Multiplying Fractions Games

What Is the Multiplication of Fractions?

Multiplication of fractions involves combining two or more fractions to find the product. When multiplying fractions, you multiply the numerators (top numbers) together to get the new numerator and the denominators (bottom numbers) together to get the new denominator. Simplifying the resulting fraction may be necessary to express it in its simplest form.

Multiplying fractions is a crucial skill as it's often used in real-life scenarios like cooking, construction, and more. For instance, if a recipe calls for \(\frac{2}{3}\) cup of flour and you want to bake half a portion, you'd multiply \(\frac{1}{2}\) (for half the recipe) by \(\frac{2}{3}\) (for the original amount of flour). This yields \(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\) cup of flour, the amount needed for half of the recipe.

A fractions represents parts of a whole. The fractional notation widely used is \frac{a}{b}\), where a and b are whole numbers, \(b \neq 0\).

 

 

Example: The colored portions in each of the models represent one part of equally divided parts of a whole.

 

 

Another way to represent a fraction is using the number line.  

Example: To represent the fractions \(\frac{1}{4}\) , \(\frac{1}{2}\), and \(\frac{3}{4}\) on a number line, we first divide the segment joining 0 to 1 into 4 equal parts. Now, each part represents one-fourth of a unit. 

 

 

Multiplication extends the concept of fractions by showing how fractions can be scaled or multiplied to find a new fraction representing a different portion of the whole. 

How to Multiply Fractions

To multiply fractions, follow these simple steps:

• Multiply the numerators (top numbers) of the fractions to get the new numerator.
• Multiply the denominators (bottom numbers) of the fractions to get the new denominator.
• Simplify the fraction if possible by reducing the numerator and denominator.

Example: Multiply \(\frac{2}{5}\) by \(\frac{3}{4}\):

\(2 \times 3 = 6\)                      (new numerator)

\(5 \times 4 = 20\)                    (new denominator)

\(\frac{2}{5} \times \frac{3}{4} = \frac{6}{20}\)

\(\frac{6}{20}\) can be further reduced to \(\frac{3}{10}\).

Multiplication of Fractions: Different Types and Methods

Let’s understand fraction multiplication through its various types and methods.

Multiplication of a Fraction by a Whole Number

To multiply a fraction by a whole number, visual models like fraction strips are used. This helps children to get the geometric picture of arithmetic.

Example: Identify the multiplication represented in the below fraction strip.

 

 

Here, each of the addends is a unit fraction \(\frac{1}{2}\) or one-half. There are 4 such addends.

So, the multiplication represented is \(\frac{1}{2} \times 4 = 2\).

If you arrange the shaded parts in consecutive one-halves, you will get 2 wholes.

Example 2: Now, let us consider the multiplication of a non-unit fraction with a whole number. Identify the multiplication represented in the fraction strip.

 

 

Each addends is \(\frac{2}{5}\) since two-fifth of the parts are shaded. There are 3 such addends.

Thus, the multiplication represented is \(\frac{2}{5} \times 3\). .

If you arrange the shaded parts in the consecutive one-fifths we get:

 

 

This is precisely the product \(\frac{2}{5} \times 3 = \frac{6}{5}\).

The same thing can be represented using a number line as shown:

 

 

Each leap moves two-fifth of a unit to the right. Since the multiplication is by 3, after the third leap it reaches the product.

The arithmetic computation of this would be 

\(\frac{2}{5} \times 3 = \frac{2}{5} \times \frac{3}{1} = \frac{2 \times 3}{5 \times 1} = \frac{6}{5}\)

Looking for multiplying fractions by whole numbers games? Check out Multiply a Fraction and a Whole Number Game and have a fun-filled practice!

Multiplication of a Fraction by a Fraction:

When the multiplication is with two fractions then both have to be shown as different fraction strips. Consider the product \(\frac{2}{3} \times \frac{3}{4}\). This can be represented as:

 

 

The arithmetic computation of the multiplication can be done by multiplying the numerators and denominators separately as shown.

\(\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}\)

The simplified fraction of \(\frac{6}{12}\) will be \(\frac{1}{2}\). Arranging the shaded parts differently will show exactly half of the given strip.

Multiplication of Mixed Numbers (Mixed Fractions):

When two fractions are multiplied with at least one of them being a mixed fraction, the first step is to convert the mixed fraction into an improper fraction. Then, multiply the numerators and the denominators separately, just like two fractions.

Example 1: To multiply \(\frac{5}{8}\) and \(\frac{3}{12}\), we first rewrite  \(3\frac{1}{2}\) as an improper fraction.

 

  

Next, we will multiply the fractions.  

 

 

The improper fraction \(\frac{35}{16}\) can be written as a mixed fraction as \(2\frac{3}{16}\).

Example 2: Multiplying two mixed fractions

Now, to multiply mixed fractions, the procedure is similar. First, simplify fractions.

 

 

Now, cancel the common factors of the two fractions to be multiplied.

 

 

For multiplying 3 fractions the procedure is similar. The denominators, as well as the numerators, need to be multiplied separately. If you are looking for multiplying mixed numbers games, check out Multiply Mixed Fractions Game!

