Steps, Examples | How To Multiply Fractions? - Cuemath

Multiplying Fractions

Multiplying fractions starts with the multiplication of the given numerators, followed by the multiplication of the denominators. Then, the resultant fraction is simplified further and reduced to its lowest terms, if needed. Let us learn more about the multiplication of fractions, how to multiply fractions with whole numbers, how to multiply improper fractions, multiplying mixed fractions, and fraction multiplication rules in this article.

1.	How to Multiply Fractions?
2.	Rules of Multiplying Fractions
3.	Multiplying Fractions with Same Denominator
4.	Multiplying Fractions with Different Denominators
5.	Multiplying Fractions with Whole Numbers
6.	Multiplying Fractions with Mixed Numbers
7.	How to Multiply Improper Fractions?
8.	FAQs on Multiplying Fractions

How to Multiply Fractions?

The multiplication of fractions is not like the addition or subtraction of fractions, where the denominator should be the same. Here, any two fractions with different denominators can easily be multiplied. The only thing to be kept in mind is that the fractions should not be in the mixed form, they should either be proper fractions or improper fractions. Let us learn how to multiply fractions through the following steps:

• Step 1: Multiply the numerators.
• Step 2: Multiply the denominators.
• Step 3: Reduce the resultant fraction to its lowest terms.

Note: Another way to multiply fractions is to simplify and reduce the fractions among themselves and then multiply the numerators together and the denominators together to get the final product.

Let us understand these steps with the help of an example.

Example: Multiply the following fractions: 1/3 × 3/5.

Solution: We start by multiplying the numerators: 1 × 3 = 3, then, multiply the denominators: 3 × 5 = 15. This can be written as: (1 × 3)/(3 × 5) = 3/15. Now, reduce this value to its lowest form. 3 is the Greatest Common Factor (GCF) of 3 and 15, so, divide both 3 and 15 by 3 to simplify the fraction. Therefore, 1/3 × 3/5 = 1/5.

Method 2: Now, let us use the other method to multiply these fractions, where we can simplify the fractions among themselves and then multiply the numerators together, then the denominators together to get the final product. Here, it will be, 1/3 × 3/5→ 1/1 × 1/5 = 1/5 and we get the same answer.

Rules of Multiplying Fractions

While multiplying fractions, the following rules should be kept in mind:

• Rule 1: The first rule is to convert mixed fractions to improper fractions if any. Then, multiply the numerators of the given fractions.
• Rule 2: Multiply the denominators separately.
• Rule 3: Simplify the value obtained to its lowest term.
• Rule 4: Another simple way to multiply fractions is to simplify and reduce the fractions among themselves and then multiply the numerators together and the denominators together to get the final product.

These rules can be applied to any two fractions to find their product. Now, let us learn the individual cases of multiplying fractions with different types of fractions.

Multiplying Fractions with Same Denominator

Multiplying fractions with the same denominator does not change the rule of multiplication of fractions. Fractions that have the same denominator are termed like fractions. Although addition and subtraction of like fractions are different from the addition and subtraction of unlike fractions, in the case of multiplication and division the method remains the same. We multiply the numerators, then the denominators, and then the fraction is reduced to its lowest terms.

Example: Multiply 1/3 × 5/3

Solution: We can multiply these fractions using the following steps.

• Step 1: Multiply the numerators, 1 × 5 = 5.
• Step 2: Multiply the denominators, 3 × 3 = 9.
• Step 3: The product that we get is 5/9. This cannot be reduced any further, therefore, 5/9 is the answer.

Multiplying Fractions with Different Denominators

Multiplying fractions with unlike denominators is exactly the same as the multiplication of like fractions. Let us understand this with an example.

Example: Multiply 4/12 × 16/24.

We can multiply these fractions using the following steps:

• Step 1: Multiply the numerators, 4 × 16 = 64.
• Step 2: Multiply the denominators, 12 × 24 = 288.
• Step 3: The product that we get is 64/288. This can be reduced to 2/9. Therefore, 2/9 is the answer.

Alternative Method

The same fractions can be multiplied using another method in which we simplify the fractions among themselves and then multiply the numerators, then the denominators to get the final product.

Example: Multiply 4/12 × 16/24.

