Step-by-Step Multiply Fractions Calculator: Understand the Math Behind the Results!

What is Multiplying Fractions?

Multiplying fractions is a mathematical operation that involves finding the product of two or more fractions. It is the process of combining the numerical values and the parts of fractions to determine the result. Multiplying fractions is an important concept in arithmetic and is commonly used in various mathematical applications.

Numerator and Denominator

In a fraction, the top number is called the numerator, and the bottom number is called the denominator. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts that make up a whole. When multiplying fractions, we multiply the numerators together and the denominators together separately.

Multiplying Fractions with the Same Denominator

When multiplying fractions with the same denominator, we simply multiply the numerators together and multiply the denominators together. The resulting fraction will have the same denominator as the original fractions. For example, to multiply 2/5 by 3/5, we multiply the numerators (2 × 3 = 6) and multiply the denominators (5 × 5 = 25). The product is 6/25.

Multiplying Fractions with Different Denominators

When multiplying fractions with different denominators, we need to find a common denominator before multiplying. The common denominator is a shared multiple of the denominators of the fractions being multiplied. Once we have the common denominator, we convert each fraction so that they have the same denominator. Then, we multiply the numerators together and multiply the denominators together to get the product. Finally, we simplify the resulting fraction, if possible.

Example:

To multiply 2/3 by 4/5, we find the least common multiple (LCM) of 3 and 5, which is 15. We convert both fractions so they have the common denominator of 15. Thus, 2/3 becomes 10/15 (multiply numerator and denominator by 5) and 4/5 becomes 12/15 (multiply numerator and denominator by 3). Now, we multiply the numerators (10 × 12 = 120) and multiply the denominators (15 × 15 = 225). The product is 120/225, which can be simplified to 8/15.

In summary, multiplying fractions is the process of finding the product of two or more fractions. It involves multiplying the numerators together and multiplying the denominators together separately. When the fractions have the same denominator, the multiplication is straightforward. When the fractions have different denominators, a common denominator is found before multiplying. Multiplying fractions is an important concept in mathematics and is used in various real-life applications where quantities or parts need to be multiplied or scaled.