Multiplying numbers is so easy compared to Multiplying Fractions. The fraction is represented as the division of the whole. The fraction is in the form of “x/y” where “x” is the numerator and “y” is the denominator. One can apply the fraction concept to real-time examples easily after reading the entire concept here. If you have an apple and you made it into 4 equal parts, then it can represent as \(\frac { 1 }{ 4 } \). Or else if it cut into 7 pieces then it can represented as \(\frac { 1 }{ 7 } \).

## How to Multiply Fractions?

We have provided simple steps to multiply fractions and find the solution of multiplying fractions. It is easy to find out the solution using the below procedure. Multiplying fractions can be defined as the product of a fraction with another fraction or with the variables or with an integer. Follow the below process to multiply fractions

- Multiply the numerator with numerator
- Multiply the denominator with the denominator
- Simplify the fractions, if needed

Example:

1. Multiply \(\frac { 2 }{ 3 } \) × \(\frac { 1 }{ 5 } \)

Solution:

Given that \(\frac { 2 }{ 3 } \) × \(\frac { 1 }{ 5 } \)

To multiply the above fractions, firstly multiply the numerators

2 × 1 = 2

multiply the denominators

3 × 5 = 15

Now, simplify the fraction, we get \(\frac { 2 }{ 15 } \)

If \(\frac { x }{ y } \) and \(\frac { m }{ n } \) are the multiplicand and multiplier, then the output is \(\frac { xm }{ yn } \)

Product of Fraction = Product of Numerator/Product of Denominator

### Fractions Parts and Types

A fraction consists of two parts. One is the numerator and another one is the denominator. If \(\frac { a }{ b } \) is a fraction, then the two parts are a and b where a is the numerator and b is the denominator. Or else if \(\frac { 3 }{ 4 } \) is a fraction, then the two parts are 3 and 4 where 3 is the numerator and 4 is the denominator.

Mainly, there are three types of fractions considered. They are proper fractions, improper fractions, and mixed fractions.

Proper fractions: A fraction is said to be a proper fraction when the numerator of a fraction is less than the denominator.

Examples: \(\frac { 1 }{ 4 } \), \(\frac { 5 }{ 6 } \), \(\frac { 7 }{ 11 } \)

Improper fractions: A fraction is said to be an improper fraction when the numerator is greater than the denominator.

Examples: \(\frac { 5 }{ 4 } \), \(\frac { 7 }{ 6 } \), \(\frac { 13 }{ 11 } \)

Mixed Fraction: A fraction is said to be a mixed fraction when we write the improper fraction in the combination of a whole number and a fraction.

Examples: 1 \(\frac { 5 }{ 4 } \), 3 \(\frac { 9 }{ 6 } \), 2 \(\frac { 6 }{ 7 } \)

Also, Read:

- Worksheet on Multiplication of Fractions
- Multiplication of Fractions
- Addition and Subtraction of Fractions

### Fractional Simplification

Generally, the multiplication of fractions can be finished by multiplying numerators with numerators and multiplying denominators with denominators. To make the fractional multiplication simpler, we can reduce the fraction by canceling the common factors. By canceling out the common factors from the given factor, it becomes easier to find the exact output.

Example: \(\frac { 9 }{ 4 } \) and \(\frac { 2 }{ 3 } \)

\(\frac { 9 }{ 4 } \) can written as \(\frac { 3 × 3 }{ 2×2 } \)

\(\frac { 3 × 3 }{ 2×2 } \) × \(\frac { 2 }{ 3 } \) = \(\frac { 3 }{ 2 } \)

If there is no common factors, then the numerators and denominators are multiplied directly.

### Types of Fraction Multiplication

There are different types of Fraction Multiplication available. They are

- Multiplication of Fraction with Whole Numbers
- Multiplication of Fraction with another Fraction
- Multiplication of Fraction with Variables

#### Multiplication of Fractional Number by a Whole Number

In Multiplication of Fractional Number by a Whole Number, we multiply the numerator with the numerator and the denominator remains the same. Before you multiply, reduce the fraction to the lowest terms. Check out different problems on the Multiplication of Fractional Number by a Whole Number below.

1. Multiply 2 \(\frac { 2 }{ 3 } \) by 9

Solution:

Given that multiply 2 \(\frac { 2 }{ 3 } \) by 9.

