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## Estimating Quotients

#### Introduction

A quotient is the result of one number divided by another. For example, the quotient of 100 and 5 is 20, because 100 ÷ 5 = 20. To quickly work out a rough answer to a quotient, we can use rounding to give us an estimate. For example, because we know the quotient of 100 and 5 is 20, we can estimate that the quotient of 102 and 5 is somewhere around 20.

Estimating gives us a rough (i.e. not precise) answer, but lets us do it quickly and effectively.

## Lesson

To estimate the quotient of a number, you need to round the numbers to ones you are comfortable working with. For example, if you try and work out the quotient of 1027 and 11, you will struggle; however, if you round the numbers to 1000 and 10, you can get an estimated quotient of 100.

To round numbers, you need to find a 'landmark' number that you can round to. Most of the time, these are numbers with a single digit followed by zeroes (for example, 50, 100, 12,000) although there may be some single digit numbers you are capable of using (generally 1 to 5). Don't round any numbers to 0 or you won't be able to estimate a quotient.

So, let's take the following sum:

597 ÷ 31 = ?

To estimate, let's round 597 to 600 and 31 to 30.

That gives us 600 ÷ 30, which gives us a quotient of 20. The actual answer is 19.26, so our estimate was close.

We can also estimate quotients involving decimals with the same principle. For example, if we have 7.789 and 1.917, we can find an estimated quotient by rounding. We can round 7.789 to 8 and 1.917 to 2.

That gives us 8 ÷ 2, which is 4. The actual answer is 4.06, so our estimate was very close.

## Examples

$620 \div 29$
$620$ / $29$ -> $580$ / $29$
$620$ / $29$ ~ $20$