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

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:** \( 6.3 \times 2.8 = 17.64 \) ✅