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Math & numbers Ideas & discovery

How to understand percentages once and for all

Understand percentages once and stop getting caught by them.

A course on understanding and practising percentages. It covers what a percent really is, why a twenty percent rise and a twenty percent fall do not cancel, the difference between percent and percentage points, and how to calculate discounts, growth and interest in your head with confidence.

iPhone App Store Get Cadence free

Open Cadence on the App Store, type the sentence when it asks what you want to learn, and answer a few setup questions. Free to start. Android testers can request early access.

Start with three things you can do today

Type this when Cadence asks what you want to learn

Percentages confuse me: percent off, percent increase, percentage points, percent of a percent. Explain them once, properly, with examples from money and the news, so I stop getting them wrong.

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.

  1. Always ask: percent of what?

    Twenty percent off 50 is 10; twenty percent of 500 is 100. The base is the whole game.

  2. Know that up twenty then down twenty is not back to zero

    100 up twenty is 120; 120 down twenty is 96. Percentages apply to the current amount, so rises and falls are not symmetric.

  3. Separate points from percent

    Interest going from ten to fifteen percent is five percentage points and a fifty percent rise. A headline picks whichever sounds bigger.

Best for
Math & numbers
Prerequisites
None. Bring the situation you have.
Course length
7 to 30 lessons, sized to your goal
Lesson pace
About 10 minutes a day
Format
Read it, or play the audio
Access
Available on the App Store, with early features and Android testing access

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.

  1. Where do percentages trip you up: shopping, pay rises, interest, or the news?
  2. Can you find ten percent of a number quickly now?
  3. Is this for daily life, work, or exams?

Right for now

If any of this sounds familiar, start here.

Percent off never comes out right

You are not sure whether the deal is good.

Rises and falls confuse you

Up twenty, down twenty, and you are somehow worse off.

Percentage points sound like a trick

Because in a headline they very often are one.

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

Parts of a hundred

The idea, and the base it always depends on.

Percent of and percent off

Fast methods, in your head.

Increase and decrease

Why they are not symmetric.

Percentage points

The difference, and the headlines that blur it.

Reverse percentages

Finding the original price from the sale price.

Compounding

Repeated percentages, from interest to inflation.

What changes

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

You will be able to

Understand what a percent is

Parts of a hundred, and why the base matters most.

Calculate the common cases

Of, off, increase, decrease, and reverse.

Tell percent from percentage points

And spot when a headline is using the wrong one.

Handle growth and interest

Compounding, and why repeated percentages multiply.

Ideas this course corrects

A twenty percent drop after a twenty percent rise puts you back where you started

It leaves you four percent down. Percentages are always of the current amount.

Percent and percentage points are the same

From ten to fifteen percent is five points and a fifty percent increase. Both describe the same change; a clear explanation identifies which measure it uses.

Course questions

What to know before you start.

How to understand percentages once and for all: what can I do today?

Always ask: percent of what?. Twenty percent off 50 is 10; twenty percent of 500 is 100. The base is the whole game. Know that up twenty then down twenty is not back to zero. 100 up twenty is 120; 120 down twenty is 96. Percentages apply to the current amount, so rises and falls are not symmetric. Separate points from percent. Interest going from ten to fifteen percent is five percentage points and a fifty percent rise. A headline picks whichever sounds bigger.

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?

A course on understanding and practising percentages. It covers what a percent really is, why a twenty percent rise and a twenty percent fall do not cancel, the difference between percent and percentage points, and how to calculate discounts, growth and interest in your head with confidence. It sits under Math & numbers in the Ideas & discovery part of the library.

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?

Courses run 7 to 30 lessons of about 10 minutes, sized to what you asked for. One lesson a day is the intended pace, and you can go faster. 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.

Start today

Type it, answer a few questions, open Lesson 1.

The sentence to type

Percentages confuse me: percent off, percent increase, percentage points, percent of a percent. Explain them once, properly, with examples from money and the news, so I stop getting them wrong.
iPhone App Store Get Cadence free

Open Cadence on the App Store, type the sentence when it asks what you want to learn, and answer a few setup questions. Free to start. Android testers can request early access.

Android early access

Join Cadence on Android.

Tell us your goal and Google Play email. We will send your tester invite when it is ready.

Use the email on the Google account you use with Google Play. We only use it for your tester invite and Android testing updates.