Firstly, convert given mixed fraction 2 \(\frac { 2 }{ 3 } \) to fraction.

2 \(\frac { 2 }{ 3 } \) = \(\frac { 8 }{ 3 } \)

Now, multiply \(\frac { 8 }{ 3 } \) by 9.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

8 × 9 = 72.

So, the fraction is \(\frac { 72 }{ 3 } \)

Simplify the fraction to get the final answer.

\(\frac { 72 }{ 3 } \) = 24.

The final answer is 24.

(ii) Multiply \(\frac { 3 }{ 4 } \) by 6

Solution:

Given that multiply \(\frac { 3 }{ 4 } \) by 6

multiply \(\frac { 3 }{ 4 } \) by 6.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

3 × 6 = 18.

So, the fraction is \(\frac { 18 }{ 4 } \)

Simplify the fraction to get the final answer.

\(\frac { 18 }{ 4 } \) = \(\frac { 9 }{ 2 } \).

The final answer is \(\frac { 9 }{ 2 } \).

(iii) Multiply 3 \(\frac { 3 }{ 2 } \) by 6

Solution:

Given that multiply 3 \(\frac { 3 }{ 2 } \) by 6.

Firstly, convert given mixed fraction 3 \(\frac { 3 }{ 2 } \) to fraction.

3 \(\frac { 3 }{ 2 } \) = \(\frac { 9 }{ 2 } \)

Now, multiply \(\frac { 9 }{ 2 } \) by 6.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

9 × 6 = 54.

So, the fraction is \(\frac { 54 }{ 2 } \)

Simplify the fraction to get the final answer.

\(\frac { 54 }{ 2 } \) = 27.

The final answer is 27.

#### Multiplication of Fractional Number by Another Fractional Number

Multiplying Fraction with Another Fraction is explained with the below examples.

(i). Multiply \(\frac { 3 }{ 5 } \) by \(\frac { 6 }{ 5 } \)

Solution:

Given that Multiply \(\frac { 3 }{ 5 } \) by \(\frac { 6 }{ 5 } \).

Firstly, multiply the numerators with numerators.

3 × 6 = 18.

Next, multiply the denominators with denominators.

5 × 5 = 25.

Finally, write the fraction in the simplest form.

\(\frac { 18 }{ 25 } \)

The final answer is \(\frac { 18 }{ 25 } \)

(ii) Multiply \(\frac { 3 }{ 4 } \) by \(\frac { 7 }{ 2 } \)

Solution:

Given that Multiply \(\frac { 3 }{ 4 } \) by \(\frac { 7 }{ 2 } \).

Firstly, multiply the numerators with numerators.

3 × 7 = 21.

Next, multiply the denominators with denominators.

4 × 2 = 8.

Finally, write the fraction in the simplest form.

\(\frac { 21 }{ 8 } \)

The final answer is \(\frac { 21 }{ 8 } \).

(iii) Multiply \(\frac { 2 }{ 3 } \), \(\frac { 2 }{ 5 } \), and \(\frac { 2 }{ 7 } \)

Solution:

Given that Multiply \(\frac { 2 }{ 3 } \), \(\frac { 2 }{ 5 } \), and \(\frac { 2 }{ 7 } \).

Firstly, multiply the numerators with numerators.

2 × 2 × 2 = 8.

Next, multiply the denominators with denominators.

3 × 5 × 7 = 105.

Finally, write the fraction in the simplest form.

\(\frac { 8 }{ 105 } \)

The final answer is \(\frac { 8 }{ 105 } \).

#### Multiplication of a Mixed number by Another Mixed Number

To find the multiplication of a mixed number with another mixed number, we need to change the mixed fractions to fractions and multiply them.

(i) Multiply 3 \(\frac { 2 }{ 5 } \) and 2 \(\frac { 3 }{ 7 } \)

Solution:

Given that multiply 3 \(\frac { 2 }{ 5 } \) and 2 \(\frac { 3 }{ 7 } \).

Firstly, convert given mixed fractions 3 \(\frac { 2 }{ 5 } \) and 2 \(\frac { 3 }{ 7 } \) to fractions.

3 \(\frac { 2 }{ 5 } \) = \(\frac { 17 }{ 5 } \)

2 \(\frac { 3 }{ 7 } \) = \(\frac { 17 }{ 7 } \)

Now, multiply \(\frac { 17 }{ 5 } \) by \(\frac { 17 }{ 7 } \).

