How do you subtract different fractions? Subtracting fractions can sometimes seem like a complex task, especially when the fractions have different denominators. However, with a few simple steps and a clear understanding of the concept, you can easily subtract fractions and find the correct answer. In this article, we will guide you through the process of subtracting different fractions, ensuring that you can perform this operation with confidence.
When subtracting fractions, the first step is to identify the common denominator. The denominator is the bottom number of a fraction, and it represents the number of equal parts that make up the whole. To find a common denominator, you need to find a number that is a multiple of both denominators. This can be done by listing the multiples of each denominator and finding the smallest common multiple.
For example, let’s say you want to subtract the fractions 1/3 and 2/5. The denominators are 3 and 5, respectively. To find the common denominator, you can list the multiples of 3 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120) and the multiples of 5 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120). The smallest common multiple is 15, so the common denominator is 15.
Once you have identified the common denominator, the next step is to convert each fraction to an equivalent fraction with the common denominator. To do this, you can multiply the numerator and denominator of each fraction by the same number, as long as you do it to both the numerator and the denominator. This will not change the value of the fraction.
Continuing with our example, we need to convert 1/3 and 2/5 to equivalent fractions with a denominator of 15. To convert 1/3, we multiply both the numerator and denominator by 5, resulting in 5/15. To convert 2/5, we multiply both the numerator and denominator by 3, resulting in 6/15.
Now that both fractions have the same denominator, you can subtract the numerators and keep the denominator. In our example, 5/15 – 6/15 equals -1/15. The negative sign indicates that the result is a negative fraction.
In conclusion, subtracting different fractions involves finding a common denominator, converting each fraction to an equivalent fraction with the common denominator, and then subtracting the numerators while keeping the denominator. By following these steps, you can subtract different fractions with ease and accuracy.
