Understanding ratios

Learning Objectives Define what a ratio is and identify its components. Express ratios in three different forms (a:b, a/b, a to b). Simplify ratios to their simplest form by finding the Greatest Common Factor (GCF). Identify and create equivalent ratios. Distinguish between part-to-part and part-to-whole ratios. Apply ratios to solve real-world problems involving comparisons of quantities. Have you ever followed a recipe that says '2 parts flour to 1 part sugar'? 🍰 That's a ratio! It's a way we compare amounts of different things. In this lesson, you'll learn all about ratios – what they are, how to write them, and how to simplify them. Understanding ratios is a fundamental skill that helps us compare quantities and make sense of relationships in t...

TermDefinitionExample RatioA ratio is a comparison of two quantities by division. It shows how much of one quantity there is compared to another quantity.If there are 3 apples and 2 bananas, the ratio of apples to bananas is 3 to 2. AntecedentThe first term in a ratio. It is the quantity being compared.In the ratio 3:2 (apples to bananas), '3' is the antecedent. ConsequentThe second term in a ratio. It is the quantity to which the first quantity is being compared.In the ratio 3:2 (apples to bananas), '2' is the consequent. Forms of a RatioRatios can be written in three main ways: using a colon (a:b), as a fraction (a/b), or using the word 'to' (a to b).The ratio of 3 apples to 2 bananas can be written as 3:2, 3/2, or 3 to 2. Equivalent RatiosEquivalent ratios...

Expressing a Ratio A ratio comparing quantity $a$ to quantity $b$ can be written as: $a:b$, $rac{a}{b}$, or $a \text{ to } b$. This rule defines the three standard notations for writing any ratio. The order of the quantities is crucial and must match the order of comparison. Simplifying Ratios To simplify a ratio $a:b$ (or $rac{a}{b}$), divide both $a$ and $b$ by their Greatest Common Factor (GCF). The simplified ratio is $rac{a \div \text{GCF}}{b \div \text{GCF}}$. This rule is used to reduce a ratio to its simplest form, making it easier to understand and compare. Both quantities must be divided by the same factor. Finding Equivalent Ratios To find an equivalent ratio for $a:b$, multiply or divide both $a$ and $b$ by the same non-zero number $k$: $(a \times k):(b...