1. **State the problem:** Find the quotient for the division problems given and verify by multiplication. 2. **Formula used:** Quotient $= \frac{\text{Dividend}}{\text{Divisor}}$ 3. **Important rule:** To check the quotient, multiply the quotient by the divisor. The product should equal the dividend. 4. **Solve each division and check:** **Problem 1:** $\frac{2.3}{0.1}$ $$\frac{2.3}{0.1} = \frac{2.3 \times 10}{0.1 \times 10} = \frac{23}{1} = 23$$ Check: $23 \times 0.1 = 2.3$ **Problem 2:** $\frac{6.563}{0.001}$ $$\frac{6.563}{0.001} = \frac{6.563 \times 1000}{0.001 \times 1000} = \frac{6563}{1} = 6563$$ Check: $6563 \times 0.001 = 6.563$ **Problem 3:** $\frac{6.56}{0.01}$ $$\frac{6.56}{0.01} = \frac{6.56 \times 100}{0.01 \times 100} = \frac{656}{1} = 656$$ Check: $656 \times 0.01 = 6.56$ **Problem 4:** $\frac{95.67}{1.000}$ $$\frac{95.67}{1.000} = 95.67$$ Check: $95.67 \times 1.000 = 95.67$ **Problem 5:** $\frac{90.1647}{10.000}$ $$\frac{90.1647}{10.000} = 9.01647$$ Check: $9.01647 \times 10.000 = 90.1647$ **Problem 6:** $\frac{9}{0.6}$ Multiply numerator and denominator by 10: $$\frac{9}{0.6} = \frac{9 \times 10}{0.6 \times 10} = \frac{90}{6}$$ Simplify: $$\frac{\cancel{90}}{\cancel{6}} = 15$$ Check: $15 \times 0.6 = 9$ **Problem 7:** $\frac{18.75}{2.50}$ Multiply numerator and denominator by 100: $$\frac{18.75}{2.50} = \frac{1875}{250}$$ Simplify by dividing numerator and denominator by 125: $$\frac{\cancel{1875}^{15}}{\cancel{250}^{2}} = 7.5$$ Check: $7.5 \times 2.50 = 18.75$ **Problem 8:** $\frac{29.21}{6.23}$ Multiply numerator and denominator by 100: $$\frac{29.21}{6.23} = \frac{2921}{623}$$ Divide 2921 by 623: $623 \times 4 = 2492$, remainder $429$; $623 \times 4.69 \approx 2921$ So quotient $\approx 4.69$ Check: $4.69 \times 6.23 \approx 29.21$ **Problem 9:** $\frac{65.60}{45}$ Divide directly: $$\frac{65.60}{45} = 1.4577...$$ Check: $1.4577 \times 45 \approx 65.60$ **Problem 10:** $\frac{33.75}{12.75}$ Divide directly: $$\frac{33.75}{12.75} = 2.6471...$$ Check: $2.6471 \times 12.75 \approx 33.75$ **Final answers:** 1. 23 2. 6563 3. 656 4. 95.67 5. 9.01647 6. 15 7. 7.5 8. 4.69 (approx) 9. 1.4577 (approx) 10. 2.6471 (approx)