How to Easily Multiply Fractions Step-by-Step Process

Understanding Fractions

Fractions are a mathematical concept that allow us to represent parts of a whole. A fraction is written with two numbers separated by a diagonal line. The number on top is called the numerator, and the number on the bottom is called the denominator.

The denominator indicates the total number of equal parts the whole has been divided into. The numerator indicates how many of those parts we are referring to. For example, in the fraction 3/5:

• The denominator is 5, so the whole has been divided into 5 equal parts
• The numerator is 3, so we are referring to 3 of those 5 equal parts

Simplifying Fractions

Before multiplying fractions, it helps to simplify them first. To simplify, we determine if the numerator and denominator have any common factors that we can divide out.

For example, the fraction 6/9 can be simplified by dividing both the numerator and denominator by 3:

6/9 = 2/3

Simplifying fractions makes them easier to work with in calculations.

Multiplying Fractions Step-by-Step

Now let’s walk through the process of multiplying two fractions together:

1. Simplify the fractions if possible
2. Multiply the numerators together to get a new numerator
3. Multiply the denominators together to get a new denominator
4. If needed, simplify the resulting fraction from steps 2 and 3
5. Write the final fraction

Let's see an example:

Multiply: 3/4 x 2/3

1. The fractions 3/4 and 2/3 are already simplified
2. Numerators: 3 x 2 = 6
3. Denominators: 4 x 3 = 12
4. The fraction 6/12 simplifies to 1/2
5. The product is: 1/2

Why This Process Works

To understand why we multiply the numerators and multiply the denominators when multiplying fractions, it helps to use a visual representation.

Let's again use the fractions 3/4 and 2/3. We'll draw a rectangle divided into fourths and another rectangle divided into thirds.

The fraction 3/4 represents 3 out of 4 equal fourths. The fraction 2/3 represents 2 out of 3 equal thirds.

When we multiply these fractions, we want to end up with parts that are equal fourths and equal thirds at the same time. By multiplying the denominators, we get twelfths (4 x 3 = 12), which allows us to represent fourths and thirds simultaneously.

By multiplying the numerators, we determine how many of these new 12th parts we have: 3 groups of 2 is 6. So our final fraction is 6/12, which simplifies to 1/2.

Multiplying Mixed Numbers

Sometimes when multiplying fractions we'll need to work with mixed numbers, which contain whole numbers and fractions combined together. For example:

3 1/2 x 2/3

To multiply mixed numbers:

1. Convert the mixed numbers to improper fractions
2. Multiply the fractions using the process outlined before
3. Convert the resulting improper fraction back to a mixed number, if needed

Let's see it in action with our example:

3 1/2 x 2/3

Convert to improper fractions:

7/2 x 2/3

Multiply the fractions:

Numerators: 7 x 2 = 14

Denominators: 2 x 3 = 6

The product is 14/6

Convert back to a mixed number:

14/6 = 2 2/6

The final answer is 2 2/6, which can also be written as 2 1/3.

FAQs

Why do we multiply the numerators and multiply the denominators to multiply fractions?

Multiplying the numerators and denominators allows us to find a common denominator when multiplying fractions. This common denominator represents parts that are both equal fractions from the original denominators. Multiplying the numerators then determines how many of those new common parts we have.

When do I need to simplify fractions before multiplying them?

It's a good idea to simplify fractions first if the numerator and denominator have any common factors. This makes the numbers smaller to work with. But even if no simplification is possible, you can still multiply fractions using the basic fraction multiplication process.

What is an improper fraction and when will I encounter them?

An improper fraction has a numerator that is larger than its denominator. Improper fractions allow us to convert mixed numbers into fractions to multiply them. After multiplying, you may need to convert any improper fraction results back into mixed numbers.

Is there an easy way to check my work when multiplying fractions?

Definitely! An easy way is to draw fraction models or fraction circles representing the original fractions. If your multiplication result represents the same area as shown in the models, you likely performed the multiplication correctly.