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

Question

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.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Arithmetic Questions