Progression of Multiplication of Fraction Concepts with Grades

 

Grade	Concept
Grade 3	• Introduction to fractions (understanding of fractions as numbers) and identifying fractions • Introduction to simple fractions with denominators 2, 3, 4, 6, and 8 using pictures and models.  • Understanding fractions as sums of unit fractions. • Learning the representation of fraction on the number line. • Learning about the concept of equivalent fractions  • Comparing fractions with the same numerator or same denominator.
Grade 4	• Multiplication of a fraction by a whole number introduced using fraction strip visual models and number lines.  • Unit and non-unit fractions treated separately for clear understanding. • Learning decomposition of fractions  • Addition, subtraction, and multiplication of fractions and mixed numbers
Grade 5	• Direct multiplication of fractions by considering whole numbers as fractions with a denominator of 1.  • Multiplication of fractions with fractions or whole numbers. • Simplifying multiplication using numerators and denominators separately.  • Multiplication of more complex fractions and mixed numbers, along with solving real-world problems.  • Interpretation of multiplication as scaling • Addition and subtraction of fractions by making them equivalent fractions.  • Solving real-world problems involving multiplication of fractions and mixed numbers.  • Dividing whole numbers and unit fractions.

 

Activities for Teaching Multiplying Fractions

While multiplying fractions calculators can give you the product, it is important to understand the concept behind it. Children can relate better to a topic when they have first-hand experience of the application of the concept. So, it is always a great idea to start the topic of multiplying fractions using an example of a fraction which they are familiar with, in their day-to-day life.

Multiplication of a Fraction by a Whole Number

Primary graders may find multiplying fraction as a boring mechanical calculation. Introducing it with a real-life situation like below would help the kids to relate to it better.

Example: Rhea is making Lemonade for her and her 6 friends for a birthday party. She knows that each glass of lemonade needs to be fresh lime juice. To estimate the amount of lime juice required, she can multiply the fraction \(\frac{1}{5}\) by 7.

She also has to serve a pizza to all 7 of them. So, to estimate the number of pizzas required, again she can do the multiplication \(\frac{1}{4} \times 7\).

Now, how to multiply fractions by whole numbers?

A pictorial representation of the second situation can be shown as below:

\(\frac{1}{5} \times 7\) = \(\frac{7}{5}\)

 

 

Another representation for the multiplication of a fraction by a whole number is using the number line:

\(\frac{1}{4} \times 7 = \frac{7}{4}\)
 

 

Multiplication of a Fraction by a Fraction:

Consider the area of a rectangle with fractional side lengths. It would be a good example of multiplying a fraction by another.

Example: A rectangular dining table has dimensions \(\frac{2}{7}\) units by \(\frac{3}{5}\) units. The area covered by the dining table can be obtained by multiplying the fractions \(\frac{2}{7}\) and \(\frac{3}{5}\).

A pictorial representation of multiplying two fractions can be shown as below:

 

 

How Can Children Use the Concept of Multiplying Fractions in Real Life?

• Baking and cooking: When following a recipe, kids can use multiplying fractions to adjust ingredient quantities. For example, doubling the ingredients to prepare twice the amount of a recipe. If it originally requires \(\frac{1}{2}\) cup of flour, doubling it gives you one whole cup of flour.
• DIY Projects: Planning DIY projects involves multiplying fractions, like determining the amount of wood needed for a fence or the fabric for curtains. Cutting a piece of fabric that is \(\frac{1}{4}\) the size of the original requires multiplying fractions for precise measurements.
• Sharing Treats: Dividing a pizza among friends involves multiplying fractions to figure out how much each person gets. 
• Art and craft: If you're cutting a piece of fabric that's \(\frac{3}{8}\) yard long into 5 equal pieces, each piece will be \(\frac{3}{8}\) yard  \( \times \frac{1}{5} = \frac{3}{40}\) yard
• Time Management: If you spend \(\frac{1}{4}\) of an hour on homework each day, in a week (7 days), you'll spend \(\frac{3}{8}\) hour \(\times 7 = \frac{7}{4}\) hours \(= 1\frac{3}{4}\) hours in total.

Importance of Introducing Multiplication of Fractions to Kids through Multiplication Fractions Games

• Visual Understanding: Multiplication of fractions can be abstract, but games provide visual models that help kids grasp the concept better by showing how fractions combine.
• Engaging Learning: Math games make learning fun, motivating kids to practice and apply multiplication of fractions in different scenarios.
• Concrete Practice: Interactive games on multiplying fractions provide hands-on practice, helping kids build fluency and confidence in multiplying fractions.
• Real-World Application: Multiplying fractions online games simulate real-life situations where fractions are multiplied, helping kids connect the concept to practical scenarios.

Learning to Multiply Fractions: Multiplication Math Games vs. Traditional Methods

• Engaging Visuals: Online fraction games use interactive visuals to explain fraction multiplication, making it easier to grasp complex concepts compared to traditional methods.
• Immediate Feedback: Games provide instant feedback, correcting mistakes and reinforcing learning in real-time, a feature not found in traditional methods.
• Adaptive Challenges: Online fraction multiplication games adjust difficulty levels based on progress, ensuring a personalized learning pace for each student, which traditional methods may struggle to achieve.

What Are 5 Best Fun Multiplying Fractions Games and Activities for Kids?

Here are a few amazing multiplying fractions games by SplashLearn:

• Multiply a Unit Fraction by a Whole Number Game
• Multiply Fractions using Models Game
• Find the Product of Fractions Game
• Estimate the Product of Mixed Numbers Game
• Complete the Fraction Multiplication Expression using Fraction Models