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How to Multiply Fractions: Simple Steps and Examples

Demi Liu | Contributor
Multiply Fractions

To multiply fractions, you start by multiplying the numerators of the given fractions, followed by multiplying their denominators. Afterward, simplify the resulting fraction by reducing it to its lowest terms. This straightforward process makes fraction multiplication easier to understand and apply.

In this article, we’ll dive deeper into the multiplication of fractions, including how to multiply fractions with whole numbers, improper fractions, and mixed fractions. We’ll also explore key rules and tips to help you handle fraction multiplication with confidence and accuracy.

What Are Fractions?

Fractions represent parts of a whole or a division of quantities. Understanding fractions is key to building a solid foundation in math. They help visualize and solve problems involving division, comparison, and proportionality. Mastery of fractions allows for more accurate calculations in everyday project planning.

They consist of two main parts:

For example, in the fraction 3/4, the numerator is 3, and the denominator is 4. This means the whole is divided into 4 equal parts, and we are considering 3 of those parts.

Types of Fractions

  1. Proper Fractions: The numerator is smaller than the denominator (3/4).
  2. Improper Fractions: The numerator is greater than or equal to the denominator (5/4).
  3. Mixed Numbers: A combination of a whole number and a proper fraction (1 1/2).
  4. Equivalent Fractions: Fractions that represent the same value (1/2 = 2/4).

How to Multiply Fractions?

To multiply fractions, first multiply the top numbers (numerators) together, then multiply the bottom numbers (denominators) together. If possible, simplify the fraction once you have the result by dividing the numerator and denominator by their greatest common factor.

Step 1: Multiply the Numerators

Multiply the numerators (the numbers on top) of both fractions.

For example, if you are multiplying 3/4 and 2/5, multiply 3 × 2 = 6.

Step 2: Multiply the Denominators

Next, multiply the denominators (the numbers at the bottom) of both fractions.

In this example, multiply 4 × 5 = 20.

Step 3: Simplify the Fraction

If possible, simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by that number. For example, after multiplying 3/4 by 2/5, you get 6/20.

Simplify 6/20 by dividing both the numerator and the denominator by 2:

6 ÷ 2 = 3 and 20 ÷ 2 = 10, so the simplified fraction is 3/10.

Example:

Multiply 2/3 by 4/7:

  1. Multiply the numerators: 2 × 4 = 8
  2. Multiply the denominators: 3 × 7 = 21
  3. Simplify: 8/21 is already in its simplest form.

So, 2/3 × 4/7 = 8/21.

Multiplying Fractions with Whole Numbers

How do you multiply a fraction by a whole number? Multiplying fractions by whole numbers is a simple process that can be mastered with a few easy steps. Here’s how to effectively multiply fractions by whole numbers:

Step 1: Convert the Whole Number to a Fraction

To multiply a whole number by a fraction, convert the whole number into a fraction. This is done by placing it over 1. For example:

4 = 4/1

Step 2: Multiply the Numerators and Denominators

Now that you have both numbers as fractions, you can multiply them. Multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together:

4/1 × 2/3 = (4 × 2) / (1 × 3) = 8/3

Step 3: Simplify if Necessary

The result 8/3 is in its simplest form, but if you ever end up with a fraction that can be simplified, do so. You can also convert improper fractions into mixed numbers if desired. In this case:

8/3 = 2 2/3

Example

1: Multiply 5/6 by 3.

2: Multiply 1/4 by 5.

Multiplication of Mixed Fractions

Multiplying mixed numbers involves a few additional steps compared to multiplying simple fractions or whole numbers. Mixed fractions, also known as mixed numbers, consist of a whole number and a proper fraction (e.g., 2 1/3).

To multiply mixed numbers, you first need to convert them into improper fractions, perform the multiplication, and then simplify the result if necessary. Here’s a detailed guide to help you master this process.

Step 1: Convert Mixed Fractions to Improper Fractions

A mixed fraction is a combination of a whole number and a fraction. To multiply mixed numbers, you must first convert them into improper fractions. An improper fraction has a numerator larger than or equal to its denominator.

  1. Multiply the whole number by the denominator of the fraction.
  2. Add the result to the numerator of the fraction.
  3. Write the sum as the new numerator, keeping the denominator the same.

Convert 2 1/3 to a fraction:

Similarly, convert 1 2/5 with the same method:

Step 2: Multiply the Improper Fractions

Once both mixed fractions are converted to improper fractions, multiply them using the same rules as for multiplying simple fractions:

Example: multiply two improper fractions 7/3 and 7/5:

The final answer is 49/15​.

Step 3: Simplify the Result

After multiplying, simplify the resulting fraction if possible. This involves reducing the fraction to its lowest terms or converting it back to a mixed number if it is improper.

Example: Simplify 49/15​:

  1. Divide the numerator by the denominator: 49÷15=3 with a remainder of 4.
  2. Write the result as a mixed number: 3 4/15.

Practical Example

Multiply 3 1/2 and 2 3/4.

  1. Convert to improper fractions:3 1/2 = 7/22 3/4 = 11/4
  2. Multiply both the fractions: 7/2 × 11/4 = 77/8
  3. Simplify: 77 ÷ 8 = 9 with a remainder of 5, so the result is 9 5/8.

Other Fraction Operations

Dividing Fractions:

To divide two fractions, simply multiply the first fraction by the reciprocal of the second fraction. For example, dividing 1/2 by 3/4 is the same as multiplying 1/2 by 4/3.

Subtracting Fractions:

When subtracting two or more fractions with unlike denominators, first find a common denominator. Then subtract the numerators. For example, 1/3 – 1/4 becomes (4/12 – 3/12) = 1/12.

Adding Fractions:

For adding three fractions with different denominators, find a common denominator. Multiply each numerator by the necessary number to match the common denominator, then add all the numerators. The result is a single fraction. For example, 1/2 + 1/3 + 1/4 becomes 6/12 + 4/12 + 3/12 = 13/12.

Conclusion

Multiplying fractions doesn’t have to be intimidating. With a little practice and the right approach, you’ll find it’s one of the easiest math operations to master. Remember the key steps: multiply the numerators, multiply the denominators, and simplify the result. Whether you’re solving math problems or applying fractions in real life, this skill will serve you well.

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Frequently Asked Questions

Q1: How do I multiply fractions with different denominators?

To multiply fractions with different denominators, follow these steps:

  1. Multiply the Numerators: Multiply the top numbers (numerators) of the fractions together.
  2. Multiply the Denominators: Multiply the bottom numbers (denominators) of the fractions together.
  3. Simplify if Necessary: If possible, simplify the resulting fraction.

Example: Multiply 2/3 by 4/5.

Q2: How to multiply fractions with same denominator?

When multiplying fractions with the same denominator, the process is similar:

  1. Multiply the Numerators: Multiply the top numbers (numerators) together.
  2. Keep the Same Denominator: The denominator remains the same.
  3. Simplify if necessary: If possible, simplify the resulting fraction.

​Q3: What is 1/4 multiplied by 1/4 equal?

To find 1/4​ multiplied by 1/4​:

  1. Multiply the Numerators: 1×1=1
  2. Multiply the Denominators: 4×4=16
  3. Result: 1/16

So, 1/4×1/4=1/16.

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