  Math Topics

# How to Do Mental Math (Rounding)

Estimates are something I often use when I’m doing mental arithmetic. Making an estimate involves choosing simpler numbers than the exact numbers you have. The answer is not exactly correct, but you still get an answer that is pretty close to the exact answer.

To make the best possible estimates, you have to follow some fixed rules. These rules depend on the situation you are in, when you want to make an estimate. For example, if you want to be completely sure that you have enough money at the store, you should always choose numbers that are larger than the original number. When you make an estimate, count up to the nearest ten and use that number instead. Take a look at the examples below:

Example 1

Here you can see several different examples of estimates:

The estimate of $12$ is $20$, because $20$ is the first ten you reach when you count upwards from $12$.

The estimate of $43$ is $50$, because $50$ is the first ten you reach when you count upwards from $43$.

The estimate of $79$ is $80$, because $80$ is the first ten you reach when you count upwards from $79$.

The estimate of $55$ is $60$, because $60$ is the first ten you reach when you count upwards from $55$.

What is the estimate of the numbers 30 and 97?

Because $30$ is already a ten, we do not need to make an estimate, we can keep it as it is! That means that the estimate of $30$ is $30$. This applies to all tens.

$100$ consists of $10$ tens, so when we are making an estimate of $97$, $100$ is the first ten we reach when we count upwards. That means the estimate of $97$ is $100$.

What do you think will happen if you estimate the prices to be lower than the real prices when you go shopping?

The most important thing to do when you go shopping is to bring enough money. If you always estimate the prices to be a bit higher than they really are, your estimated sum will always be higher than what you actually have to pay. If you have enough money to cover the estimated sum, you definitely have enough money to pay for the items you wanted. That’s nice!

If you estimate the prices to be lower than they actually are, the sum on the receipt might be larger than the sum you estimated in your head. Then you might have to put some items back, and go home without all the things you wanted. That’s no fun!

Example 2

You have $\text{}\text{}6.00\text{}$ in your wallet, and you are about to buy an ice cream for $\text{}\text{}1.70\text{}$ and a soda for $\text{}\text{}2.60\text{}$. Do you have enough money to buy both of them?

To answer that question, you first have to find out what the two items cost all together. That’s easier if you make an estimate. It would look like this:

The estimate of $$1.70$ is$$2.00$. The estimate of $$2.60$ is$$3.00$.

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

As $$5.00$ is less than$$6.00$, you have enough money to buy both the ice cream and the soda.

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