Learn Multiplying Fractions

With Ease

Fractions are an important part of mathematics, and understanding how to multiply them opens up a world of possibilities.

Learn Multiplying Fractions

With Ease

Fractions are an important part of mathematics, and understanding how to multiply them opens up a world of possibilities.

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No credit card required

Learn Multiplying Fractions with Smartick

Definition

How to Multiply Fractions?

Rules

Multiplying Fractions with Same Denominator

Multiplying Fractions with Different Denominator

Multiplying Fractions with Whole Numbers

Common Mistakes to Avoid

Real-Life Applications

Definition

Before we start, let’s make sure we understand what multiplying fractions means. Imagine you have two fractions: one that shows how much of something you have, and another that shows how much of something else you have. When we multiply these fractions, we’re finding out how much we’ll have if we combine both amounts. It’s like mixing two delicious ingredients to make something even more awesome!

How to Multiply Fractions?

Multiplying fractions might sound tricky, but it’s simpler than you think. Here’s the secret: you just need to multiply the top parts (numerators) of the fractions and the bottom parts (denominators) of the fractions separately. Then, you put the new numerator and new denominator together, and ta-da! You’ve got your multiplied fraction.

Rules

Let’s establish some simple yet powerful rules to guide us through the exciting math world of multiplying fractions. These rules are like a treasure map that leads us to the right answers:

  1. Multiply the Numerators (Top Numbers) Together: When we multiply fractions, we’re combining their parts to create something new. To do this, start by multiplying the numerators, which are the top numbers of the fractions. This step is like counting how many pieces of the whole we want to combine.
  2. Multiply the Denominators (Bottom Numbers) Together: But wait, we’re not done yet! Just as we need to know how many pieces we have, we also need to know how big each piece is. This is where the denominators, the bottom numbers of the fractions, come into play. Multiply these denominators to find the size of the new pieces we’re creating.
  3. Put the New Numerator over the New Denominator: Now that we have the number of pieces and their sizes, it’s time to put everything together. Place the new numerator, which we found by multiplying the numerators, over the new denominator, which we calculated by multiplying the denominators. This forms a brand-new fraction that shows the result of our multiplication.
  4. If Possible, Simplify the Fraction to Make It Simpler: Sometimes, fractions can be a bit like puzzles that have extra pieces. If the numerator and denominator share a common factor (a number they can both be divided by), we can simplify the fraction. This means making the fraction simpler without changing its value. Simplifying helps us work with neater and easier-to-understand fractions.

Remember, these rules are like magic spells that turn the complicated task and process of adding and multiplying fractions into a series of simple steps. Following these rules ensures that we create accurate and understandable answers every time we multiply fractions.

Multiplying Fractions with Same Denominator

When the fractions have the same bottom number (denominator), it’s super easy. You just have to multiply the top numbers (numerators) and keep the same denominator. Think of it as a fraction team-up where the denominator stays the same, and the numerators work together to create the new fraction.

Example 1: Multiply 2/5 by 3/5.

  • Step 1: Multiply the numerators (top numbers) together: 2 3 = 6.
  • Step 2: Multiply the denominators (bottom numbers) together: 5 5 = 25.

So, 2/5 * 3/5 = 6/25.

Example 2: Multiply 4/9 by 2/9.

  • Step 1: Multiply the numerators: 4 2 = 8.
  • Step 2: Multiply the denominators: 9 9 = 81.

Therefore, 4/9 * 2/9 = 8/81.

Example 3: Multiply 1/3 by 2/3.

  • Step 1: Multiply the numerators: 1 2 = 2.
  • Step 2: Multiply the denominators: 3 3 = 9.

Hence, 1/3 * 2/3 = 2/9.

Multiplying fractions with the same denominator is simpler because you don’t have to worry about finding a common denominator. Just multiply the numerators together and multiply the two denominators together, and you’ve got your answer! Remember, if the resulting fraction can be simplified, be sure to simplify it for the simplest form.

