The Ratio $r: H$ Is $5: 8$ And The Ratio $h: U$ Is $4: 7$.Work Out The Ratio $r: H: U$ In Its Simplest Form.

**The Ratio $r: h: u$ in Its Simplest Form** =====================================================

Introduction

In this article, we will explore the concept of ratios and how to simplify them. We will use the given ratios $r: h$ and $h: u$ to find the ratio $r: h: u$ in its simplest form.

Understanding Ratios

A ratio is a way of comparing two or more numbers. It is usually expressed as a fraction or a colon (:). For example, the ratio $a: b$ can be written as $\frac{a}{b}$ or $a:b$. Ratios can be used to compare quantities, such as the ratio of the number of boys to girls in a class, or the ratio of the length of a rectangle to its width.

Given Ratios

We are given two ratios:

• $r: h = 5: 8$
• $h: u = 4: 7$

Our goal is to find the ratio $r: h: u$ in its simplest form.

Finding the Ratio $r: h: u$

To find the ratio $r: h: u$, we need to find a common multiple of the two given ratios. We can do this by multiplying the two ratios together.

First, let's find the least common multiple (LCM) of the two ratios. The LCM of $5: 8$ and $4: 7$ is $5 \times 7 = 35$.

Now, we can multiply the two ratios together:

$$\frac{5}{8} \times \frac{4}{7} = \frac{20}{56}$$

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is $4$.

$$\frac{20}{56} = \frac{5}{14}$$

So, the ratio $r: h: u$ in its simplest form is $5: 14: 49$.

Conclusion

In this article, we used the given ratios $r: h$ and $h: u$ to find the ratio $r: h: u$ in its simplest form. We found that the ratio $r: h: u$ is $5: 14: 49$.

Q&A

Q: What is a ratio? A: A ratio is a way of comparing two or more numbers. It is usually expressed as a fraction or a colon (:).

Q: How do I find the ratio $r: h: u$ in its simplest form? A: To find the ratio $r: h: u$ in its simplest form, you need to find a common multiple of the two given ratios. You can do this by multiplying the two ratios together and then simplifying the resulting fraction.

Q: What is the least common multiple (LCM) of two ratios? A: The LCM of two ratios is the smallest number that both ratios can divide into evenly.

Q: How do I simplify a fraction? A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD) of two numbers? A: The GCD of two numbers is the largest number that both numbers can divide into evenly.

Q: How do I find the GCD of two numbers? A: To find the GCD of two numbers, you can use the Euclidean algorithm or simply list the factors of each number and find the largest common factor.

Q: What is the ratio $r: h: u$ in its simplest form? A: The ratio $r: h: u$ in its simplest form is $5: 14: 49$.

Q: How do I use ratios in real-life situations? A: Ratios can be used in a variety of real-life situations, such as comparing the number of boys to girls in a class, or comparing the length of a rectangle to its width.

Q: What are some common applications of ratios? A: Some common applications of ratios include finance, science, and engineering. Ratios can be used to compare interest rates, stock prices, or the strength of materials.

Q: How do I convert a ratio to a decimal? A: To convert a ratio to a decimal, you can simply divide the numerator by the denominator.

Q: How do I convert a decimal to a ratio? A: To convert a decimal to a ratio, you can simply express the decimal as a fraction and simplify it.

Q: What is the difference between a ratio and a proportion? A: A ratio is a comparison of two or more numbers, while a proportion is a statement that two ratios are equal.