Percentages, ratios, fractions, LCM and HCF, and simple interest — the everyday formulas behind basic number work.
These pages explain formulas for reference. They don't mean Mathover can solve every problem that uses them — interactive calculations are limited to the linked tools.
A percentage means “out of 100”, so divide the percentage by 100 to turn it into a multiplier, then multiply the quantity.
Any quantity. The result has the same units as Q.
Find 15% of 240 kg.
Answer: 36 kg
Find how much the value changed, compare it to the starting value, then express that as a percentage. A positive result is an increase; a negative result is a decrease.
The original value must not be 0 — a change from 0 has no percentage.
A price rises from $80 to $92. What is the percentage change?
Answer: 15% increase
Add the parts of the ratio to find how many equal parts there are, find the size of one part, then multiply by each person's number of parts.
Ratio parts must be positive. Extends to more parts: a ÷ (a + b + c) × T, and so on.
Share $120 in the ratio 3 : 5.
Answer: $45 and $75
Rewrite both fractions over a common denominator, add the numerators, then simplify. Using the lowest common denominator keeps numbers small.
Denominators b and d must not be 0. Simplify the result by dividing top and bottom by their HCF.
Work out 2/3 + 1/4.
Answer: 11/12
For two positive whole numbers, the highest common factor and lowest common multiple multiply to give the product of the numbers. Knowing one lets you find the other.
Exactly two positive integers. It does not hold for three or more numbers in general.
The HCF of 12 and 18 is 6. Find their LCM.
Answer: LCM = 36
Simple interest is paid only on the original amount, so it grows by the same amount each period.
Only for simple (not compound) interest. r and t must use the same time unit.
$500 is invested at 4% per year simple interest for 3 years. Find the interest.
Answer: $60
Reference only — no interactive Mathover tool for this formula yet.