Lesson 8: Partial Quotients: Strategy and Algorithm

Property

The partial quotients algorithm is a method for recording the steps of sharing division.
Each time you share a place value, you record the result as a partial quotient.
The amount shared is multiplied by the divisor and subtracted from the dividend to find what remains to be divided.

Examples

Property

To estimate the quotient when dividing by a multiple of 10, use basic division facts. Think of the dividend and divisor in terms of tens.
For example, to solve $84 \div 20$, you can think of it as $8 \text{ tens} \div 2 \text{ tens}$, which simplifies to $8 \div 2$.

Examples

• To estimate $72 \div 30$, think: How many 3s are in 7? The answer is 2. So, $72 \div 30 \approx 2$. ($60 \div 30 = 2$)
• To estimate $154 \div 50$, think: How many 5s are in 15? The answer is 3. So, $154 \div 50 \approx 3$. ($150 \div 50 = 3$)
• To estimate $430 \div 60$, think: How many 6s are in 43? The answer is 7. So, $430 \div 60 \approx 7$. ($420 \div 60 = 7$)

Explanation

Estimating helps you find an answer that is close to the exact quotient before you start long division. By using basic facts, you can simplify the problem and make a reasonable guess. This strategy is useful for determining the first digit of your quotient in the standard algorithm. It also helps you check if your final answer makes sense.

Property

Partial quotients is a method for solving division problems by repeatedly subtracting "friendly" multiples of the divisor from the dividend.
The final quotient is the sum of all the partial quotients.

Examples