers:**
   
   $$
   6.3 \times 2.8
   $$
   
2. **Break Down the Multiplication:**
   
   - **Multiply 6 by 2.8:**
     
     $$
     6 \times 2.8 = 16.8
     $$
   
   - **Multiply 0.3 by 2.8:**
     
     $$
     0.3 \times 2.8 = 0.84
     $$
   
3. **Add the Results:**
   
   $$
   16.8 + 0.84 = 17.64
   $$
   
4. **Verification:**
   
   Since $$ 6.3 \times 2.8 = 17.64 $$, which matches the original dividend, our division is correct.

### **Conclusion**

- **Quotient:** $$ 2.8 $$
- **Verification:** $$ 6.3 \times 2.8 = 17.64 $$ ✅
The quotient is 2.8.

Find the quotient in (a) and check it in (b) using multiplication. \( \begin{array}{ll}\text { (a) } 6 . 3 \longdiv { 1 7 . 6 4 } & \text { (b) Check with multiplication: }\end{array} \)

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