Compare 35/12 & 43/15: Two Fraction Comparison Methods

Hey guys! Today, we're diving into the world of fractions and tackling a fun problem: comparing 35/12 and 43/15. We'll explore two different strategies to figure out which fraction is bigger, and then we'll chat about which method we think is the best. So, grab your thinking caps and let's get started!

Understanding the Challenge: Why Can't We Just Look?

When you first glance at 35/12 and 43/15, it's not immediately obvious which one is larger. Unlike comparing fractions with the same denominator (like 2/5 and 4/5, where 4/5 is clearly bigger), these fractions have different denominators. This means the 'slices' we're dealing with are different sizes, making a direct comparison tricky. To accurately compare them, we need to find a common ground, a way to express them in comparable terms.

This is where our strategies come in handy. We'll look at methods that allow us to either give the fractions the same denominator or convert them into a format that makes the comparison straightforward. Think of it like trying to compare the heights of two people, one measured in feet and the other in meters. You'd need to convert one measurement to the other before you could accurately see who's taller. Similarly, with fractions, we need a conversion method to see which represents a larger portion of the whole.

It's essential to grasp this initial hurdle because it highlights the core concept of fraction comparison. We're not just blindly following steps; we're understanding why those steps are necessary. This understanding will help you in countless other fraction-related problems down the road. So, let's jump into our first strategy and see how we can conquer this challenge!

Strategy 1: Finding a Common Denominator – The LCM Approach

Our first strategy involves finding a common denominator. This means we want to rewrite both fractions so they have the same number on the bottom. Why? Because when fractions share a denominator, we can directly compare their numerators (the top numbers) to see which is larger. It's like comparing apples to apples instead of apples to oranges.

The most efficient way to find a common denominator is to determine the Least Common Multiple (LCM) of the original denominators. The LCM is the smallest number that both denominators divide into evenly. In our case, we need to find the LCM of 12 and 15.

Let's break down how to find the LCM. One way is to list the multiples of each number until we find a common one:

• Multiples of 12: 12, 24, 36, 48, 60, 72,...
• Multiples of 15: 15, 30, 45, 60, 75,...

See that? 60 is the smallest number that appears in both lists. So, the LCM of 12 and 15 is 60. This means we want to rewrite both 35/12 and 43/15 with a denominator of 60.

Now, how do we do that? We need to multiply both the numerator and denominator of each fraction by a factor that will turn the original denominator into 60. For 35/12, we ask ourselves,