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Method for Estimating Quotients

WHAT IS AN ESTIMATION

Estimation is an approximate data close to the accurate data. In real life situations, many times one needs to work out with certain figures which need not be accurate. However, these figures should be compatible to the actual figures and should be used only for guidance.

Estimation is mostly required in division problems as most of the numbers can not be evenly divided by all the numbers. The estimate of a quotient in a division is worked out by suitably rounding off the dividend or/and the divisor in such a way that you don’t get a reminder.

Method for Estimating Quotients

To estimate a quotient in a division, one must have an idea of the common multiples of the divisor and must be mentally able to figure out the correct multiple which is closer to the dividend.

For example, if the dividend is 47 and the divisor is 16, you know 47, lies between 48 and 36. Since 47 is closer to 48 than to 35, the dividend can be rounded as 48 and the quotient can be estimated as 48/16 = 3. This is called rounded up estimate hence if the dividend is 38 for the same divisor 16, the estimated quotient becomes 2. This is called rounded down estimate.

In other words, the approximate quotient lies between two successive multiples of the divisor and you have to choose the one which gives the product closer to the dividend when multiplied with the divisor.

Some times both the dividend and the divisor may not be compatible numbers and in such a case the divisor also rounded suitably to get the estimate of the quotient as a whole number.

Examples on Estimating Quotients

Let us work out a few examples on word problems related to estimation of a quotient.

Example 1

What is the estimate of 2490 ÷ 24?

Both the dividend and the divisor are not compatible numbers for an even division. But if you round up 24 as 25 and 2490 as 2500, the quotient can be estimated as 2500 ÷ 25 = 100.

The actual quotient of 2490 ÷ 24 is 103.75 and is very much closer to 100.

Therefore the estimate of 2490 ÷ 24 is 100.

Example 2

What is the estimate of 9012 ÷ 46?

Both the dividend and the divisor are not compatible numbers for an even division. But if you round down 46 as 45 and 9012 as 9000, the quotient can be estimated as 9000 ÷ 45 = 200.

The actual quotient of 9012 ÷ 46 is 195.91… and is very much closer to 200.

Therefore the estimate of 9012 ÷ 46 is 200.

Logical Reasoning in Estimation

The methods described for estimation of a quotient is only for a general idea. Of course, they can be used to arrive at a solution in real life situations also. But one must be very careful and use the logical reasoning power to properly use the estimates in real life situations. The following example explains such a situation.

Example

A car on an average, runs 485 miles with 25 gallons of gas. Estimate its mileage (the number of miles it could run for 1 gallon of gas).

This is a problem of estimating the quotient by rounding 485 to 500 and then dividing that by 25 which gives an answer of 20.

So, the estimate of mileage of this car is 20 miles per gallon.

The estimate gives only an idea how much fuel you need to top up from time to time.

But if the tank of the car is dry and if you wish to travel 100 miles by filling just 5 gallons of gas, you will land yourself in trouble!