Multiplication of Fractions steps and methods are here. Check rules, tricks, and tips to solve fraction multiplication problems. Refer to the important formulae and also types involved in it. Know the fraction multiplication solved examples, types, and parts of fractions, variables, etc. Go through the below sections to get the complete details regarding multiplication methods, formulae, rules, etc.

### Multiplication of Fractions – Introduction

Fractions multiplication starts with numerators multiplication followed by denominators multiplication. The resultant fraction of the multiplication fraction can be simplified further and can be reduced to its lowest terms. Fraction Multiplication is not the same as adding or subtracting the fraction values.

Any two or more fractions with different denominators can easily be multiplied. The main thing to be considered is the fractions should not be mixed fractions, they should be either proper or improper fractions. There are various steps involved in multiplying the fractions. They are:

- In the fractions multiplication, we multiply the numerator with the numerator term to get the desired result of the numerator.
- In the fractions multiplication, we multiply the denominator with the denominator term to get the desired result of the denominator.
- After finding the resultant numerator and denominator values, check for simplification if possible
- Once the simplification is done, we get the final resultant value.

### How to Multiply Mixed Fractions?

Consider a mixed fraction which is the form of a \(\frac { b }{ c } \).

In the above-mixed fraction, convert the fraction value into an improper fraction. After converting it into an improper fraction, apply all the above steps we do in the multiplication of fractions. To convert mixed fractions into improper fractions, we apply the following steps:

- Multiply the whole number (a) with the denominator (c). We get the result value (a * c)
- To the above result value (a * c), add the numerator value (b). After the addition of the numerator, we find the numerator of the improper fraction.
- The denominator value of the improper fraction will be the denominator of the same mixed fraction.
- Generally, we can write it as a \(\frac { b }{ c } \) = \(\frac { c*a + b}{ c } \)

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### Multiplication of Proper Fractions

Multiplication of proper fractions is the easiest form of all the fractions multiplication.

**Example:**

Solve the equation \(\frac { 2 }{ 3 } \) × \(\frac { 4 }{ 6 } \)?

**Solution:**

As given in the question,

The equation is \(\frac { 2 }{ 3 } \) × \(\frac { 4 }{ 6 } \)

Here, \(\frac { 2 }{ 3 } \), \(\frac { 4 }{ 6 } \) are the proper fractions. To multiply the proper fractions, we have to follow the steps.

**Step 1: **First of all, multiply the numerators together i.e., 2 and 4. The solution is 2 * 4 = 8

**Step 2:** Next, multiply the denominators together ie., 3 and 6. The solution is 3 * 6 = 18. The fraction value can be written as \(\frac { 2*4 }{ 3*6 } \) = \(\frac { 8 }{ 18 } \)

**Step 3:** Check if you can simplify the resultant equation. On simplification, we can write it as \(\frac { 4 }{ 9 } \)

### Multiplication of Improper Fractions

An improper fraction is the one that has a greater denominator than the numerator. If we multiply an improper fraction, we result in an improper fraction.

**Example: **

Solve the equation \(\frac { 3 }{ 2 } \) × \(\frac { 7 }{ 5 } \) of the improper fractions?

**Solution:**

As given in the question,

The equation is \(\frac { 3 }{ 2 } \) × \(\frac { 7 }{ 5 } \)

Here, \(\frac { 3 }{ 2 } \), \(\frac { 7 }{ 5 } \) are improper fractions. To multiply the improper fractions, we have to follow the steps.

**Step 1:** First of all, multiply the numerators together i.e., 3 and 7. The solution is 3 * 7 = 21

**Step 2:** Next, multiply the denominators together i.e., 2 and 5. The solution is 2 * 5 = 10. The fraction value can be written as \(\frac { 3*7 }{ 2*5 } \) = \(\frac { 21 }{ 10 } \)

**Step 3:** Check if you can simplify the resultant equation. In the above equation, simplification is not possible.

**Step 4:** Now, convert the fraction into an improper fraction. Hence, the result is 2[/latex] = \(\frac { 1 }{ 10 } \)

### Multiplication of Mixed Fractions

Mixed Fractions are those fractions which have a whole number and a fraction like 2 [/latex] = \(\frac { 1 }{ 2 } \). When multiplying both the mixed fractions, we have to convert the mixed fractions into improper fractions.