Multiplying Fractions with Different Denominators

If the denominators are different, don’t worry! We can still multiply the fractions. First, we’ll find a common denominator by multiplying the two denominators. Then, we’ll adjust the numerators and subtract fractions to match the new denominator. After that, it’s just like multiplying fractions with the same denominator.

Example 1: Multiply 2/3 by 1/4.

Step 1: Find a common denominator. The least common multiple of 3 and 4 is 12. Step 2: Adjust the fractions to have the common denominator:

  • 2/3 becomes 8/12 (multiply numerator and denominator by 4).

  • 1/4 becomes 3/12 (multiply numerator and denominator by 3). Step 3: Multiply the adjusted fractions:

  • 8/12 3/12 = (8 3) / (12 * 12) = 24/144.

This fraction can be simplified further, which gives 1/6.

Example 2: Multiply 5/6 by 2/5.

Step 1: Find a common denominator. The least common multiple of 6 and 5 is 30. Step 2: Adjust the fractions to have the common denominator:

  • 5/6 becomes 25/30 (multiply numerator and denominator by 5).

  • 2/5 becomes 12/30 (multiply numerator and denominator by 6). Step 3: Multiply the adjusted fractions:

  • 25/30 12/30 = (25 12) / (30 * 30) = 300/900.

Simplify the fraction to get 1/3.

Example 3: Multiply 3/7 by 4/9.

Step 1: Find a common denominator. The least common multiple of 7 and 9 is 63. Step 2: Adjust the fractions to have the common denominator:

  • 3/7 becomes 27/63 (multiply numerator and denominator by 9).

  • 4/9 becomes 28/63 (multiply numerator and denominator by 7). Step 3: Multiply the adjusted fractions:

  • 27/63 28/63 = (27 28) / (63 * 63) = 756/3969.

This fraction can be simplified to 4/21.

Multiplying Fractions with Whole Numbers

Sometimes, we need to multiply fractions by whole numbers. It’s like having a whole batch of fractions! Just turn the whole number into a fraction (by putting it over 1) and follow the same steps as before. It’s like having one big piece of the puzzle.

Example 1: Multiply 2/3 by 5.

Step 1: Turn the whole number into a fraction: 5 becomes 5/1. Step 2: Multiply the fractions: (2/3) (5/1) = (2 5) / (3 * 1) = 10/3.

This figure can also be expressed as a mixed number: 3 1/3.

Example 2: Multiply 3/8 by 7.

Step 1: Turn the whole number into a fraction: 7 becomes 7/1. Step 2: Multiply the following fractions by: (3/8) (7/1) = (3 7) / (8 * 1) = 21/8.

No simplification is necessary.

Multiplying a fraction by a whole number is like having many pieces of that fraction. Remember that a whole number can be turned into a fraction by putting it over 1, and then you can use the same rules for multiplying fractions as before. If the resulting fraction can be simplified, make sure to simplify it.

 

Multiplying Fractions with Whole Numbers

Mixed numbers might look confusing, but they’re actually pretty cool. First, change the mixed number into an improper fraction. Then, follow the steps for multiplying the improper fractions together. It’s like turning a mixed-up puzzle piece into a single, simple fraction.

Representing Multiplication of Fractions Using Models 

multiplying fractions

Models can be a helpful tool to visualize the multiplication of fractions. One commonly used model is the area model, where each fraction is represented by a rectangle, and the product is determined by finding the area of the resulting rectangle. By first dividing fractions of each rectangle into equal parts based on the denominators, we can determine the area of the product.

Properties of Multiplying Fractions

Numbers have special properties, and fractions are no exception. The order you multiply fractions doesn’t matter (commutative property), and you can group them differently and still get the same answer (associative property). These properties make the problem of multiplying fractions even more interesting!

Common Mistakes to Avoid

Even experts make mistakes, but we’re here to help you avoid them. Remember to multiply, write the numerators and denominators separately, and simplify your final answer, if you can. Don’t rush, and you’ll do great!

Real-Life Applications

Believe it or not, multiplying fractions is super useful in everyday life. When you’re cooking, measuring, or building things, subtracting and adding fractions can help you get things just right. You’re turning math into real-world superpowers! 

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