Firstly, multiply the numerators with numerators.

17 × 17 = 289.

Next, multiply the denominators with denominators.

5 × 7 = 35.

Finally, write the fraction in the simplest form.

\(\frac { 289 }{ 35 } \)

The final answer is \(\frac { 289 }{ 35 } \).

(ii) Multiply 2 \(\frac { 4 }{ 3 } \) and 1 \(\frac { 6 }{ 5 } \)

Solution:

Given that multiply 2 \(\frac { 4 }{ 3 } \) and 1 \(\frac { 6 }{ 5 } \).

Firstly, convert given mixed fractions 2 \(\frac { 4 }{ 3 } \) and 1 \(\frac { 6 }{ 5 } \) to fractions.

2 \(\frac { 4 }{ 3 } \) = \(\frac { 10 }{ 3 } \)

1 \(\frac { 6 }{ 5 } \) = \(\frac { 11 }{ 5 } \)

Now, multiply \(\frac { 10 }{ 3 } \) by \(\frac { 11 }{ 5 } \).

Firstly, multiply the numerators with numerators.

10 × 11 = 110.

Next, multiply the denominators with denominators.

5 × 3 = 15.

Finally, write the fraction in the simplest form.

\(\frac { 110 }{ 15 } \) = \(\frac { 22 }{ 3 } \)

The final answer is \(\frac { 22 }{ 3 } \).

(i) Multiply 4 \(\frac { 2 }{ 9 } \) and 5 \(\frac { 1 }{ 4 } \)

Solution:

Given that multiply 4 \(\frac { 2 }{ 9 } \) and 5 \(\frac { 1 }{ 4 } \).

Firstly, convert given mixed fractions 4 \(\frac { 2 }{ 9 } \) and 5 \(\frac { 1 }{ 4 } \) to fractions.

4 \(\frac { 2 }{ 9 } \) = \(\frac { 38 }{ 9 } \)

5 \(\frac { 1 }{ 4 } \) = \(\frac { 21 }{ 4 } \)

Now, multiply\(\frac { 38 }{ 9 } \) by \(\frac { 21 }{ 4 } \).

Firstly, multiply the numerators with numerators.

38 × 21 = 798.

Next, multiply the denominators with denominators.

9 × 4 = 36.

Finally, write the fraction in the simplest form.

\(\frac { 798 }{ 36 } \)

The final answer is \(\frac { 798 }{ 36 } \).

### Multiplying Fractions Examples

I. Find the product

(i) \(\frac { 5 }{ 4 } \) × 1

(ii) \(\frac { 3 }{ 5 } \) × 6

(iii) \(\frac { 10 }{ 15 } \) × 7

(iv) \(\frac { 2 }{ 3 } \) × 0

(v) \(\frac { 1 }{ 4 } \) × \(\frac { 2 }{ 7 } \)

(vi) 2\(\frac { 9 }{ 13 } \) × 4

(vii) \(\frac { 1 }{ 6 } \) × \(\frac { 7 }{ 1 } \)

(viii) \(\frac { 1 }{ 4 } \) × \(\frac { 8 }{ 6 } \) × \(\frac { 3 }{ 10 } \)

(ix) \(\frac { 5 }{ 16 } \) × \(\frac { 11 }{ 23 } \)

(x) \(\frac { 1 }{ 2 } \) of 50

(xi) \(\frac { 1 }{ 3 } \) of 90

(xii) \(\frac { 5 }{ 6 } \) of \(\frac { 9 }{ 12 } \)

(i) \(\frac { 5 }{ 4 } \) × 1

Solution:

Given that \(\frac { 5 }{ 4 } \) × 1

Now, multiply \(\frac { 5 }{ 4 } \) by 1.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

5 × 1 = 5.

So, the fraction is \(\frac { 5 }{ 4 } \)

The final answer is \(\frac { 5 }{ 4 } \).

(ii) \(\frac { 3 }{ 5 } \) × 6

Solution:

Given that \(\frac { 3 }{ 5 } \) × 6

multiply \(\frac { 3 }{ 5 } \) by 6

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

3 × 6 = 18.

So, the fraction is \(\frac { 18 }{ 5 } \)

Simplify the fraction to get the final answer.

\(\frac { 18 }{ 5 } \).

The final answer is \(\frac { 18 }{ 5 } \).

