what is 30 of 42

2 min read 25-12-2024

The question "What is 30/42?" asks us to simplify a fraction. Let's break down how to solve this and understand the concept of simplifying fractions.

Understanding Fractions

A fraction represents a part of a whole. It's written as a numerator (the top number) over a denominator (the bottom number). In the fraction 30/42, 30 is the numerator and 42 is the denominator. This means we have 30 parts out of a total of 42 parts.

Simplifying Fractions: Finding the Greatest Common Factor (GCF)

Simplifying a fraction means reducing it to its lowest terms. We do this by finding the greatest common factor (GCF) of both the numerator and the denominator. The GCF is the largest number that divides evenly into both numbers.

To find the GCF of 30 and 42, we can list the factors of each number:

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

The largest number that appears in both lists is 6. Therefore, the GCF of 30 and 42 is 6.

Simplifying 30/42

Now that we know the GCF is 6, we divide both the numerator and the denominator by 6:

30 ÷ 6 = 5 42 ÷ 6 = 7

Therefore, 30/42 simplified is 5/7.

Visualizing the Fraction

Imagine you have a pizza cut into 42 slices. You eat 30 of them. The fraction 30/42 represents the portion of the pizza you consumed. Simplifying to 5/7 means that you ate 5 slices out of every 7 slices. It's the same amount of pizza, just expressed in a simpler way.

Other Methods for Finding the GCF

Besides listing factors, you can also use the prime factorization method to find the GCF. This involves breaking down each number into its prime factors:

30 = 2 x 3 x 5
42 = 2 x 3 x 7

The common prime factors are 2 and 3. Multiplying them together (2 x 3 = 6) gives us the GCF.

Conclusion: The Simplified Fraction

In conclusion, 30/42 simplified is 5/7. Understanding how to simplify fractions is a fundamental skill in mathematics, useful in various contexts from baking to advanced calculations. By finding the greatest common factor, we can express fractions in their simplest and most easily understood form.