Multiplying Fractions

Multiplying fractions begins with the numerators being multiplied, followed by the denominators being multiplied. The resultant fraction is then simplified further and, if necessary, reduced to its simplest terms.

• What Is the Best Way for Multiplying Fractions?

Multiplication of fractions differs from addition and subtraction in that the denominator does not have to be the same. The key thing to remember is that the fractions should not be combined; instead, they should be either proper or improper fractions. Let’s have a look at how to multiply fractions using the techniques below:

Step 1: Multiply the numerators in step one.

Step 2: Divide the numerators by the denominators.

Step 3: Take the generated fraction and reduce it to its simplest words.

Multiply the following fractions, for example: 1/3 x 3/5. To begin, multiply the numerators: If the numerators are 1 x 3 = 3, the denominators are 3 x 5 = 15. This is calculated as (1 x 3)/ (3 x 5) = 3/15. Reduce this value to its simplest form now. Because 3 is the highest common factor of 3 and 15, simplify the fraction by dividing both 3 and 15 by 3. As a result, 1/3 x 3/5 Equals 1/5.

• Using Visual Models to Multiply Fractions

Visualizing fraction multiplication with fractional squares is a fun way to grasp the subject. Multiply these two fractions together: Using the visual model, 1/4 to 1/3. Divide the length of a rectangle into four equal pieces. Each column will take up a quarter of the rectangle. Now divide its breadth into three equal portions, each representing 1/3 of the whole. Now all we have to do is find the section of the rectangle that is shared by both 1/4 and 1/3, which is 1/12th of the entire rectangle.

• Fraction Multiplication Rules

The following rules must be kept in mind when multiplying fraction:

Rule 1: If there are any mixed fractions, turn them to improper fractions. After that, multiply the numerators of the supplied fractions.

Rule 2: Divide the numerators by the denominators separately

Rule 3: Reduce the derived value to its simplest form.

These three rules can be used to find the product of any two fractions.

• Multiplication of Fractions with the Same Denominator

Multiplying fractions with the same denominator has no effect on the rule of fraction multiplication. Fractions with the same denominator are called fractions. While adding and subtracting like fractions differs from subtracting and adding unlike fractions, the multiplication and division methods are the same. The numerators are multiplied first, followed by the denominators, and lastly the fraction is reduced to its simplest form.

• Fraction Multiplication with Different Denominators

Multiplying fractions with unlike denominators is the same as multiplying fractions with like denominators.

• Multiplying Fractions with Whole Numbers

We utilise the simple rule of multiplying the numerators, then multiplying the denominators, and then reducing them to the lowest terms to multiply fractions with whole numbers. Whole numbers, on the other hand, are written in fractional form with a ‘1’ in the denominator.

• Fraction Multiplication with Mixed Numbers

Mixed numbers, also known as mixed fractions, are fractions made up of a whole number and a proper fraction, such as 234, where 2 is the entire number and 3/4 is the proper fraction. Before multiplying mixed fractions, we must first convert the mixed fractions to an improper fraction. For instance, if the number is 223, we must alter it to 8/3.

• Fraction Multiplication with improper fractions

Let’s have a look at how to multiply incorrect fractions. An improper fraction is one in which the numerator is greater than the denominator, as we already know. We usually get an inappropriate fraction when multiplying two improper fractions. For example, to multiply 3/2 x 7/5, which are two improper fractions, we must follow the procedures below:

Multiply the numerators and denominators in step one. (3 x 7) / (2 x 5) = 21/10

Step 2: The fraction 21/10 cannot be reduced to its simplest form any further.

Step 3: As a result, the solution is 21/10, which is written as 2110.

• Multiplying Fractions Tips & Tricks:

Here are a few useful techniques and tricks for multiplication of fractions.

After multiplying a fraction, students usually simplify it. Check if the two fractions to be multiplied are already in their lowest forms to make calculations easier. If not, simplify them first before multiplying. For example, multiplying 4/12 by 5/13 will be challenging.

We get 1/3 x 5/13 = 5/39 if we simplify the fraction first.

Simplification can also be accomplished by combining two fractions. If the numerator of one of the fractions and the denominator of the other fraction have a common factor, you can simplify them and move on. Before multiplying, for example, 5/28 x 7/9 can be simplified to 5/4 x 1/9.

Conclusion:

When multiplying fractions, start with the numerators and work your way down to the denominators. The resultant fraction is then simplified even more and, if necessary, reduced to its most basic form.