(iii) \(\frac { 10 }{ 15 } \) × 7

Solution:

Given that \(\frac { 10 }{ 15 } \) × 7

multiply \(\frac { 10 }{ 15 } \) by 7

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

10 × 7 = 70.

So, the fraction is \(\frac { 70 }{ 15 } \)

Simplify the fraction to get the final answer.

\(\frac { 70 }{ 15 } \) = \(\frac { 14 }{ 3 } \).

The final answer is \(\frac { 14 }{ 3 } \).

(iv) \(\frac { 2 }{ 3 } \) × 0

Solution:

Any fraction that multiplies with 0 gives 0.

Therefore, the answer is 0.

(v) \(\frac { 1 }{ 4 } \) × \(\frac { 2 }{ 7 } \)

Solution:

Given that Multiply \(\frac { 1 }{ 4 } \) by \(\frac { 2 }{ 7 } \).

Firstly, multiply the numerators with numerators.

1 × 2 = 2.

Next, multiply the denominators with denominators.

4 × 7 = 28.

Finally, write the fraction in the simplest form.

\(\frac { 2 }{ 28 } \)

Simplify the fraction to get the final answer.

\(\frac { 1 }{ 14 } \).

The final answer is \(\frac { 1 }{ 14 } \).

(vi) 2\(\frac { 9 }{ 13 } \) × 4

Solution:

Given that multiply 2\(\frac { 9 }{ 13 } \) × 4.

Firstly, convert given mixed fraction 2\(\frac { 9 }{ 13 } \) to fraction.

2\(\frac { 9 }{ 13 } \) = \(\frac { 35 }{ 13 } \)

Now, multiply \(\frac { 35 }{ 13 } \) by 4.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

35 × 4 = 140.

So, the fraction is \(\frac { 140 }{ 13 } \)

Simplify the fraction to get the final answer.

\(\frac { 140 }{ 13 } \).

The final answer is \(\frac { 140 }{ 13 } \).

(vii) \(\frac { 1 }{ 6 } \) × \(\frac { 7 }{ 1 } \)

Solution:

Given that Multiply \(\frac { 1 }{ 6 } \) × \(\frac { 7 }{ 1 } \).

Firstly, multiply the numerators with numerators.

1 × 7 = 7.

Next, multiply the denominators with denominators.

6 × 1 = 6.

Finally, write the fraction in the simplest form.

\(\frac { 7 }{ 6 } \)

Simplify the fraction to get the final answer.

\(\frac { 7 }{ 6 } \).

The final answer is \(\frac { 7 }{ 6 } \).

(viii) \(\frac { 1 }{ 4 } \) × \(\frac { 8 }{ 6 } \) × \(\frac { 3 }{ 10 } \)

Solution:

Given that Multiply \(\frac { 1 }{ 4 } \) × \(\frac { 8 }{ 6 } \) × \(\frac { 3 }{ 10 } \).

Firstly, multiply the numerators with numerators.

1 × 8 × 3 = 24.

Next, multiply the denominators with denominators.

4 × 6 × 10 = 240.

Finally, write the fraction in the simplest form.

\(\frac { 24 }{ 240 } \)

Simplify the fraction to get the final answer.

\(\frac { 1 }{ 10 } \).

The final answer is \(\frac { 1 }{ 10 } \).

(ix) \(\frac { 5 }{ 16 } \) × \(\frac { 11 }{ 23 } \)

Solution:

Given that Multiply \(\frac { 5 }{ 16 } \) × \(\frac { 11 }{ 23 } \).

Firstly, multiply the numerators with numerators.

5 × 11 = 55.

Next, multiply the denominators with denominators.

16 × 23 = 368.

Finally, write the fraction in the simplest form.

\(\frac { 55 }{ 368 } \)

Simplify the fraction to get the final answer.

\(\frac { 55 }{ 368 } \).

The final answer is \(\frac { 55 }{ 368 } \).

(x) \(\frac { 1 }{ 2 } \) of 50

Solution:

Given that \(\frac { 1 }{ 2 } \) of 50

multiply \(\frac { 1 }{ 2 } \) by 50

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

1 × 50 = 50.

So, the fraction is \(\frac { 50 }{ 2 } \)

Simplify the fraction to get the final answer.

\(\frac { 50 }{ 2 } \) = 25.

The final answer is 25.

