Estimating Quotients by Rounding Dividends & Divisors

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

Have you ever wanted to complete tricky division problems without a calculator? If you learn how to round dividends and divisors, you can get an estimation for the answer or quotient.

Mental Math

You are trying to get a job to make some money! Your friend says that at his job, he worked 29 hours last week and made $265.32. He says he could get you a job, but you want to know what his hourly pay is because you got offered $8 an hour at another place. You don't have your calculator on you and need to make a quick decision. No worries! We can round those numbers and figure out the hourly pay real quick.

It is pretty hard to do $265.32 divided by 29 in your head. What you can do is round 265.32 up to $270 and 29 up to 30. Then, you can easily see that 270 divided by 30 is 9. So it makes sense for you to take the job your friend is offering because you will make almost an entire dollar more per hour. Let's see how your calculations compare to the actual division. $265.32 / 29 hour = $9.15 dollars per hour. Pretty close for a quick estimation!


Let's get technical for a bit. What does this all mean...Estimating Quotients by Rounding Dividends and Divisors?

When you divide two numbers, the solution you arrive at is the quotient. In other words, it's the answer you get to a division problem. The dividend is the number that gets divided, while the divisor is the number you divide by. In other words, the dividend will be 'inside the house' and the divisor will be 'outside the house'. If you are using a fraction bar, the dividend will be on top and the divisor will be on bottom.

So when we say we are rounding the dividend and divisor, we are rounding the two starting numbers so we can estimate the final answer or the quotient. This is exactly what we did in our example. We rounded the dividend of $265.32 to $270 and rounded the divisor of 29 to 30. This way, we estimated our quotient to be $9 per hour.

Division Example

Compatible Numbers

When estimating quotients, we want to round our dividends and divisor so that they are compatible. Compatible numbers are two numbers that can easily be divided. For example, 90 and 9 are compatible numbers because 90 can be divided by 9 evenly to equal 10. 91 and 9 are not compatible numbers because 9 does not go into 91 evenly. 91 divided by 9 equals 10.11 which is not a nice rounded number. The quotient must be a whole number without decimals to be compatible.

Compatible Numbers


So, how does this all work? To divide more complicated numbers, all you need to do is round the dividend and divisor so that they are compatible! Let's look at some more examples to see this in action!

Example 1

Let's say you are trying to divide 3,754 by 587. When you divide those two numbers with a calculator, you will get the decimal 6.39522998... Not pretty! We can estimate this without even using a calculator by finding compatible numbers. There is not a simple trick to this - it's more about knowing your times tables.

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