Subtracting Unlike Fractions: Step-by-Step Explanation

When subtracting fractions with different denominators, we can't simply subtract directly.Let's see why. Here's three-fourths and one-sixth visualized.Notice how the parts are different sizes! We can't subtract pieces of different sizes.To solve this, we need to find the Least Common Multiple of our denominators, four and six.Four factors into two times two, while six factors into two times three.The Least Common Multiple includes all prime factors: two times two times three, which equals twelve.With twelve as our common denominator, we can divide our whole into twelve equal parts.Now we're ready to convert our original fractions to equivalent fractions with denominator twelve.Now we'll convert each fraction to an equivalent fraction with our common denominator of twelve.Let's start with three-fourths. To convert it to twelfths, we multiply both top and bottom by three.For one-sixth, we multiply both top and bottom by two to get equivalent twelfths.Notice how these new fractions are equal in value to our original fractions. We've just changed how we write them.So three-fourths becomes nine-twelfths, and one-sixth becomes two-twelfths. Now our fractions have the same denominator and are ready for subtraction.Now that we have equivalent fractions with the same denominator, we can move on to subtracting them.Now that our fractions have the same denominator, we can subtract them directly.When fractions have the same denominator, we keep the denominator the same and only subtract the numerators.Let's focus on the numerators. Nine minus two equals seven.So our answer is seven twelfths.Now, let's check if we can simplify this fraction by finding common factors of seven and twelve.Seven has only two factors: one and seven.Twelve has factors of one, two, three, four, six, and twelve.Looking at these factors, we can see that one is the only common factor, which means this fraction cannot be simplified further.Therefore, seven twelfths is our final answer in its simplest form.