# Mental math

Mental math is a term usually used to refer to doing calculations such as addition, subtraction, multiplication, or division without using paper and pencil or a calculator. Essentially, mental math refers to doing the math in your head. The use of the term is usually reserved for simpler arithmetic applications, but it is possible to perform more complicated mathematics in your head; this would qualify as "mental math" as well.

## Mental math strategies

There are many ways to do mental math. Below are some examples, but there are many others.

### Counting on

For simpler addition problems, such as 5 + 3, we can just keep adding 1. 3 is made up of 3 1's, so we can add 3 1's to 5.

5 + 1 = 6

6 + 1 = 7

7 + 1 = 8

Therefore:

5 + 3 = 8

This method could be helpful for those who are just starting to learn addition.

### Using basic facts

If a 6-pack of candy bars costs \$2.40, How much does each candy bar cost?

2.40 ÷ 6 = ?

One solution strategy is to think 24 ÷ 6 = 4 (using a basic fact). Based on this fact, and how the decimal numeration system works, we can shift the decimal point as follows to solve the problem:

2.40 ÷ 6 = 0.40

Therefore each candy bar costs \$0.40.

### Using front-end estimation

Bob and Joan traveled 313 miles on the first day of their trip and 178 miles on the second day. How many miles did they travel in total?

313 + 178 = ?

We can simplify the addition problem by breaking the values up and adding the 100s, 10s, and 1s values separately. After that, we can add them back together:

300 + 100 = 400

10 + 70 = 80

3 + 8 = 11

400 + 80 + 11 = 491

Thus, Bob and Joan traveled 491 miles in total.

We can do this because of the way our number system, the decimal system works. In this system, each place value represents a power of 10.

### Using compatible numbers:

The 32 students in Mr. Clark's class surveyed their favorite fast foods. Of these students, 13 listed pizza as their favorite. How many listed some other food?

32 - 13 = ?

One solution strategy is to think 32 is close to 33. 33 and 13 are compatible numbers. That is, 33 - 13 is easy to compute mentally:

33 - 13 = 20

33 is 1 more than 32, so we need to subtract 1 from 20.

20 - 1 = 19

Therefore, in Mr. Clark's class, 19 students listed some fast food other than pizza as their favorite.