Writing the Ratio Statement as a Fraction

Oct 13, 2025 by wbrum.org 12 views

Introduction

In mathematics, ratios are used to compare the size of two or more quantities. A ratio can be expressed as a fraction, which is a way of representing a part-to-part comparison. In this article, we will focus on simplifying fractions, specifically the ratio statement 56:119, by writing it as a fraction and reducing it to its lowest terms if possible.

What is a Ratio?

A ratio is a comparison of two or more quantities. It is a way of expressing the relationship between two or more numbers. Ratios can be expressed as a fraction, which is a way of representing a part-to-part comparison. For example, the ratio of 2:3 can be expressed as the fraction 2/3.

Writing the Ratio Statement as a Fraction

The ratio statement 56:119 can be written as a fraction by placing the first number (56) on top and the second number (119) on the bottom. This gives us the fraction 56/119.

Reducing the Fraction to Lowest Terms

To reduce a fraction to its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

Finding the Greatest Common Divisor (GCD)

To find the GCD of 56 and 119, we can use the Euclidean algorithm. This algorithm involves dividing the larger number by the smaller number and then replacing the larger number with the remainder. We repeat this process until the remainder is zero.

Step 1: Divide 119 by 56

119 ÷ 56 = 2 with a remainder of 7.

Step 2: Replace 119 with the remainder

We replace 119 with the remainder 7.

Step 3: Divide 56 by 7

56 ÷ 7 = 8 with a remainder of 0.

Step 4: The GCD is 7

Since the remainder is zero, the GCD of 56 and 119 is 7.

Reducing the Fraction

Now that we have found the GCD, we can reduce the fraction 56/119 by dividing both the numerator and the denominator by the GCD.

Reduced Fraction

56 ÷ 7 = 8 119 ÷ 7 = 17

The reduced fraction is 8/17.

Conclusion

In this article, we have learned how to write the ratio statement 56:119 as a fraction and reduce it to its lowest terms. We used the Euclidean algorithm to find the greatest common divisor (GCD) of the numerator and the denominator, and then reduced the fraction by dividing both the numerator and the denominator by the GCD. The reduced fraction is 8/17.

Example Problems

Write the ratio statement 24:36 as a fraction and reduce it to its lowest terms.
Write the ratio statement 48:64 as a fraction and reduce it to its lowest terms.
Write the ratio statement 72:108 as a fraction and reduce it to its lowest terms.

Answer Key

The reduced fraction is 2/3.
The reduced fraction is 3/4.
The reduced fraction is 2/3.

Tips and Tricks

When reducing a fraction, make sure to divide both the numerator and the denominator by the GCD.
Use the Euclidean algorithm to find the GCD of two numbers.
Practice reducing fractions to become more comfortable with the process.

Glossary of Terms

Greatest Common Divisor (GCD): The largest number that divides both the numerator and the denominator without leaving a remainder.
Numerator: The top number in a fraction.
Denominator: The bottom number in a fraction.
Euclidean Algorithm: A method for finding the GCD of two numbers by repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder.
Frequently Asked Questions (FAQs) about Simplifying Fractions ================================================================

Q: What is a fraction?

A: A fraction is a way of representing a part-to-part comparison. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction 3/4 represents the ratio of 3 parts to 4 parts.

Q: How do I write a ratio as a fraction?

A: To write a ratio as a fraction, place the first number (the numerator) on top and the second number (the denominator) on the bottom. For example, the ratio 2:3 can be written as the fraction 2/3.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. It is used to reduce a fraction to its lowest terms.

Q: How do I find the GCD of two numbers?

A: There are several methods for finding the GCD of two numbers, including:

Using the Euclidean algorithm
Listing the factors of each number and finding the greatest common factor
Using a calculator or online tool

Q: What is the Euclidean algorithm?

A: The Euclidean algorithm is a method for finding the GCD of two numbers by repeatedly dividing the larger number by the smaller number and replacing the larger number with the remainder. For example, to find the GCD of 56 and 119, we would divide 119 by 56 and get a remainder of 7. We would then replace 119 with 7 and repeat the process until the remainder is zero.

Q: How do I reduce a fraction to its lowest terms?

A: To reduce a fraction to its lowest terms, you need to find the GCD of the numerator and the denominator and divide both numbers by the GCD. For example, to reduce the fraction 56/119, we would find the GCD (which is 7) and divide both numbers by 7 to get 8/17.

Q: Why is it important to reduce fractions to their lowest terms?

A: Reducing fractions to their lowest terms is important because it makes them easier to work with and understand. It also helps to avoid errors when performing calculations.

Q: Can I use a calculator or online tool to simplify fractions?

A: Yes, you can use a calculator or online tool to simplify fractions. Many calculators and online tools have built-in functions for simplifying fractions.

Q: What are some common mistakes to avoid when simplifying fractions?

A: Some common mistakes to avoid when simplifying fractions include:

Not finding the GCD correctly
Not dividing both numbers by the GCD
Not checking for errors when performing calculations

Q: How can I practice simplifying fractions?

A: You can practice simplifying fractions by working through examples and exercises, such as:

Simplifying fractions with different numerators and denominators
Finding the GCD of two numbers
Reducing fractions to their lowest terms

Q: What are some real-world applications of simplifying fractions?

A: Simplifying fractions has many real-world applications, such as:

Cooking and measuring ingredients
Building and construction
Science and engineering
Finance and economics

Q: Can I use simplifying fractions in other areas of mathematics?

A: Yes, simplifying fractions is a fundamental concept in mathematics and is used in many areas, such as:

Algebra
Geometry
Trigonometry
Calculus

Q: How can I use simplifying fractions in my everyday life?

A: Simplifying fractions can be used in many everyday situations, such as:

Measuring ingredients for recipes
Calculating costs and prices
Understanding and working with proportions and ratios
Solving problems in science and engineering