1. **State the problem:** We need to perform the division calculations given, starting with the first one: dividing 8.64 by 1.12. 2. **Formula used:** Division is the process of finding how many times the divisor fits into the dividend. The formula is: $$\text{Quotient} = \frac{\text{Dividend}}{\text{Divisor}}$$ 3. **First division: 8.64 \div 1.12** - Convert to whole numbers by multiplying numerator and denominator by 100 to avoid decimals: $$\frac{8.64}{1.12} = \frac{8.64 \times 100}{1.12 \times 100} = \frac{864}{112}$$ - Simplify the fraction by dividing numerator and denominator by 8: $$\frac{\cancel{864}^{108}}{\cancel{112}^{14}}$$ - Now divide 108 by 14: $$108 \div 14 = 7.7142857...$$ - So, the quotient is approximately $7.7143$. 4. **Second division: 15.72 \div 2.24** - Multiply numerator and denominator by 100: $$\frac{15.72}{2.24} = \frac{1572}{224}$$ - Simplify by dividing numerator and denominator by 4: $$\frac{\cancel{1572}^{393}}{\cancel{224}^{56}}$$ - Divide 393 by 56: $$393 \div 56 = 7.0178571...$$ - Quotient approximately $7.018$. 5. **Third division: 56 \div 3.1817** - Multiply numerator and denominator by 10000: $$\frac{56}{3.1817} = \frac{560000}{31817}$$ - Perform the division: $$560000 \div 31817 \approx 17.6$$ 6. **Fourth division: 9.84 \div 4.24** - Multiply numerator and denominator by 100: $$\frac{9.84}{4.24} = \frac{984}{424}$$ - Simplify by dividing numerator and denominator by 4: $$\frac{\cancel{984}^{246}}{\cancel{424}^{106}}$$ - Divide 246 by 106: $$246 \div 106 = 2.3207...$$ - Quotient approximately $2.321$. 7. **Fifth division: 128.9 \div 5.45** - Multiply numerator and denominator by 100: $$\frac{128.9}{5.45} = \frac{12890}{545}$$ - Simplify by dividing numerator and denominator by 5: $$\frac{\cancel{12890}^{2578}}{\cancel{545}^{109}}$$ - Divide 2578 by 109: $$2578 \div 109 = 23.64$$ **Final answers:** - $8.64 \div 1.12 \approx 7.7143$ - $15.72 \div 2.24 \approx 7.018$ - $56 \div 3.1817 \approx 17.6$ - $9.84 \div 4.24 \approx 2.321$ - $128.9 \div 5.45 = 23.64$ Each division was done by converting decimals to whole numbers, simplifying fractions, and then performing the division to get the quotient.