(xi) \(\frac { 1 }{ 3 } \) of 90

Solution:

Given that \(\frac { 1 }{ 3 } \) of 90

multiply \(\frac { 1 }{ 3 } \) by 90

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

1 × 90 = 90.

So, the fraction is \(\frac { 90 }{ 3 } \)

Simplify the fraction to get the final answer.

\(\frac { 90 }{ 3 } \) = 30.

The final answer is 30.

II. Multiply and write the product in the lowest terms.

(i) \(\frac { 1 }{ 2 } \) × 60

(ii) \(\frac { 1 }{ 3 } \) × 18

(iii) \(\frac { 2 }{ 5 } \) × 25

(iv) \(\frac { 4 }{ 3 } \) × 0

(v) \(\frac { 7 }{ 29 } \) × 1

(vi) 6 × \(\frac { 7 }{ 36 } \)

(vii) \(\frac { 5 }{ 34 } \) × \(\frac { 34 }{ 8 } \)

(viii) \(\frac { 12 }{ 25 } \) × \(\frac { 5 }{ 6 } \)

(ix) \(\frac { 6 }{ 14 } \) × \(\frac { 56 }{ 7 } \)

(x) \(\frac { 1 }{ 3 } \) × \(\frac { 4 }{ 5 } \) × \(\frac { 5 }{ 8 } \)

(xi) \(\frac { 6 }{ 3 } \) × \(\frac { 1 }{ 2 } \) × \(\frac { 3 }{ 3 } \)

(xii) 3\(\frac { 8 }{ 5 } \) × \(\frac { 5 }{ 4 } \)

(i) \(\frac { 1 }{ 2 } \) × 60

Solution:

Given that \(\frac { 1 }{ 2 } \) × 60

Now, multiply \(\frac { 1 }{ 2 } \) by 60.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

1 × 60 = 60.

So, the fraction is \(\frac { 60 }{ 2 } \)

Simplify the fraction to get the final answer.

\(\frac { 60 }{ 2 } \) = 30.

The final answer is 30.

(ii) \(\frac { 1 }{ 3 } \) × 18

Solution:

Given that \(\frac { 1 }{ 3 } \) × 18

Now, multiply \(\frac { 1 }{ 3 } \) by 18.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

1 × 18 = 18.

So, the fraction is \(\frac { 18 }{ 3 } \)

Simplify the fraction to get the final answer.

\(\frac { 18 }{ 3 } \) = 6.

The final answer is 6.

(iii) \(\frac { 2 }{ 5 } \) × 25

Solution:

Given that \(\frac { 2 }{ 5 } \) × 25

Now, multiply \(\frac { 2 }{ 5 } \) by 25.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

2 × 25 = 50.

So, the fraction is \(\frac { 50 }{ 5 } \)

Simplify the fraction to get the final answer.

\(\frac { 50 }{ 5 } \) = 10.

The final answer is 10.

(iv) \(\frac { 4 }{ 3 } \) × 0

Solution:

Any fraction that multiplies with 0 gives 0.

Therefore, the answer is 0.

(v) \(\frac { 7 }{ 29 } \) × 1

Solution:

Any fraction that multiplies with 1 gives the same output.

Therefore, the answer is \(\frac { 7 }{ 29 } \).

(vi) 6 × \(\frac { 7 }{ 36 } \)

Solution:

Given that 6 × \(\frac { 7 }{ 36 } \)

Now, multiply 6 by \(\frac { 7 }{ 36 } \).

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

6 × 7 = 42.

So, the fraction is \(\frac { 42 }{ 36 } \)

Simplify the fraction to get the final answer.

\(\frac { 42 }{ 36 } \) = \(\frac { 21 }{ 18 } \).

The final answer is \(\frac { 21 }{ 18 } \).

(vii) \(\frac { 5 }{ 34 } \) × \(\frac { 34 }{ 8 } \)

Solution:

Given that Multiply \(\frac { 5 }{ 34 } \) × \(\frac { 34 }{ 8 } \).

Firstly, multiply the numerators with numerators.

5 × 34 = 170.

Next, multiply the denominators with denominators.

34 × 8 = 272.

Finally, write the fraction in the simplest form.

\(\frac { 170 }{ 272 } \)

Simplify the fraction to get the final answer.

\(\frac { 5 }{ 8 } \).

The final answer is \(\frac { 5 }{ 8 } \).

