Estimation simply means an approximated value.
- Estimation gives the range of the first digit of the quotient
- Multiplication is the inverse of division.
- [tex]663 \div 3 = 112[/tex].
- [tex]487 \div 8 = 60\ R\ 7[/tex].
- [tex]1641 \div 4 = 410\ R\ 1[/tex].
- [tex]2765 \div 9 = 307\ R\ 2[/tex]
Estimation in whole-number quotient
A whole number quotient is represented as:
[tex]\frac ab = c[/tex]
Where:
[tex]a,b, c \to[/tex] whole numbers
When the numbers are estimated, one would get the idea of the range of values the first digit can assume.
Take for instance:
[tex]\frac{117}{3}[/tex]
117 can be estimated as 120. So, we have:
[tex]\frac{117}{3} \approx \frac{120}{3}[/tex]
120 divided by 3 is 40.
The first digit of 120 divided by 3 is 4.
So, estimating 117 as 120 makes us know that the first digit of 117 divided by 3 would either be 4 or less.
(b) Multiplication in division problem
Multiplication and division are both inverse operations.
So, multiplication is used to check the dividend of the division problem.
Take for instance:
[tex]\frac{117}{3} = 39[/tex]
If the above division is correct, then 39 multiplied by 3 must be 117 i.e.
[tex]39 \times 3 = 117[/tex]
[tex](c)\ 663 \div 3[/tex]
Start by dividing the first 6 by 3
[tex]663 \div 3 \to 1[/tex]
Divide the next 6 by 3
[tex]663 \div 3 \to 11[/tex]
Divide the last 3 by 3
[tex]663 \div 3 = 112[/tex]
[tex](d)\ 487 \div 8[/tex]
Divide 4 by 8
[tex]487 \div 8 \to 0[/tex]
Since the result is 0 and 4 is not the last digit, we then try 48.
Divide 48 by 8
[tex]487 \div 8 \to 06[/tex]
Divide 7 by 8.
[tex]487 \div 8 \to 060[/tex]
7 is less than 8; this means that 8 cannot divide 7.
So, we write 7 as the remainder
[tex]487 \div 8 = 060\ R\ 7[/tex]
Remove the leading 0
[tex]487 \div 8 = 60 R 7[/tex]
[tex](e)\ 1641 \div 4[/tex]
Divide 1 by 4
[tex]1641 \div 4 \to 0[/tex]
Divide 16 by 4
[tex]1641 \div 4 \to 04[/tex]
Divide 4 by 4
[tex]1641 \div 4 \to 041[/tex]
Divide 1 by 4
[tex]1641 \div 4 \to0410[/tex]
1 is less than 4; this means that 8 cannot divide 1.
So, we write 1 as the remainder
[tex]1641 \div 4 \to 0410\ R\ 1[/tex]
Remove the leading 0
[tex]1641 \div 4 = 410\ R\ 1[/tex]
[tex](f)\ 2765 \div 9[/tex]
Divide 2 by 9
[tex]2765 \div 9 \to 0[/tex]
Divide 27 by 9
[tex]2765 \div 9 \to 03[/tex]
Divide 6 by 9
[tex]2765 \div 9 \to 030[/tex]
6 is less than 9; this means that 9 cannot divide 6.
So, the next division will be 65 by 9
[tex]2765 \div 9 \to 0307[/tex]
9 divides 63 in 7 places, with a remainder of 2.
So, we have:
[tex]2765 \div 9 = 0307 R 2[/tex]
Remove the leading 0
[tex]2765 \div 9 = 307 R 2[/tex]
Read more about division and multiplications at:
https://brainly.com/question/19928607
