14 72 simplified

2 min read 26-02-2025

Fractions can sometimes seem intimidating, but simplifying them is a fundamental math skill. This article will guide you through simplifying the fraction 14/72, explaining the process step-by-step and offering tips for tackling similar problems. Learning to simplify fractions like 14/72 is crucial for understanding more complex mathematical concepts later on.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator (top number) and the denominator (bottom number) and dividing both by that number. The result is an equivalent fraction that's easier to work with.

Finding the Greatest Common Divisor (GCD) of 14 and 72

To simplify 14/72, we first need to find the GCD of 14 and 72. There are several ways to do this:

Method 1: Listing Factors

List all the factors of 14 and 72:

Factors of 14: 1, 2, 7, 14
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The largest number that appears in both lists is 2. Therefore, the GCD of 14 and 72 is 2.

Method 2: Prime Factorization

Break down 14 and 72 into their prime factors:

14 = 2 x 7
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²

The only common prime factor is 2 (it appears once in the prime factorization of 14 and three times in the prime factorization of 72). Therefore, the GCD is 2.

Simplifying 14/72

Now that we know the GCD is 2, we divide both the numerator and the denominator by 2:

14 ÷ 2 = 7

72 ÷ 2 = 36

Therefore, the simplified form of 14/72 is 7/36.

Why Simplify Fractions?

Simplifying fractions makes them easier to understand and use in calculations. A simplified fraction provides a clearer representation of the value. It also makes comparisons between fractions simpler.

Practicing Fraction Simplification

Here are a few more examples to practice:

20/30: Find the GCD of 20 and 30 (it's 10) and divide both by 10 to get 2/3.
15/45: Find the GCD of 15 and 45 (it's 15) and divide both by 15 to get 1/3.
24/36: Find the GCD of 24 and 36 (it's 12) and divide both by 12 to get 2/3.

Mastering fraction simplification is a key building block in mathematics. By understanding the process of finding the greatest common divisor and applying it consistently, you can confidently simplify any fraction. Remember, practice makes perfect!