Math & numbers Ideas & discovery

How to do mental math fast

Do the sums in your head before anyone reaches for a phone.

A suggested learning goal for everyday arithmetic. Practice splitting numbers, calculating percentages and checking estimates. Start with the worked examples below, then ask Cadence for a course shaped around the situations you want to handle.

Want new features first?

Start with three things you can do today

A starting goal

I want to do mental arithmetic quickly: tips, discounts, splitting bills and rough estimates. Teach me the tricks people use and get me practicing until they are automatic.

Change any word so it fits your situation. The course is built from what you type and a few setup questions.

Start today

Three things you can do before the course exists.

Useful on their own. The course is for when you want the whole skill, not just the first move.

Split a sum, then check it
Try 47 + 38. Split 38 into 30 and 8: 47 + 30 = 77, then 77 + 8 = 85. A second route is 47 + 40 - 2 = 85. Both work; choose the one you can explain. Your turn: 58 + 27. Answer: 58 + 20 + 7 = 85. These are worked practice examples, not a speed test.
Build a percentage from smaller pieces
For 17.5% of 80, find 10% = 8, 5% = 4 and 2.5% = 2. Add them: 8 + 4 + 2 = 14. If that is a discount on an 80 price, the new price is 80 - 14 = 66, before any extra charges. Your turn: find 15% of 60. Answer: 6 + 3 = 9. The percentage amount and the final price are different answers.
Round a multiplication, then undo the extra
For 49 x 6, use 50 x 6 = 300, then subtract the extra 1 x 6: 294. Subtracting just 1 would give 299, which is wrong because all six groups were rounded up. Your turn: 39 x 7. Answer: 40 x 7 - 7 = 273. An estimate of about 280 checks the scale; it does not replace the exact answer.

Sources: OpenStax: why splitting and compensating work; Open University: everyday arithmetic and percentages. Practical examples are starting points, not promised results.

Best for: Math & numbers
Prerequisites: None. Bring the situation you have.
Course length: 7 to 30 lessons
Pace: Yours. One lesson at a time, as often as you like.
Format: Read it, or play the audio
Access: Available on the App Store and Google Play, with an optional early testing list

Before the course is built

Setup asks about your situation first.

Lesson 1 opens on the moment you describe, and the examples use your role. For this request, expect questions like these.

Where do you want to be quicker: shopping, restaurants, work numbers, or generally?
Which feels comfortable already: times tables, addition, or neither yet?
Would you rather be exact, or fast and roughly right?

Right for now

If any of this sounds familiar, start here.

You reach for the calculator for everything

You would like another way to handle everyday sums.

Splitting a bill takes a minute of silence

You want to understand the steps before finding the total.

You want to sanity check numbers

You want to check whether a figure is in the right range.

Course arc

Where the course goes, in order.

Cadence writes the lessons for you, so the exact path follows your answers. This is the ground a course built from this sentence covers.

01 / 06

Choose friendly numbers

Split a sum into parts and explain why the result stays the same.

Addition and subtraction

Rounding and compensating.

Multiplication

Doubling, halving and splitting.

Percentages, tips, discounts

Find the percentage amount, then distinguish it from the final bill or price.

Estimation

Being roughly right fast.

Practice

Try a fresh example and explain how you checked it.

What changes

What you will be able to do, and what you will stop believing.

You will be able to

Break numbers apart

Rounding, compensating, and working left to right.

Handle percentages

Build common percentages from 10%, 5% and smaller parts.

Estimate well

Use a rough range to check an answer, then calculate exactly when needed.

Practice and check

Explain a method, try a new sum, and check your answer.

Ideas this course corrects

Mental math is a memory feat

Remembered number facts can help, but you can also split a calculation into smaller steps and check each one.

Estimating is cheating

An estimate checks the scale of an answer. Use an exact calculation when the precise amount matters; a calculator is a useful check.

Course questions

What to know before you start.

How to do mental math fast: what can I do today?

Split a sum, then check it. Try 47 + 38. Split 38 into 30 and 8: 47 + 30 = 77, then 77 + 8 = 85. A second route is 47 + 40 - 2 = 85. Both work; choose the one you can explain. Your turn: 58 + 27. Answer: 58 + 20 + 7 = 85. These are worked practice examples, not a speed test. Build a percentage from smaller pieces. For 17.5% of 80, find 10% = 8, 5% = 4 and 2.5% = 2. Add them: 8 + 4 + 2 = 14. If that is a discount on an 80 price, the new price is 80 - 14 = 66, before any extra charges. Your turn: find 15% of 60. Answer: 6 + 3 = 9. The percentage amount and the final price are different answers. Round a multiplication, then undo the extra. For 49 x 6, use 50 x 6 = 300, then subtract the extra 1 x 6: 294. Subtracting just 1 would give 299, which is wrong because all six groups were rounded up. Your turn: 39 x 7. Answer: 40 x 7 - 7 = 273. An estimate of about 280 checks the scale; it does not replace the exact answer.

Is this a fixed course?

No. Cadence builds the course when you type the sentence and answer a few setup questions, so the lessons follow your situation. This page describes what a course built from this request covers. You see the whole path before Lesson 1.

Who is this course for?

Do I need any prior experience?

No. Setup asks what you already know and where you want to use it, and the course starts from there. Bring a real situation if you have one; the examples are built around it.

How long does it take?

Most courses run 7 to 30 lessons. The course length is sized to what you asked for. You set the pace: one lesson at a time, as often as you like. Lessons can be read or played as audio.

Does this course award a certificate or degree?

No. Cadence is for practical self-learning and does not award accredited degrees or professional certification.