Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Definition: A ratio is a way to compare two or more quantities of the same kind to show how much of one thing there is compared to another.
Notation: Ratios are written using a colon (:) to separate the numbers, for example, 2:3 (read as 'two to three').
Order Matters: The order of numbers in a ratio must match the order of the objects being described (e.g., if there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3).
Simplifying Ratios: Like fractions, ratios can be simplified by dividing all numbers in the ratio by their Highest Common Factor (HCF).
Ratios vs. Fractions: A ratio compares part-to-part (2:3), while a fraction usually compares part-to-whole (2/5).
📐Formulae
Ratio of A to B =
Simplest Form = (where is the HCF of and )
Total Parts =
💡Examples
Problem 1:
In a pencil case, there are 5 blue pens and 7 red pens. What is the ratio of blue pens to red pens?
Solution:
5 : 7
Explanation:
Since we want the ratio of 'blue to red', we place the number of blue pens (5) first and the number of red pens (7) second.
Problem 2:
A recipe uses 10 cups of flour and 4 cups of sugar. Write the ratio of flour to sugar in its simplest form.
Solution:
5 : 2
Explanation:
The initial ratio is 10:4. Both 10 and 4 can be divided by their highest common factor, which is 2. and .
Problem 3:
In a bag of marbles, the ratio of green marbles to yellow marbles is 3:5. What is the total number of 'parts' in this ratio?
Solution:
8 parts
Explanation:
To find the total number of parts in a ratio, you add the terms together: .