What is mental math?

A barista says $13.75, and you hand over a $20 bill. Before the drawer opens, you already know about $6 is coming back. That quick sum is mental math: working out numbers in your head, without paper or a calculator.

Quick answer: What is mental math?

• Mental math is solving arithmetic in your head, such as a tip, a split bill, or a sale price, without writing anything down or using a calculator.

• The main moves are using numbers you already know by heart (like 6 × 8 = 48), splitting numbers into easier parts, and rounding to an easier number (47 becomes 50) and then adjusting.

• Mental math feels hard because your working memory, the mental workspace that holds numbers while you use them, holds only about three to five chunks of information at a time.

• Practice makes mental math easier.

What is an example of mental math?

A classic example of mental math is adding 47 and 65 in your head. There are three common ways to do it, and all three land on 112:

1. Split both numbers. Add the tens (40 + 60 = 100), then the ones (7 + 5 = 12), then put them together to get 112.

2. Jump. Keep 47 whole and add 65 in two hops: 47 + 60 = 107, then 107 + 5 = 112.

3. Round and adjust. Turn 47 into 50, which adds 3. Then 50 + 65 = 115, and taking the 3 back off gives 112.

Math researchers call round and adjust "compensation." Some mental math gives an exact answer, like 112. Some gives a quick estimate, like knowing that three shirts at $19.99 cost about $60. Exact answers and estimates both count.

What is the mental math method?

The mental math method is a habit, not a single recipe: You look at the numbers and pick the move that makes them easiest. Math education researchers call this flexibility and treat it as an important aim of teaching. Here's how the habit plays out on three everyday errands:

• A 20% tip on a $45 dinner. Find 10% first by moving the decimal point one place left, which gives $4.50. Then double it to get 20%, or $9.

• An $84 bill split four ways. Break $84 into $80 and $4, divide each by four, and each person pays $20 + $1, or $21.

• Three items at $19.99. Round each to $20, which adds a cent to each price. That makes $60, and taking back the three extra cents gives $59.97.

A handful of moves covers most of the math in a normal week. For more of them, try these 10 mental math tricks or this guide to calculating a tip without a calculator.

Why is mental math hard?

Mental math is hard because it runs in your working memory, the small mental workspace that holds information while you use it. Adults can hold only about three to five chunks there at a time. Even single-digit sums draw on working memory. Done the way you learned on paper, 47 + 65 has you add 7 and 5, keep the 2, carry the 1, add the tens, and remember all of it while you finish. That's a lot to hold at once. Splitting, jumping, and rounding each turn that crowded problem into two easy steps.

Stress makes mental math harder, too. People with high math anxiety, a tense or worried feeling about math, have smaller working memory spans on number tasks. That's why a sum that's easy at home can slip away at a busy checkout. There's more on math anxiety in why math feels so hard, and how to make it easier.

If numbers feel tough, you're far from alone. In a 2023 government survey, 34% of US adults ages 16 to 65 scored at the lowest level for numeracy, the skill of using numbers in daily life, up from 29% in 2017.

Is mental math related to IQ?

Mental math is partly tied to IQ, and how much depends on the type of math. One study of 170 young adults found a moderate link: People who scored higher on an intelligence test also tended to solve more arithmetic problems in a set time. In another study of 134 adults, simple sums and exact calculations weren't linked to general thinking skills. So a slow answer at the register isn't a verdict on your intelligence. Practice is the part you control.

How can you get better at mental math?

You get better at mental math with regular practice and quick feedback on your answers. In a small study of 46 university students, the ones who did six 45-minute sessions of arithmetic practice with feedback improved their arithmetic substantially. Here are three ways to start:

• Use the math already in your day. Before you reach for your phone, work out the tip, the split, or the sale price in your head. Then check your answer on your phone, so you get that quick feedback.

• Find your slowest type of problem. The free 60-second mental math game shows your average time per right answer for each type, so you can see whether percents or subtraction slow you down. Then you know which type to practice first.

• Practice a little, often. A few minutes a day keeps the moves fresh, so you reach for them without having to think about which one to use.

What app can you use to practice mental math?

Elevate is a brain training app with 40+ games for memory, reading, writing, and math. Twelve of those games train math, and several are built around everyday money math. A game called Tipping trains common tip percentages, and one called Percentages helps you work out markups and discounts in your head. Division helps you split bills and household expenses, and Estimation makes your quick calculations more accurate. Each game gets harder as you get better, so the practice stays challenging without becoming overwhelming.

You can play one three-game workout a day for free. Elevate Premium, the paid plan, unlocks every game. Try Elevate's math games the next time you have five spare minutes.