Estimate then divide 75578÷53
The Correct answer and Explanation is:
To estimate the division of ( 75578 \div 53 ), we can round the numbers to make the calculation simpler. Rounding ( 53 ) to ( 50 ) and ( 75578 ) to ( 76000 ) allows us to estimate:
[
\frac{76000}{50} = 1520
]
This gives us a rough estimate that the quotient is around ( 1520 ).
Now, to find the exact quotient, we will perform the long division of ( 75578 ) by ( 53 ).
- Long Division Process:
- Determine how many times ( 53 ) goes into ( 755 ) (the first three digits of ( 75578 )):
- ( 53 \times 14 = 742 ), so we can write ( 14 ) above the line.
- Subtract ( 742 ) from ( 755 ) to get ( 13 ). Bring down the next digit, ( 7 ), making it ( 137 ).
- Now determine how many times ( 53 ) goes into ( 137 ):
- ( 53 \times 2 = 106 ), write ( 2 ) above the line next to ( 14 ).
- Subtract ( 106 ) from ( 137 ) to get ( 31 ). Bring down the next digit, ( 8 ), making it ( 318 ).
- Now determine how many times ( 53 ) goes into ( 318 ):
- ( 53 \times 6 = 318 ), write ( 6 ) above the line.
- Subtract ( 318 ) from ( 318 ) to get ( 0 ). Since there are no more digits to bring down, we are done.
- Result:
- Therefore, ( 75578 \div 53 = 1426 ).
Conclusion
The exact answer to ( 75578 \div 53 ) is ( 1426 ). The estimated quotient was ( 1520 ), showing that our estimate was reasonably close. Estimating division in this manner can help quickly assess the range in which the true answer lies, making it easier to verify the result after performing the exact calculation. This technique is especially useful in situations where quick approximations are needed, such as in mental math or during standardized tests.