How do you Estimate the Sum, Difference, Product and Quotient
Estimation
Estimation plays an important role in our daily life. Before going to the market, we prepare a list of items to be purchased and we make an estimate of the total expenditure of those items. It enables us to carry enough money to make the payment.
Let us consider an example.
Example: Raman purchased a notebook for Rs 37, a Parker pen for Rs 104, and a storybook for Rs 52. He wanted to save time in making payment. Without doing the actual calculations, Raman quickly estimates Rs 37 as Rs 40, Rs 104 as Rs 100, and Rs 52 as Rs 50. The estimated price is Rs 190 (because 40 + 100 + 50 = 190), whereas the actual price is Rs 193 (because 37 + 104 + 52 = 193).
Thus, we conclude that estimation makes our calculations easier and faster. It saves our time and energy both in dealing with day-to-day problems of life. Estimation gives only approximate value, that is, a value which is close to the actual value.
Estimation by rounding off the numbers
Estimation by rounding off the numbers is a very popular and commonly used method. In this method, we round off the numbers nearest to tens, hundreds, thousands, and so on.
Estimating sum, difference, product, and quotient
We will illustrate these with the help of examples:
1. We can estimate the sum and difference of two or more numbers by rounding off the numbers.
Let us consider some examples.
Example 1: Let us estimate the sum of 77 and 2135 to the nearest tens and compare this with the actual sum.
Solution:
In number 77, the digit at ones place is 7 and 7 > 5, so the estimated number = 80.
In number 2135, the digit at ones place is 5 and 5 = 5, so the estimated number = 2140.
∴ Estimated sum = 80 + 2140
= 2220
Actual sum = 77 + 2135 = 2212
Comparing the two sums we see that 2220 > 2212, i. e., estimated sum > actual sum.
Hence, 2220 is the approximate answer.
Example 2: Let us estimate the difference between 54862 and 55610 to the nearest thousands and compare this with the actual difference.
Solution:
In number 54862, the digit at hundreds place is 8 and 8 > 5, so the estimated number = 55000.
In number 55610, the digit at hundreds place is 6 and 6 > 5, so the estimated number = 56000.
∴ Estimated difference = 56000 – 55000
= 1000
Actual difference =55610-54862 = 748
Comparing the two differences, we see that 1000 > 748, i.e.,
Estimated difference > Actual difference.
Hence, 1000 is the approximate answer.
2. We can estimate the product and quotient of numbers by rounding off the numbers to the greatest place.
Example 3: Let us estimate 97 × 472 to the nearest hundred.
Solution:
97 is rounded off to 100 and 472 is rounded off to 500.
∴ Estimated product = 100 × 500
= 50000
Example 4: Let us estimate the quotient of 4428 ÷ 359 to the nearest hundred.
Solution:
4428 is rounded off to 4400 and 359 is rounded off to 400.
Estimated quotient = 4400 ÷ 400
= 11
Note:
If a number contains two digits then round off the number to the nearest ten and if the number contains three digits then round off the number to the nearest hundred and so on.