Welcome to subtracting fractions with unlike denominators. When fractions have different denominators, like three-fourths minus one-sixth, we cannot subtract them directly. We need to find a common denominator first. Let's see how these fractions look visually.
To subtract fractions with different denominators, we first need to find a common denominator. The best choice is the least common multiple, or LCM, of the denominators. For four and six, we list their multiples. Multiples of four are four, eight, twelve, sixteen, twenty. Multiples of six are six, twelve, eighteen, twenty-four. The smallest number that appears in both lists is twelve, so our LCM is twelve.
Now we convert each fraction to have the common denominator of twelve. For three-fourths, we multiply both numerator and denominator by three to get nine-twelfths. For one-sixth, we multiply both numerator and denominator by two to get two-twelfths. Notice how the visual representations show the same amounts, just divided into more equal parts.
Now we can perform the subtraction. We have nine-twelfths minus two-twelfths. Since the denominators are the same, we subtract the numerators: nine minus two equals seven. So our answer is seven-twelfths. Finally, we check if this can be simplified. Since seven and twelve have no common factors other than one, seven-twelfths is already in its simplest form.
To summarize what we have learned about subtracting fractions with unlike denominators: First, find the least common multiple of the denominators. Second, convert each fraction to an equivalent fraction with the common denominator. Third, subtract the numerators while keeping the common denominator. Fourth, simplify the result if possible. Remember to always check that your final answer is in simplest form.