# How to Make Estimates (Mental Math)

Making an estimate is to simplify a problem in order to make it easier to solve in your head. The purpose is to find an approximate answer. When you make an estimate, it’s important to follow these rules in order to get an approximation that is as close as possible to the real answer:

Rule

### MakinganEstimate

Round up and down for every other number

Subtraction and division:

Round each number up or each number down

Example 1

If you’re at the store buying three bananas for $\text{}1.07$ per banana and one gallon of milk for $\text{}1.92$, it’s easier to make an estimate than to find the exact sum. Using the rules above, the calculation is as follows:

You round the price of the banana down from $\text{}1.07$ to $\text{}1.00$. That makes the estimated price of the bananas $\text{}1.00\cdot 3=\text{}3.00$. The price of the milk, $\text{}1.92$, can be rounded up to $\text{}2.00$. The estimated price of your items is

 $\text{}3.00+\text{}2.00=\text{}5.00.$

The real price of the items is

 $3\cdot \text{}1.07+\text{}1.92=\text{}5.13,$

which isn’t far off from \$$5.00$. In this example, you might have noticed that the estimate is lower than the actual price. This is unfortunate, because you might have tricked yourself into believing you had enough money. For that reason, you should always make your estimate at the store in such a way that it’s higher than the actual price. That way, you are certain to have enough money. You could do like this, for instance:

You round the price of the banana from $\text{}1.07$ to $\text{}1.00$. Then, the estimated price of the bananas is $\text{}1.00\cdot 3=\text{}3.00$. You can estimate the price of the milk, which is $\text{}1.92$, to be $\text{}2.50$. Your estimate of the price is then

 $\text{}2.50+\text{}3.00=\text{}5.50.$

If you have \$$5.50$, you know that you have enough to pay for the items.

Example 2

You have $\text{}\text{}5.36\text{}$, and are about to buy a t-shirt for $\text{}\text{}3.79\text{}$. How much money do you have left after buying the t-shirt?

In this problem, we’re dealing with differences, and you should therefore either round both numbers up or down. In this instance, you choose to round up. That means you estimate to have

 $\text{}5.50-\text{}4.00=\text{}1.50$

The exact difference is

 $\text{}5.36-\text{}3.79=\text{}1.57,$

so you have \$$0.07$ more left in your wallet than you estimated.

Note! When estimating calculations, it’s important to think through whether you want the estimate to be too high or too low. This is a good rule of thumb:

Rule

### Tips

If it’s money going out of your wallet, the estimate should be too high. If it’s money going into your wallet, the estimate should be too low.

Math Vault

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