Understanding Ratio Applications

What Are Ratios?

A ratio is a way to compare two or more quantities. It tells us how much of one thing there is compared to another. Ratios can be written in three different ways:

• Using a colon: 3:2
• As a fraction: $\frac{3}{2}$
• In words: 3 to 2

Using Ratios in Real Life

Ratios are used in various real-life situations, such as:

• Cooking: Recipes often use ratios to ensure the right balance of ingredients.
• Maps: Scale ratios help us understand distances on maps.
• Mixing: Ratios are used to mix paints or chemicals in specific proportions.

Proportion and Similar Ratios

Proportion means that two ratios are equal. For example, if $\frac{a}{b} = \frac{c}{d}$, then $a, b, c,$ and $d$ are in proportion.

When comparing similar ratios, we can find unknown values using cross-multiplication.

Rates

A rate is a special type of ratio where two quantities with different units are compared. For example, speed is a rate that compares distance to time, like 60 km/h.

Solving Rate Problems

To solve rate problems, use the formula:

$$\text{Rate} = \frac{\text{Distance}}{\text{Time}}$$