(viii) \(\frac { 12 }{ 25 } \) × \(\frac { 5 }{ 6 } \)

Solution:

Given that Multiply \(\frac { 12 }{ 25 } \) × \(\frac { 5 }{ 6 } \).

Firstly, multiply the numerators with numerators.

12 × 5 = 60.

Next, multiply the denominators with denominators.

25 × 6 = 150.

Finally, write the fraction in the simplest form.

\(\frac { 60 }{ 150 } \)

Simplify the fraction to get the final answer.

\(\frac { 60 }{ 150 } \) = \(\frac { 2 }{ 5 } \).

The final answer is \(\frac { 2 }{ 5 } \).

(ix) \(\frac { 6 }{ 14 } \) × \(\frac { 56 }{ 7 } \)

Solution:

Given that Multiply \(\frac { 6 }{ 14 } \) × \(\frac { 56 }{ 7 } \).

Firstly, multiply the numerators with numerators.

6 × 56 = 336.

Next, multiply the denominators with denominators.

14 × 7 = 98.

Finally, write the fraction in the simplest form.

\(\frac { 336 }{ 98 } \)

Simplify the fraction to get the final answer.

\(\frac { 336 }{ 98 } \) = 168.

The final answer is 168.

(x) \(\frac { 1 }{ 3 } \) × \(\frac { 4 }{ 5 } \) × \(\frac { 5 }{ 8 } \)

Solution:

Given that Multiply \(\frac { 1 }{ 3 } \) × \(\frac { 4 }{ 5 } \) × \(\frac { 5 }{ 8 } \).

Firstly, multiply the numerators with numerators.

1 × 4 × 5 = 20.

Next, multiply the denominators with denominators.

3 × 5 × 8 = 120.

Finally, write the fraction in the simplest form.

\(\frac { 20 }{ 120 } \)

Simplify the fraction to get the final answer.

\(\frac { 20 }{ 120 } \) = \(\frac { 1 }{ 6 } \).

The final answer is \(\frac { 1 }{ 6 } \).

(xi) \(\frac { 6 }{ 3 } \) × \(\frac { 1 }{ 2 } \) × \(\frac { 3 }{ 3 } \)

Solution:

Given that Multiply \(\frac { 6 }{ 3 } \) × \(\frac { 1 }{ 2 } \) × \(\frac { 3 }{ 3 } \).

Firstly, multiply the numerators with numerators.

6 × 1 × 3 = 18.

Next, multiply the denominators with denominators.

3 × 2 × 3 = 18.

Finally, write the fraction in the simplest form.

\(\frac { 18 }{ 18 } \)

Simplify the fraction to get the final answer.

\(\frac { 18 }{ 18 } \) = 1.

The final answer is 1.

(xii) 3\(\frac { 8 }{ 5 } \) × \(\frac { 5 }{ 4 } \)

Solution:

Given that multiply 3\(\frac { 8 }{ 5 } \) × \(\frac { 5 }{ 4 } \).

Firstly, convert given mixed fraction 3\(\frac { 8 }{ 5 } \) to fraction.

3\(\frac { 8 }{ 5 } \) = \(\frac { 23 }{ 5 } \)

Multiply \(\frac { 23 }{ 5 } \) × \(\frac { 5 }{ 4 } \).

Firstly, multiply the numerators with numerators.

23 × 5 = 115.

Next, multiply the denominators with denominators.

5 × 4 = 20.

Finally, write the fraction in the simplest form.

\(\frac { 115 }{ 20 } \)

Simplify the fraction to get the final answer.

\(\frac { 115 }{ 20 } \) = \(\frac { 23 }{ 4 } \).

The final answer is \(\frac { 23 }{ 4 } \).

III. Find the given quantity.

(i) \(\frac { 1 }{ 6 } \) of 48 kg apples

Solution:

Given that \(\frac { 1 }{ 6 } \) of 48 kg apples.

\(\frac { 1 }{ 6 } \) × 48 kg

8 kg

The answer is 8 kg.

(ii) \(\frac { 1 }{ 7 } \) of $280

Solution:

Given that \(\frac { 1 }{ 7 } \) of $280.

\(\frac { 1 }{ 7 } \) × $280

$40

The answer is $40.

(iii) \(\frac { 6 }{ 3 } \) of 54 km

Solution:

Given that \(\frac { 6 }{ 3 } \) of 54 km.

