Practice with Our Flashcards

Example 1: Dividing 833 by 7

To divide 833 by 7 using partial quotients, follow these steps:

1. Rewrite the Problem:Rewrite 833 ÷ 7 as a division problem formatted to use partial quotients.
   

2. Estimate the Quotients:Estimate how many times 7 can go into 833 without exceeding it. Start with larger, easy-to-calculate numbers.
   7 goes into 833 at least 100 times (700), so write 100 as the first partial quotient.
   Subtract 700 from 833, leaving 133.
   

3. Continue Estimating:Next, estimate how many times 7 can go into 133.
   7 goes into 133 at least 10 times (70), so write 10 as the next partial quotient.
   Subtract 70 from 133, leaving 63.
   

4. Final Estimate:Estimate how many times 7 goes into 63.
   7 goes into 63 exactly 9 times, so write 9 as the final partial quotient.
   Subtract 63 from 63, leaving 0.
   

5. Add the Partial Quotients:Add the partial quotients: 100 + 10 + 9 = 119.
   Therefore, 833 ÷ 7 equals 119.
   

Example 2: Dividing 856 by 8

To divide 856 by 8 using partial quotients, follow these steps:

1. Rewrite the Problem:Rewrite 856 ÷ 8 as a division problem formatted to use partial quotients.
   

2. Estimate the Quotients:Estimate how many times 8 can go into 856 without exceeding it. Start with larger, easy-to-calculate numbers.
   8 goes into 856 at least 100 times (800), so write 100 as the first partial quotient.
   Subtract 800 from 856, leaving 56.
   

3. Continue Estimating:Next, estimate how many times 8 can go into 56.
   8 goes into 56 exactly 7 times, so write 7 as the next partial quotient.
   Subtract 56 from 56, leaving 0.
   

4. Add the Partial Quotients:Add the partial quotients: 100 + 7 = 107.
   Therefore, 856 ÷ 8 equals 107.
   

Conclusion

Using partial quotients to simplify division problems can make complex calculations easier and more intuitive. By breaking down the division process into manageable steps and leveraging basic arithmetic properties, students can confidently tackle division.

Practice these techniques with our flashcards and video to become proficient in dividing using partial quotients, and don't forget to check out Khan Academy’s detailed explanations and examples for a deeper understanding.