what is partial-quotient divison???
Partial-quotient division is a method used to divide two numbers. It involves repeatedly subtracting multiples of the divisor from the dividend until the remainder becomes zero or less than the divisor. The partial quotients obtained in each subtraction step are then combined to find the quotient.
To understand partial-quotient division, let's go through an example of dividing 84 by 7:
Step 1: Start by writing the dividend (84) and the divisor (7) as a long division problem:
84 ÷ 7 = ?
Step 2: Now, we need to find partial quotients by subtracting multiples of 7 from 84. Start with the highest multiple of 7 that is less than or equal to 84, which is 70:
84 - 70 = 14
The first partial quotient is 10 since 70 can be subtracted from 84 ten times.
Step 3: Write the partial quotient (10) above the long division symbol:
84 ÷ 7 = 10 …
Step 4: Now, we have a new dividend of 14. Repeat the process of finding partial quotients by subtracting multiples of 7 from 14. The highest multiple of 7 that is less than or equal to 14 is 7:
14 - 7 = 7
The second partial quotient is 1 since 7 can be subtracted from 14 once.
Step 5: Write the second partial quotient (1) next to the first one:
84 ÷ 7 = 10 … 1 …
Step 6: Finally, we are left with a new dividend of 7. Since 7 is equal to the divisor, we have no remainder. The partial quotients we obtained are combined to form the quotient:
84 ÷ 7 = 10 … 1
So, the quotient is 10 with a remainder of 1.
Partial-quotient division is a way to break down division problems into smaller subtractions, making it easier to mentally compute the steps.