Multiplying Fractions: Understanding the Basics

Fractions - Multiplying Fractions

Fractions represent parts of a whole, allowing us to describe and work with decimal values. When multiplying fractions, we multiply the numerators and denominators separately. For example, if we have two fractions (a/b) and (c/d), their product will be ac/bd. This rule works because when you multiply two fractions together, you're essentially finding how many parts of one fraction fit into another multiplied by the number of parts of the second fraction that can fit inside it.

Let's look at some examples:

Example 1

Multiply 6/7 by 5/8:

(6/7) * (5/8) = 30/56

In this case, 6 parts of the first fraction fit into 5 parts of the second fraction, so the result is 30/56 parts.

Example 2

Multiply 5/9 by 4/7:

(5/9) * (4/7) = 20/63

Here, 5 parts of the first fraction fit into 4 parts of the second fraction, resulting in 20/63 parts.

When dealing with improper fractions, it's important to convert them to mixed numbers before performing the multiplication. Improper fractions exceed 1 whole part, while mixed numbers represent more than 1 whole part and a fractional part. To convert an improper fraction to a mixed number, divide the denominator of the improper fraction by its numerator and round down to get the integer part of the quotient. Then, use the remainder as the numerator of the fraction.

For instance, let's consider the following problem:

Example 3

Convert 8/3 from an improper fraction to a mixed number:

8/3 → 2 + 4/3

Here, 8 divided by 3 gives 2 as the integer part, which means there are 2 full parts (or 6 parts total since there are three parts per whole), and the remaining term, 4/3, represents the fractional part.

Once converted back to an improper fraction, it's easier to perform calculations such as multiplication. In this case, the mixed number becomes 2 4/3, which simplifies to 10/3. Now, we can multiply this by 5/4:

(2 4/3) * (5/4) = 12/4

Simplifying further, we find that 12/4 equals 3. So, the final result is 3 x 10/3 = 30/3, which can also be written as 3 + 0/3 = 3 or 10/1, depending on whether you want to keep the fractional representation or simplify it completely.