Simplifying 136 Divided by 200

Simplifying Fractions: A Step-by-Step Guide

When dealing with fractions, it’s essential to simplify them to their lowest terms to make calculations easier and more efficient. In this article, we will focus on simplifying the fraction 136 divided by 200.

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

Step 1: Find the Greatest Common Divisor (GCD)

To find the GCD of 136 and 200, we can use the following methods: * Prime Factorization: Break down both numbers into their prime factors and find the common factors. * Euclidean Algorithm: Use a series of division steps to find the GCD.

Let’s use the prime factorization method: - The prime factors of 136 are: 2^3 * 17 - The prime factors of 200 are: 2^3 * 5^2

The common factors are 2^3.

Step 2: Simplify the Fraction

Now that we have found the GCD, we can simplify the fraction: - Divide both the numerator and the denominator by the GCD (2^3 = 8). - Simplified fraction: (136 ÷ 8) / (200 ÷ 8) = 17 / 25

So, 136 divided by 200 simplifies to ¹⁷⁄₂₅.

Importance of Simplifying Fractions

Simplifying fractions is crucial in various mathematical operations, such as: * Addition and Subtraction: Simplifying fractions makes it easier to find a common denominator. * Multiplication and Division: Simplifying fractions reduces the risk of calculation errors. * Comparing Fractions: Simplifying fractions allows for easier comparison of fractions.

📝 Note: Always simplify fractions to their lowest terms to ensure accurate calculations and to make mathematical operations more efficient.

In addition to simplifying fractions, it’s also important to understand how to compare and order fractions. This can be done by: * Converting fractions to equivalent decimals or percentages * Comparing the numerators and denominators of the fractions

Real-World Applications of Fractions

Fractions have numerous real-world applications, including: * Cooking and Recipes: Fractions are used to measure ingredients and scale recipes. * Finance and Banking: Fractions are used to calculate interest rates and investment returns. * Science and Engineering: Fractions are used to measure quantities and calculate ratios.

Fraction	Simplified Fraction
136/200	17/25
120/180	2/3
150/250	3/5

In conclusion, simplifying fractions is an essential skill in mathematics, and it’s crucial to understand the steps involved in simplifying fractions. By following these steps and practicing regularly, you can become proficient in simplifying fractions and improve your overall mathematical skills.