Welcome, math explorers! A ratio is a numerical relationship between the amounts of two or more quantities that have been represented using the same unit. It helps us compare things!
We use a special symbol ":" to show a ratio. The order matters! The first number is the first term, and the second is the second term. Since a ratio does not change with the units used, we don't need to write the unit in the final ratio.
Did you know ratios can wear disguises? An equivalent ratio looks different but has the exact same value! A ratio equivalent to a given ratio can be obtained by multiplying each term of the ratio by the same number (greater than zero).
You can also find them by dividing each term of the ratio by the same number (except zero).
Time to declutter! A ratio is in its simplest form when both terms are whole numbers and there is no whole number which both terms can be divided by.
To write it in its simplest form, keep dividing both sides of the ratio by the same number until you can't go any further without going into decimals.
What if the units are different? When quantities are measured in different units, the relationship is called a Rate.
For example, measuring the speed of a vehicle (km and hours) or the price of items (rupees and amount). Even the relationship between two currencies of different countries is an exchange rate!