# Mastering Quantity Division in Ratios: A Step-by-Step Guide

Hey there, math enthusiasts! Today, we’re diving into the world of dividing quantities in specified ratios. If you’ve ever wondered how to divide a given quantity in a given ratio, such as dividing \( 200 \) in the ratio \( 2:3 \) or dividing \( 600 \) in the ratio \( 2:3:5 \), you’re in the right place. In this expert guide, we’ll demystify the process of dividing quantities using ratios. By the end of this article, you’ll be equipped with step-by-step techniques to tackle quantity division like a pro.

## Understanding Ratios and Their Significance

### What Are Ratios?

Ratios are the building blocks of mathematics, providing a means to compare two quantities. For instance, when you have \( 2 \) apples and \( 3 \) bananas, the ratio of apples to bananas is expressed as \( 2:3 \). Ratios are incredibly versatile and can be found everywhere, from kitchen recipes to financial calculations and even in construction projects.

### Why Do Ratios Matter?

Ratios hold immense significance as they serve as the foundation for more complex mathematical concepts. Moreover, they find extensive applications in real-life scenarios, allowing us to scale recipes for gatherings, calculate interest rates, and determine the right proportions of ingredients in chemical reactions.

## The Step-by-Step Approach: Dividing Quantity in Ratios

Now, let’s embark on the exciting journey of dividing quantities within ratios. We’ll explore three fundamental techniques to simplify the process effectively.

Let’s put this into practice with an example:

**Example 1:** Divide \( 200 \) in the ratio \( 2:3 \).

\( \displaystyle \begin{align} 200 \times \frac{2}{2+3} &=80 \\ 200 \times \frac{3}{2+3} &= 120 \end{align} \)

**Example 2:** Divide \( 1000 \) in the ratio \( 2:3:5 \).

\( \displaystyle \begin{align} 1000 \times \frac{2}{2+3+5} &= 200 \\ 1000 \times \frac{3}{2+3+5} &= 300 \\ 1000 \times \frac{5}{2+3+5} &= 500 \end{align} \)

## Real-Life Applications

Understanding these techniques holds practical implications in various real-life scenarios.

### Scaling Recipes

Imagine the need to adjust a recipe to cater to a larger or smaller group. Ratios come to your rescue, and simplifying them ensures accurate ingredient scaling.

### Financial Calculations

In finance, interest rates, investments, and loans often involve ratios. Simplifying these ratios enables you to comprehend their financial implications better.

### Engineering

In the realm of engineering, precise ratios are paramount. Simplification guarantees that you’re working with the correct proportions, a critical factor in achieving desired results.

## Conclusion

Congratulations! You’ve embarked on a journey through the realm of dividing quantities within ratios, equipping yourself with valuable skills. These skills are not only fundamental in mathematics but also highly applicable in numerous real-life situations. Keep practising, and soon you’ll be dividing quantities within ratios with the confidence and precision of an expert.

## Question 1

Divide \( 500 \) in the ratio \( 2 : 3 \).

\( \displaystyle \begin{align} \frac{2}{2+3} \times 500 &= 200 \\ \frac{3}{2+3} \times 500 &= 300 \\ 500 \text{ is divided by } &200 \text{ and } 300. \end{align} \)

## Question 2

Divide \( 600 \) in the ratio \( 2 : 3 : 5 \).

\( \displaystyle \begin{align} \frac{2}{2+3+5} \times 600 &= 120 \\ \frac{3}{2+3+5} \times 600 &= 180 \\\frac{5}{2+3+5} \times 600 &= 300 \\ 600 \text{ is divided by } &120, 180 \text{ and } 300. \end{align} \)

## Question 3

The ratio of boys to girls is \( 4 : 5 \). If there are \( 225 \) students, find how many more girls than boys.

\( \displaystyle \begin{align} \frac{4}{4+5} \times 225 &= 100 \text{ boys} \\ \frac{5}{4+5} \times 225 &= 125 \text{ girls} \\ \text{There are } 25 &\text{ more girls than boys.} \end{align} \)

## Question 4

David earns twice as much as Emily. If the sum of their wages is \( \$180 \ 000 \), how much does each earn?

\( \displaystyle \begin{align} \frac{2}{2+1} \times \$180 \ 000 &= \$120 \ 000 \text{ David} \\ \frac{1}{2+1} \times \$180 \ 000 &= \$60 \ 000 \text{ Emily} \end{align} \)

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