Estimation simply means an approximated value.
- <em>Estimation gives the range of the first digit of the quotient</em>
- <em>Multiplication is the inverse of division.</em>
- <em />
<em>.</em> - <em />
<em>.</em> - <em />
<em>.</em> - <em />
<em />
<em />
<u />
<u />
<u>Estimation in whole-number quotient</u>
A whole number quotient is represented as:
![\frac ab = c](https://tex.z-dn.net/?f=%5Cfrac%20ab%20%3D%20c)
Where:
<em />
<em> whole numbers</em>
When the numbers are estimated, one would get the idea of the range of values the first digit can assume.
<u>Take for instance:</u>
![\frac{117}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B117%7D%7B3%7D)
117 can be estimated as 120. So, we have:
![\frac{117}{3} \approx \frac{120}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B117%7D%7B3%7D%20%5Capprox%20%5Cfrac%7B120%7D%7B3%7D)
<em>120 divided by 3 is 40.</em>
The first digit of <em>120 divided by 3 </em>is 4.
So, estimating 117 as 120 makes us know that the first digit of <em>117 divided by 3 </em>would either be 4 or less.
<u />
<u>(b) Multiplication in division problem</u>
Multiplication and division are both inverse operations.
So, multiplication is used to check the dividend of the division problem.
Take for instance:
![\frac{117}{3} = 39](https://tex.z-dn.net/?f=%5Cfrac%7B117%7D%7B3%7D%20%3D%2039)
<em>If the above division is correct, then 39 multiplied by 3 must be 117 i.e.</em>
![39 \times 3 = 117](https://tex.z-dn.net/?f=39%20%5Ctimes%203%20%3D%20117)
![(c)\ 663 \div 3](https://tex.z-dn.net/?f=%28c%29%5C%20663%20%5Cdiv%203)
Start by dividing the first 6 by 3
![663 \div 3 \to 1](https://tex.z-dn.net/?f=663%20%5Cdiv%203%20%5Cto%201)
Divide the next 6 by 3
![663 \div 3 \to 11](https://tex.z-dn.net/?f=663%20%5Cdiv%203%20%5Cto%2011)
Divide the last 3 by 3
![663 \div 3 = 112](https://tex.z-dn.net/?f=663%20%5Cdiv%203%20%3D%20112)
![(d)\ 487 \div 8](https://tex.z-dn.net/?f=%28d%29%5C%20487%20%5Cdiv%208)
Divide 4 by 8
![487 \div 8 \to 0](https://tex.z-dn.net/?f=487%20%5Cdiv%208%20%5Cto%200)
Since the result is 0 and 4 is not the last digit, we then try 48.
Divide 48 by 8
![487 \div 8 \to 06](https://tex.z-dn.net/?f=487%20%5Cdiv%208%20%5Cto%2006)
Divide 7 by 8.
![487 \div 8 \to 060](https://tex.z-dn.net/?f=487%20%5Cdiv%208%20%5Cto%20060)
7 is less than 8; this means that 8 cannot divide 7.
So, we write 7 as the remainder
![487 \div 8 = 060\ R\ 7](https://tex.z-dn.net/?f=487%20%5Cdiv%208%20%3D%20060%5C%20R%5C%207)
Remove the leading 0
![487 \div 8 = 60 R 7](https://tex.z-dn.net/?f=487%20%5Cdiv%208%20%3D%2060%20R%207)
![(e)\ 1641 \div 4](https://tex.z-dn.net/?f=%28e%29%5C%201641%20%5Cdiv%204)
Divide 1 by 4
![1641 \div 4 \to 0](https://tex.z-dn.net/?f=1641%20%5Cdiv%204%20%5Cto%200)
Divide 16 by 4
![1641 \div 4 \to 04](https://tex.z-dn.net/?f=1641%20%5Cdiv%204%20%5Cto%2004)
Divide 4 by 4
![1641 \div 4 \to 041](https://tex.z-dn.net/?f=1641%20%5Cdiv%204%20%5Cto%20041)
Divide 1 by 4
![1641 \div 4 \to0410](https://tex.z-dn.net/?f=1641%20%5Cdiv%204%20%5Cto0410)
1 is less than 4; this means that 8 cannot divide 1.
So, we write 1 as the remainder
![1641 \div 4 \to 0410\ R\ 1](https://tex.z-dn.net/?f=1641%20%5Cdiv%204%20%5Cto%200410%5C%20R%5C%201)
Remove the leading 0
![1641 \div 4 = 410\ R\ 1](https://tex.z-dn.net/?f=1641%20%5Cdiv%204%20%3D%20410%5C%20R%5C%201)
![(f)\ 2765 \div 9](https://tex.z-dn.net/?f=%28f%29%5C%202765%20%5Cdiv%209)
Divide 2 by 9
![2765 \div 9 \to 0](https://tex.z-dn.net/?f=2765%20%5Cdiv%209%20%5Cto%200)
Divide 27 by 9
![2765 \div 9 \to 03](https://tex.z-dn.net/?f=2765%20%5Cdiv%209%20%5Cto%2003)
Divide 6 by 9
![2765 \div 9 \to 030](https://tex.z-dn.net/?f=2765%20%5Cdiv%209%20%5Cto%20030)
6 is less than 9; this means that 9 cannot divide 6.
So, the next division will be 65 by 9
![2765 \div 9 \to 0307](https://tex.z-dn.net/?f=2765%20%5Cdiv%209%20%5Cto%200307)
9 divides 63 in 7 places, with a remainder of 2.
So, we have:
![2765 \div 9 = 0307 R 2](https://tex.z-dn.net/?f=2765%20%5Cdiv%209%20%3D%200307%20R%202)
Remove the leading 0
![2765 \div 9 = 307 R 2](https://tex.z-dn.net/?f=2765%20%5Cdiv%209%20%3D%20307%20R%202)
Read more about division and multiplications at:
brainly.com/question/19928607