Answer:The “partial quotients algorithm”is a operation which uses place values of the dividend and allows to build on multiplication facts with numbers. It works with distributive property ,where distributive property to multiply states that multiplying the sum of two numbers by a number gives the exact same conclusion as the first number can be distributed to both of those numbers and multiplied by each of them separately and then added.
Partial quotient to divide is same as using distributive property by division.
Further Explanation:
Partial-quotients division:
This process takes many steps to find the quotient.
At each step, we get partial answer (partial quotient), then find the product of the partial quotient and divisor and subtract it from the dividend.
Finally, add all the partial quotients to find the final quotient.
For example: Take the case of division as [tex]\frac{135}{5}[/tex].
1. How many [tex]5's[/tex] are in [tex]135[/tex].
The first partial quotient is [tex]20[/tex].
[tex]20\times 5=100[/tex]
Subtract [tex]100[/tex] from [tex]135[/tex].
2. How many [tex]5's[/tex] are in [tex]35[/tex].
The second partial quotient is [tex]7[/tex].
[tex]5\times 7=35[/tex]
Subtract [tex]35[/tex] from [tex]35[/tex].
The difference is [tex]0[/tex], there is no remainder.
Add the partial quotients as [tex]20+7=27[/tex].
The answer of division [tex]\frac{135}{5}[/tex] is [tex]27[/tex].
Since here distributive property to multiply is not relevant to the partial quotient division. So, we use distributive property to divide to show the result.
Distributive property of division: As per this property division of the sum of two or more numbers by a number gives the same result as dividing each number individually by the number and then adding the numbers together.
For example: Take the case of division as [tex]\frac{135}{5}[/tex].
We can write the above expression as follows:
[tex]\dfrac{135}{5}=\dfrac{100+35}{5}[/tex]
Now, using the distributive property as follows:
[tex]\begin{aligned}\dfrac{100+35}{5}&=\dfrac{100}{5}+\dfrac{35}{5}\\&=20+7\\&=27\end{aligned}[/tex]
Therefore, a partial quotient to divide is same as using distributive property by division.
Learn more:
1. Problem on the whole numbers are positive integers https://brainly.com/question/1852063.
2. Problem on the adding and simplifying the numbers https://brainly.com/question/894273
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Simplification
Keywords: Division, partial quotient division, distributive property, multiplication, addition, subtraction, quotient, dividend, remainder.
