Solve the following problems using Partial Quotients a. 7752/17 b. 651/3
try 100
7752-1700=6052
try 300
6052-5100 = 952
try 50
952-850 = 102
try 5
102-85 = 17
try 1
17-17 = 0
add up partial quotients: 100+300+50+5+1 = 456
check: 456*17 = 7752
It's just like regular long division, but instead of trying to guess the best quotient at each step, just keep track of what you used, and add 'em up at the end.
To solve the problems using the partial quotients method, follow these steps:
a. Problem: 7752 ÷ 17
Step 1: Divide the first digit of the dividend (7) by the divisor (17). The quotient will be less than 10 in most cases.
- In this case, 7 ÷ 17 = 0. The quotient is 0.
Step 2: Bring down the next digit (7) to the right of the 0 quotient from the previous step, giving us 77.
Step 3: Divide 77 by 17.
- 77 ÷ 17 = 4. The quotient is 4.
Step 4: Bring down the next digit (5) to the right of the 4 quotient from the previous step, giving us 45.
Step 5: Divide 45 by 17.
- 45 ÷ 17 = 2. The quotient is 2.
Step 6: Bring down the next digit (2) to the right of the 2 quotient from the previous step, giving us 22.
Step 7: Divide 22 by 17.
- 22 ÷ 17 = 1. The quotient is 1.
Step 8: Bring down the next digit (0) to the right of the 1 quotient from the previous step, giving us 10.
Step 9: Divide 10 by 17. Since 10 is less than 17, we cannot divide further.
The final answer is 0.4521 (rounded to four decimal places).
b. Problem: 651 ÷ 3
Step 1: Divide the first digit of the dividend (6) by the divisor (3). The quotient will be less than 10 in most cases.
- In this case, 6 ÷ 3 = 2. The quotient is 2.
Step 2: Bring down the next digit (5) to the right of the 2 quotient from the previous step, giving us 25.
Step 3: Divide 25 by 3.
- 25 ÷ 3 = 8. The quotient is 8.
Step 4: Bring down the next digit (1) to the right of the 8 quotient from the previous step, giving us 81.
Step 5: Divide 81 by 3.
- 3 goes into 8 two times (2) with a remainder of 2. The quotient is 82.
Since there are no more digits in the dividend, we have our final answer: 2.82 (rounded to two decimal places).