The Simplified Fraction Calculator facilitates operations such as addition, subtraction, multiplication, and division between two fractions. Additionally, it simplifies the resulting fraction to its lowest terms.
A fraction is a numerical representation that expresses a part or parts of a whole. It consists of two numbers separated by a horizontal line called a fraction bar or a division slash. The number above the bar is called the numerator, and the number below the bar is called the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. Fractions can be used to represent values that are not whole numbers, allowing for precise representation of quantities that are in between whole numbers.
To add two fractions, you need to follow these steps:
Ensure that the denominators (the numbers below the fraction bar) are the same. If they are different, find a common denominator by finding the least common multiple (LCM) of the denominators.
If the denominators are already the same, proceed to the next step. If not, rewrite the fractions using the common denominator.
Add the numerators (the numbers above the fraction bar) together. Keep the denominator the same.
Simplify the resulting fraction, if possible, by reducing it to its lowest terms. This involves dividing both the numerator and denominator by their greatest common divisor (GCD).
If necessary, convert the fraction to a mixed number or a decimal, depending on the desired form of the answer.
Example: Let's add the fractions 1/4 and 3/8.
Step 1: The denominators are different (4 and 8). The LCM of 4 and 8 is 8. Step 2: Rewrite the fractions with the common denominator: 1/4 becomes 2/8 (multiply numerator and denominator of 1/4 by 2). Step 3: Add the numerators: 2/8 + 3/8 = 5/8. Step 4: The fraction 5/8 is already in its simplest form. Step 5: The result is 5/8.
So, 1/4 + 3/8 = 5/8.
To subtract two fractions, you can follow these steps:
Ensure that the denominators (the numbers below the fraction bar) are the same. If they are different, find a common denominator by finding the least common multiple (LCM) of the denominators.
If the denominators are already the same, proceed to the next step. If not, rewrite the fractions using the common denominator.
Subtract the numerators (the numbers above the fraction bar) from each other. Keep the denominator the same.
Simplify the resulting fraction, if possible, by reducing it to its lowest terms. This involves dividing both the numerator and denominator by their greatest common divisor (GCD).
If necessary, convert the fraction to a mixed number or a decimal, depending on the desired form of the answer.
Example: Let's subtract the fraction 3/5 from 7/10.
Step 1: The denominators are different (5 and 10). The LCM of 5 and 10 is 10. Step 2: Rewrite the fractions with the common denominator: 3/5 becomes 6/10 (multiply numerator and denominator of 3/5 by 2). Step 3: Subtract the numerators: 7/10 - 6/10 = 1/10. Step 4: The fraction 1/10 is already in its simplest form. Step 5: The result is 1/10.
So, 7/10 - 3/5 = 1/10.
To multiply two fractions, you can follow these steps:
Multiply the numerators (the numbers above the fraction bar) together to get the new numerator.
Multiply the denominators (the numbers below the fraction bar) together to get the new denominator.
Simplify the resulting fraction, if possible, by reducing it to its lowest terms. This involves dividing both the numerator and denominator by their greatest common divisor (GCD).
If necessary, convert the fraction to a mixed number or a decimal, depending on the desired form of the answer.
Example: Let's multiply the fractions 2/3 and 5/8.
Step 1: Multiply the numerators: 2 * 5 = 10. Step 2: Multiply the denominators: 3 * 8 = 24. Step 3: The fraction 10/24 can be simplified by dividing both the numerator and denominator by their GCD, which is 2. So, 10/24 simplifies to 5/12. Step 4: The fraction 5/12 is already in its simplest form.
So, 2/3 multiplied by 5/8 equals 5/12.