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Numbers, made useful.

Practical guides for the calculations that come up in everyday life. Follow a worked example, understand the assumptions, and try the matching calculator.

15 original guides5 topicsOne clear illustration per article

15 articles

A comparison of an original value of 80 and a new value of 100, showing a 25 percent increase.
Everyday maths3 min read

Percentage Change: Why the Starting Number Matters

Calculate an increase or decrease, distinguish percentage points, and understand why reversing a change gives a different percentage.

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Three price cards show 100 reduced to 80 by a 20 percent discount and then to 72 by a further 10 percent discount.
Shopping3 min read

Two Discounts Do Not Simply Add Together

Work out successive discounts, find the effective reduction, and reverse a sale price to recover the original amount.

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Two grocery packs compare 750 grams for 90 at 120 per kilogram with one kilogram for 125.
Shopping3 min read

Compare Unit Prices Without Being Misled by Pack Size

Put different pack sizes on the same basis, handle grams and kilograms, and compare multipacks with a worked example.

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A bill of 240 plus a tip of 36 produces a total of 276, divided among four people at 69 each.
Everyday maths3 min read

Split a Bill and Tip Without Losing Track of the Total

Calculate a shared bill, apply a tip once, and distribute rounding remainders so everyone’s payment adds up.

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An exact one-third share of 100 is allocated as 33.33, 33.33, and 33.34 so the total remains 100.
Everyday maths3 min read

When to Round: Small Decimal Choices That Change a Total

Understand intermediate rounding, line-item totals, and leftover cents using clear examples and reproducible steps.

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A starting balance of 1000 grows to 1050, 1102.50, and 1157.63 with annual compounding at a hypothetical 5 percent rate.
Money maths3 min read

Simple and Compound Interest: Follow the Balance Year by Year

Compare simple and compound interest with a hypothetical fixed-rate example, and separate a model from a promised return.

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A first monthly loan payment of about 888.49 is split into 100 of interest and 788.49 of principal on a 10000 loan.
Money maths3 min read

What a Loan Payment Contains: Principal, Interest, and the Remaining Balance

Understand a standard fixed-rate amortizing payment with a worked monthly example and a clear separation of fees.

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A value growing from 1000 to 1210 over two years has a 21 percent total return and a 10 percent compound annual growth rate.
Money maths3 min read

Total Return and Annualized Return Answer Different Questions

Compare a total gain with its equivalent compound annual growth rate, and understand when contributions make the shortcut unsuitable.

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A one metre square has sides of 100 centimetres, containing 100 times 100 or 10000 square centimetres.
Measurements3 min read

Why Area Conversions Need a Squared Conversion Factor

Convert square metres and square centimetres correctly, distinguish area from perimeter, and avoid a common factor-of-100 mistake.

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Temperature reference points show zero Celsius equals 32 Fahrenheit and 100 Celsius equals 212 Fahrenheit.
Measurements2 min read

Celsius and Fahrenheit: Convert Temperatures and Temperature Changes

Apply the offset and scale factor correctly, and see why a temperature reading differs from a temperature interval.

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A calendar strip from October 14 to October 17 highlights three elapsed days and four included calendar dates.
Dates and time3 min read

Days Between Dates: Elapsed Days and Inclusive Counts

Choose whether to include both endpoints, distinguish calendar days from working days, and check a simple date interval.

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A birth date of October 20, 2000 is compared with October 14, 2026, giving 25 completed years before the next birthday.
Dates and time3 min read

Calculating Age Means Comparing Calendar Dates

Calculate completed years accurately, understand why days divided by 365 can be misleading, and handle leap-day edge cases.

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An overnight timeline from 22:30 to midnight and then 01:15 shows 90 minutes plus 75 minutes, totaling 2 hours 45 minutes.
Dates and time3 min read

Calculate a Time Difference That Crosses Midnight

Convert clock readings to minutes, add the next-day boundary correctly, and distinguish local clock time from elapsed time.

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A route of 90 kilometres at 60 kilometres per hour takes 1.5 hours, which is 90 minutes.
Measurements3 min read

Speed, Distance, and Time: Put the Units in Agreement First

Use the distance-speed-time triangle correctly, convert minutes to hours, and distinguish moving speed from trip-average speed.

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An example combines a score of 80 with weight 40 percent and a score of 90 with weight 60 percent to produce 86.
Everyday maths3 min read

Weighted Averages: When Each Number Does Not Count Equally

Calculate weighted averages, handle counts and percentages, and avoid averaging averages without their original group sizes.

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