**Example:**

Multiply the fractions 2\(\frac { 2 }{ 3 } \) and 3\(\frac { 1 }{ 4 } \)

**Solution:**

The given equation is 2\(\frac { 2 }{ 3 } \) x 3\(\frac { 1 }{ 4 } \)

Here, 2\(\frac { 2 }{ 3 } \) and 3\(\frac { 1 }{ 4 } \) are mixed fractions. To multiply the mixed fractions, we have to follow the following steps.

**Step 1:** First of all, convert the mixed fractions to improper fractions. To convert the mixed fraction of 2\(\frac { 2 }{ 3 } \), we write it as \(\frac { (3×2+2) }{ 3 } \). The result is 8/3. To convert the mixed fraction of 3\(\frac { 1 }{ 4 } \), we write it as \(\frac { (4×3+1) }{ 4 } \). The result is 13/4

**Step 2:** Multiply the numerators together i.e., 8 and 13. The solution is 8 * 13 = 104

**Step 3:** Next, multiply the denominators together i.e., 3 and 4. The solution is 3 * 4 = 12. The fraction value can be written as \(\frac { 8*13 }{ 3*4 } \) = \(\frac { 104 }{ 12 } \)

**Step 4:** Check if you can simplify the resultant equation. In the above equation, the simplification can be done as \(\frac { 26 }{3 } \).

**Step 5:** Now, convert the fraction into an improper fraction. Hence the result is 8\(\frac { 2 }{ 3 } \)

### Multiplying Fractions Examples

**Problem 1: **

A recipe calls for \(\frac { 3 }{ 4 } \) cups of sugar. Amari is tripling the recipe. How much amount of sugar will be needed?

**Solution:**

As given in the question,

Amount of sugar for recipe = \(\frac { 3 }{ 4 } \)

No of times Amari multiplied the recipe = 3

Therefore, to find the amount of sugar we apply the multiplication of fractions

Hence, \(\frac { 3 }{ 4 } \) * \(\frac { 3 }{ 1 } \) = \(\frac { 9 }{ 4 } \)

Now, convert the proper fraction into an improper fraction i.e., 2\(\frac { 1 }{ 4 } \)

Thus, the final solution is 2\(\frac { 1 }{ 4 } \)

**Problem 2:**

\(\frac { 4 }{ 5 } \) of all students at Riverwood High School are involved in an extracurricular activities. Of those students, \(\frac { 2 }{ 3 } \) are involved in a fall activity. What fraction of students at Riverwood are involved in a fall activity?

**Solution:**

As given in the question,

No of students involved in extracurricular activities = \(\frac { 4 }{ 5 } \)

No of students involved in fall activity = \(\frac { 2 }{ 3 } \)

To find the fraction of students involved in a fall activity, we have to apply the multiplication of fractions

Hence \(\frac { 2 }{ 3 } \) x \(\frac { 4 }{ 5 } \) = \(\frac { 8 }{ 15 } \)

Thus, \(\frac { 8 }{ 15 } \) fraction of students are involved in a fall activity.

Therefore, the final solution is \(\frac { 8 }{ 15 } \)

**Problem 3:**

Jimmy has a collection of 18 video games. Of the 18 video games. \(\frac { 1 }{ 3 } \) are sports games. How many of his games are sports games?

**Solution:**

As given in the question,

No of video games = 18

Part of sports games = \(\frac { 1 }{ 3 } \)

To find the no of sports games, we apply multiplication of fractions

Hence \(\frac { 1 }{ 3 } \) x \(\frac { 18 }{ 1 } \)

=\(\frac { 18 }{ 3 } \)

On further simplications, we get the result as 6.

Therefore, Jimmy has a collection of 6 sports games.