Question

Find the estimated quotient of $567\div 24$\[\]
A.20\[\]
B.21\[\]
C.22\[\]
D.23\[\]

Answer 1

Hint: Use the rule of 5 to approximate the nearest multiple of 10 for both number and divisor. If they cannot be approximated to a whole number choose the next nearest multiple of 10 for the number and proceed.

Complete step by step answer:
We know that when we divide a number it can exactly divide it or it can divide fractionally. When we divide two numbers say we divide $a$ by $b$ then if $a$ is exactly divisible by $b$ then we say $b$ is a factor$a$. When $b$ cannot divide $a$ exactly we get a quotient and a remainder. If we denote quotient to $q$and remainder to $r$ then
\[a=bq+r\]
 We estimate when we face difficult calculations to find a value closer to the exact calculation. \[\]
Rules of Rounding off:-\[\]
We estimate by the rule of 5 for the nearest multiple of 10. If the nest digit is greater than 5 we round up by increasing 1 and if the next digit is less than 5 we round down by dropping the digit . For example if we want to round off 58 to the nearest multiple of 10 we will get 60 and if we round off 53 it will round down and we will get 50. If the digit is 5 then we look at the previous digit and round off so that the rounded off number will be even. \[\]
Method-1:
We calculate the exact value of the given quotient that is $\dfrac{567}{22}=23.625$. \[\]
We now round off the result 23. 625. The digit at the thousandth place after decimal point is 5. The digit right before is even .So we just drop 5 and the number is rounded down to 23.62. \[\]
Now the digit at hundredth place after the decimal point is 2, the digit right before 2 is 6. As 2 is less than 6 we just drop 2 and the number is rounded down to 23.6\[\]
Now the digit at unit place after the decimal point is 6, the digit right before 6 is 3. As 6 is larger than 5 .We increase 3 by 1 and the number rounded up to 24 which is not in the options. \[\]
Method-2:\[\]
The given problem has asked us to estimate the quotient of $567\div 24$. We round up the number 567 to the nearest multiple of 10 and we get 570 but at the same time we cannot round up the divisor . We have to round down both of the numbers. So if 567 is rounded down to the nearest multiple of 10, we get 560. If 24 is rounded down we get 20. So the estimated quotient is $\dfrac{560}{20}=23$ which is in the options. \[\]

So the correct choice is D.23. The exact value is $\dfrac{567}{22}=23.625$. So estimation is correct.

Note: It is to be noted that two numbers are not always compatible for quotient estimation for example $567\div 3$. You can also convert the given division to a mixed fraction like $\dfrac{567}{22}=23\dfrac{15}{24}$ to estimate the quotient.