Let us multiply the given fractions using the following steps:

• Step 1: We will simplify the given fractions among themselves. In other words, these fractions can be reduced to 1/3 × 2/3.
• Step 2: Let us multiply the numerators, 1 × 2 = 2.
• Step 3: Now, let us multiply the denominators, 3 × 3 = 9.
• Step 4: Therefore, the product that we get is 2/9.

Multiplying Fractions with Whole Numbers

Multiplying fractions by whole numbers is an easy concept. As we know that multiplication is the repeated addition of the same number, this fact can be applied to fractions as well.

Multiplying Fractions with Whole Numbers Visual Model

Let us consider this example: 4 × 2/3. This means 2/3 is added 4 times. Let us represent this example using a visual model. Four times two-thirds is represented as:

Steps of Multiplying Fractions with Whole Numbers

In order to multiply fractions with whole numbers, we use the simple rule of multiplying the numerators, then multiplying the denominators, and then reducing them to the lowest terms. However, in the case of whole numbers, we write them in the fractional form by placing '1' in the denominator. Let us understand this with an example.

Example: Multiply: 5 × 3/4

Solution: Let us use the following steps to multiply the given fraction with a whole number.

• Step 1: Here, 5 is a whole number that can be written as 5/1, and then it can be multiplied as we multiply regular fractions.
• Step 2: This means, we need to multiply 5/1 × 3/4
• Step 3: Multiply the numerators, 5 × 3 = 15
• Step 4: Multiply the denominators, 1 × 4 = 4
• Step 5: The resultant product is 15/4 which cannot be reduced further.
• Step 6: Since 15/4 is an improper fraction, we will change it to a mixed fraction, 15/4 = \(3\frac{3}{4}\)

Multiplication of Mixed Fractions

Mixed numbers or mixed fractions are fractions that consist of a whole number and a proper fraction, like \(2\frac{3}{4}\), where 2 is the whole number and 3/4 is the proper fraction. For multiplying mixed fractions, we need to change the mixed fractions into an improper fraction before multiplying. For example, if the number is \(2\frac{2}{3}\), we need to change this to 8/3. Let us understand this with the help of an example.

Example: Multiply \(2\frac{2}{3}\) and \(3\frac{1}{4}\)

Solution: The following steps can be used to multiply fractions with mixed numbers.

• Step 1: Change the given mixed fractions to improper fractions, i.e., (8/3) × (13/4).
• Step 2: Multiply the numerators of the improper fractions, and then multiply the denominators. This will give 104/12.
• Step 3: Now, reduce the resultant fraction to its lowest terms, which will make it 26/3.
• Step 4: Further, convert the answer back to a mixed fraction which will be \(8\frac{2}{3}\).

How to Multiply Improper Fractions?

Now let us understand the multiplication of improper fractions. We already know that an improper fraction is one where the numerator is bigger than the denominator. When multiplying two improper fractions, we frequently end up with an improper fraction. For example, to multiply 3/2 × 7/5 which are two improper fractions, we need to take the following steps:

• Step 1: Multiply the numerators and denominators. (3 × 7)/(2 × 5) = 21/10.
• Step 2: The fraction 21/10 cannot be reduced further to its lowest terms.
• Step 3: Hence, the answer is 21/10 which can be written as \(2\frac{1}{10}\).

Tips and Tricks of Multiplying Fractions

Here are a few important tips and tricks which are helpful in the multiplication of fractions.

• Generally, students simplify a fraction after multiplication. However, to make calculations easier, check if the two fractions to be multiplied are already in their lowest forms. If not, first simplify them and then multiply. For example, 4/12 × 5/13 will be difficult to multiply directly.
• Now, if we simplify the fraction first, we get 1/3 × 5/13 = 5/39
• Simplification can also be done across two fractions. If there is a common factor between the numerator of one of the fractions and the denominator of the other fraction, you can simplify them and proceed. For example, 5/28 × 7/9 can be simplified to 5/4 × 1/9 before multiplying.

☛ Related Topics

• Multiplying Fractions Calculator
• Reciprocal of Fractions
• Multiplying Decimals
• Multiplication and Division of Integers
• Addition of Fractions
• Subtraction of Fractions
• Division of Fractions

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