How to multiply fractions with mixed numbers?

In this article, we are going to discuss about the multiplication of fractions with mixed numbers. We will also discuss some frequently asked questions (FAQs) related to fractions and also related to mixed numbers.

In starting, multiplication of fractions might look a little bit challenging, but once you know how to multiply fractions, you will be able to solve the problem without taking much time.

So let's first see a brief description of fractions.

What are fractions?

Fractions are the number written in the form of p/q (such that q ≠ 0), where p is the numerator and q is the denominator. For example, 1/2, 3/7, 4/3, etc. A fraction indicates the part of a whole thing. As an instance, the fraction ¾ is read as three-fourth of a whole.

Let's see the types of fractions. There are three types of fractions that are defined as follows -

Proper fraction - The numerator can be equal to the denominator but not higher than the denominator. This type of fraction is known as a proper fraction. In short, we can say that, in proper fractions, the numerator of the fraction is less than or equal the denominator. For example - 7/9, 1/2, 3/4, etc.

Improper fraction - In a fraction, when the numerator is greater than the denominator, the fraction is called as an improper fraction. For example - 7/3, 8/5, 5/4, etc.

Mixed fraction - It is the combination of proper fraction and whole number. It is also known as a mixed number. For example -

5/2 = 2½,

17/6 = 2⅚, etc.

Now, let's understand mixed numbers.

What are Mixed numbers?

Mixed numbers are mixed fractions that are one of the types of fractions. Mixed numbers or mixed fractions are the form of a fraction in which there is a combination of proper fraction and whole number. For example -

7/2 = 3½,

11/4 = 2¾, etc.

Mixed fractions are represented with their remainder and quotient. As an instance, in 3½, 3 is the quotient, and 1 is the remainder.

Let's see the conversion of an improper fraction into a mixed number or vice versa.

Conversion of improper fraction into a mixed number (or mixed fraction)

It is easy to convert an improper fraction into a mixed number. The steps are listed as follows -

Step1 - First, we have to divide the numerator of the fraction by the denominator.

Step2 - Now, take the quotient as the whole number and write remainder as the numerator of the proper fraction and keep the denominator same.

As an instance, suppose we have to convert 5/2 into a mixed number. So, on dividing 5 by 2 we will get 2 as quotient and 1 as remainder. Therefore,

5/2 = 2½

Conversion of Mixed fraction into an improper fraction

It is also easy to convert a mixed number into an improper fraction. The steps are listed as follows -

Step1 - First, we have to multiply the denominator of the proper fraction with the whole number attached to it.

Step2 - Then, add the numerator with the multiplication and keep the denominator same.

As an instance, suppose we have to convert 3½ into an improper fraction. So, on multiplying 3 with 2 we will get 6. Then add it with numerator, i.e., 1, it will be 7. Therefore,

3½ = 7/2

Now, let's see the multiplication of fractions with mixed numbers.

Multiplication of fractions with mixed numbers

If we require solving the mixed fraction problem, we have to change the mixed number to an improper fraction and multiply them as usual. For Example, if we have to multiply (1 and 2/3) with (3 and 2/5). The first thing we need to do is change the mixed fraction into improper fractions; it means the numerator will be greater than the denominator. The process of multiplying the given mixed fractions is given as follows -

1 and 2/3 = 5/3, when made into an improper fraction, the denominator will always be the same.

For 3 and 2/5, multiply the denominator by the given whole number, i.e., (3*5), and add the given solution to the numerator, i.e., (3*5) + 2 = 17. Thus, after conversion, we will get 17/5.

Now, we only have to multiply 5/3 and 17/5 together. After the multiplication, the answer is -

(5/3) x (17/5) = 85/15 = 17/3

Now, let's see the multiplication of fractions and mixed numbers using some examples.

Example1 - What will be the product of [1 and (2/5)] and 5/9?

Answer1 - The step by step process of solving the given question is stated below -

Step1 - First, we have to convert the mixed fraction into an improper fraction -

(1 and 2/5) = 7/5

Step2 - Now, multiply both fractions, i.e., 7/5 and 5/9 -

(7/5) x (5/9) = 35/45 or 7/9.

Example2 - What will be the product of [2 and (1/3)] and 2/5?

Answer2 - The step by step process of solving the given question is stated below -

Step1 - First, we have to convert the mixed fraction into an improper fraction -

(2 and ⅓) = 7/3

Step2 - Now, multiply both fractions, i.e., 7/3 and 2/5 -

(7/3) x (2/5) = 14/15.

Example3 - What will be the product of [5 and (3/20)] and 2/15?

Answer3 - The step by step process of solving the given question is stated below -

Step1 - First, we have to convert the mixed fraction into an improper fraction -

(5 and 3/20) = 7/3

Step2 - Now, multiply both fractions, i.e., 7/3 and 2/5 -

(7/3) x (2/5) = 14/15.

So, from the above examples, one can easily understand the multiplication of fractions with mixed numbers. Therefore, there are some steps required to perform the multiplication. Let's highlight those steps -

Step 1: First, we always have to convert the given mixed fraction or mixed number into an improper fraction.

Step 2: Now, secondly, we have to multiply the numerators of both fractions.

Step 3: Then, multiply the denominators of both fractions.

Step 4: At last, combine them and simplify the fractions into their lowest form.

So, that's all about the multiplication of a fraction with mixed numbers. Now, let's solve some practice questions.

Question 1 - Find the product of 2⅓ and 3/2.

Answer 1 - After converting the given mixed fraction into an improper fraction, we will get -

2⅓ = 7/3

Now, multiply both fractions, we will get

7/3 x 3/2 = 21/6 or, 7/2.

Question 2 - Find the product of 1⅓ and 3.

Answer 2 - After converting the given mixed fraction into an improper fraction, we will get -

1⅓ = 4/3

On multiplying both, we will get

4/3 x 3/1 = 12/3 or, 4.

So, that's all about the article. Hope this article is beneficial for you and provides you the sufficient information about fractions, mixed fractions, and multiplication between them.