Calculator Soup

The fastest method is to move the decimal point. To find 10% of any number, divide it by 10. To find 20%, divide by 10 and double it. To find 5%, halve the 10% figure. For less round percentages, the reliable formula is (percentage / 100) × number. For example, 18% of = (18 / 100) × 50 = . Most people find it easiest to calculate 10% first and build from there for quick mental math.

You cannot add fractions directly unless their denominators match. The first step is finding the least common denominator, which is the smallest number that both denominators divide into evenly. Then convert each fraction so it has that denominator, keeping the overall value the same. Once both fractions share a denominator, add the numerators and leave the denominator unchanged. For example, 1/3 + 1/4 requires a common denominator of 12, giving you 4/12 + 3/12 = 7/12.

The mean is the arithmetic average: add all values and divide by the count. The median is the middle value when data is sorted. They give the same result when data is symmetrical, but they diverge significantly when a dataset contains outliers. For example, if five people earn ,000, ,000, ,000, ,000, and 0,000, the mean is 0,000, which misrepresents most people in the group. The median is ,000, which is far more representative. Median is almost always preferred for income, housing prices, and any dataset with extreme values.

The most reliable manual method is prime factorisation. Break each number down into its prime factors, then identify which prime factors appear in both, taking the lowest power of each shared factor. Multiply those shared factors together to get the GCF. For example, GCF of 48 and 60: 48 = 2⁴ × 3 and 60 = 2² × 3 × 5. The shared factors are 2² and 3, so GCF = 4 × 3 = 12. An alternative is the Euclidean algorithm, which is faster for large numbers: repeatedly replace the larger number with the remainder of dividing the two, until the remainder is zero.

The area of a circle is calculated using the formula A = π × r², where r is the radius (the distance from the centre to the edge) and π is approximately 3.14159. If you are given the diameter instead of the radius, divide it by 2 first. For example, a circle with a radius of 7 cm has an area of π × 49 = 153.94 cm². Circumference, which is the distance around the circle, uses a different formula: C = 2 × π × r. It is important not to confuse the two formulas, as they answer different geometric questions.

Unit conversion always involves multiplying or dividing by a fixed conversion factor. For length: 1 inch = 2.54 cm, and 1 mile = 1.609 km. For weight: 1 pound = 0.4536 kg. For volume: 1 US gallon = 3.785 litres. To convert from a larger unit to a smaller one, multiply by the conversion factor. To go the other direction, divide. For temperature, the formulas are: Celsius to Fahrenheit = (C × 9/5) + 32, and Fahrenheit to Celsius = (F - 32) × 5/9. Keeping a short list of these conversion factors at hand covers the vast majority of everyday conversion needs.

Percentage change measures how much a value has grown or shrunk relative to its starting point, using the formula ((new - old) / old) × 100. Percentage points, by contrast, describe the absolute arithmetic difference between two percentages. If an interest rate rises from 3% to 5%, that is a 2 percentage point increase, but a 66.7% change (because 2 is 66.7% of 3). This distinction matters enormously in finance, economics, and statistics reporting. Saying a figure "increased by 2%" is very different from saying it "increased by 2 percentage points," and confusing the two is one of the most common errors in data communication.