\(\frac { 6 }{ 3 } \) × 54 km

108 km

The answer is 108 km.

(iv) \(\frac { 2 }{ 8 } \) of 40 chairs

Solution:

Given that \(\frac { 2 }{ 8 } \) of 40 chairs.

\(\frac { 2 }{ 8 } \) × 40 chairs

10 chairs

The answer is 10 chairs.

#### Word problems on Multiplying Fractions

1. 3\(\frac { 5 }{ 8 } \) m of cloth is required to make a shirt. Sam wants to make 32 shirts, what length of cloth does he need?

Solution:

Given that 3\(\frac { 5 }{ 8 } \) m of cloth is required to make a shirt.

Sam wants to make 32 shirts.

3\(\frac { 5 }{ 8 } \) m of 32.

Firstly, convert given mixed fraction 3\(\frac { 5 }{ 8 } \) to fraction.

3\(\frac { 5 }{ 8 } \) = \(\frac { 29 }{ 8 } \)

\(\frac { 29 }{ 8 } \) × 32

Now, multiply \(\frac { 29 }{ 8 } \) by 32.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

29 × 32 = 928.

So, the fraction is \(\frac { 928 }{ 8 } \)

Simplify the fraction to get the final answer.

\(\frac { 928 }{ 8 } \) = 116.

The final answer is 116.

2. \(\frac { 5 }{ 2 } \) cups of milk is required to make a cake of 1 kg. How many cups of milk is required to make a cake of \(\frac { 2 }{ 5 } \) kg?

Solution:

Given that \(\frac { 5 }{ 2 } \) cups of milk is required to make a cake of 1 kg.

To make a cake of \(\frac { 2 }{ 5 } \) kg, multiply \(\frac { 5 }{ 2 } \) with \(\frac { 2 }{ 5 } \).

Firstly, multiply the numerators with numerators.

2 × 5 = 10.

Next, multiply the denominators with denominators.

5 × 2 = 10.

Finally, write the fraction in the simplest form.

\(\frac { 10 }{ 10 } \)

Simplify the fraction to get the final answer.

\(\frac { 10 }{ 10 } \) = 1.

The final answer is 1.

3. Shelly bought \(\frac { 11 }{ 9 } \) liters of juice. If the cost of 1-liter juice is $36, find the total cost of juice?

Solution:

Given that Shelly bought \(\frac { 11 }{ 9 } \) liters of juice.

If the cost of 1-liter juice is $36, multiply \(\frac { 11 }{ 9 } \) with $36.

\(\frac { 11 }{ 9 } \) × $36 = $44.

The final answer is $44.

4. The weight of each bag is 7\(\frac { 1 }{ 9 } \) Kg. What would be the weight of 36 such bags?

Solution:

Given that the weight of each bag is 7\(\frac { 1 }{ 9 } \) Kg.

If the weight of 36 such bags is 7\(\frac { 1 }{ 9 } \) Kg × 36.

Firstly, convert given mixed fraction 7\(\frac { 1 }{ 9 } \) to fraction.

7\(\frac { 1 }{ 9 } \) = \(\frac { 64 }{ 9 } \)

Now, multiply \(\frac { 64 }{ 9 } \) by 36.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

64 × 36 = 2304.

So, the fraction is \(\frac { 2304 }{ 9 } \)

Simplify the fraction to get the final answer.

\(\frac { 2304 }{ 9 } \) = 256.

The final answer is 256.

5. Sam works for 1 \(\frac { 5 }{ 6 } \) hours each day. For how much time will she work in a month if she works for 24 days in a month?

Solution:

Given that Sam works for 1 \(\frac { 5 }{ 6 } \) hours each day.

If she works for 24 days in a month, 1 \(\frac { 5 }{ 6 } \) hours each day × 24

Firstly, convert given mixed fraction 1 \(\frac { 5 }{ 6 } \) to fraction.

1 \(\frac { 5 }{ 6 } \) = \(\frac { 11 }{ 6 } \)

Now, multiply \(\frac { 11 }{ 6 } \) by 24.

Multiply the numerator of the fractional number by the whole number. The denominator remains the same.

11 × 24 = 264.

So, the fraction is \(\frac { 264 }{ 6 } \)

Simplify the fraction to get the final answer.

\(\frac { 264 }{ 6 } \) = 44.

The final answer is 44.