1. **State the problem:** We want to divide 10.64 by 0.14 using long division. 2. **Convert to whole numbers:** To simplify, multiply both numbers by 100 to remove decimals: $$10.64 \div 0.14 = \frac{10.64 \times 100}{0.14 \times 100} = \frac{1064}{14}$$ 3. **Set up long division:** Divide 1064 by 14. 4. **Divide step-by-step:** - 14 goes into 106 how many times? 14 \times 7 = 98, which is less than 106. - Write 7 above the division bar. - Subtract 98 from 106: $$106 - 98 = 8$$ - Bring down the next digit 4, making 84. - 14 goes into 84 exactly 6 times because $$14 \times 6 = 84$$. - Write 6 next to 7 in the quotient. - Subtract 84 from 84: $$84 - 84 = 0$$ 5. **Quotient:** The quotient is 76. 6. **Answer:** Therefore, $$10.64 \div 0.14 = 76$$ This means 0.14 fits into 10.64 exactly 76 times.