How to Multiply Fractions with Whole Numbers

Last Updated : 23 Jul, 2025

To Multiply Fractions with Whole Numbers, the whole numbers are written in the form of Fractions, and then multiplied with the given fractions, because fraction is a part of a whole and It has two parts:

  • Numerator: This is the number on top. It tells how many parts you have.
  • Denominator: This is the number on the bottom. It tells how many equal parts the whole is divided into.

For Example: In the fraction 3/4, 3 is the numerator, and 4 is the denominator. It means you have 3 out of 4 equal parts.

How to Multiply Fractions with Whole Numbers?

To multiply a fraction by a whole number, follow these easy steps:

Step 1: Change the Whole Number to a Fraction.

First, you need to turn the whole number into a fraction. You can do this by putting the whole number over 1. For example, if the whole number is 5, it becomes 5/1.

Step 2: Multiply the Numerators.

Next, multiply the top number (numerator) of the fraction by the top number of the whole number fraction.

Example: If you are multiplying 3/4 by 5

  • The top number of the fraction is 3, and the top number of the whole number fraction is 5.
  • Multiply: 3 × 5 = 15

Step 3: Multiply the Denominators.

Now, multiply the bottom number (denominator) of the fraction by the bottom number of the whole number fraction, which is always 1.

Continuing with our example:

  • The bottom number of the fraction is 4, and the bottom number of the whole number is 1.
  • Multiply: 4 × 1 = 4.

Step 4: Write the Result as a Fraction

Now, you can write the answer as a fraction. In our example, it becomes:

  • 15/4

Step 5: Simplify the Fraction and change it to Mixed Fraction. (if needed)

Fractions can be simplified, by dividing numerator and denominator by greatest common divisor (GCD). In this case, 15/4 cannot be simplified further.

If your answer is an improper fraction (when the top number is larger than the bottom number), you can change it to a mixed number.

For Example, 15/4 is an Improper Fraction:

  • Divide 15 by 4, which gives you 3 with a remainder of 3.
  • This means 15/4 equals 3 with a remainder of 3, or 3 3/4.

Examples of Multiplying Fractions with Whole Numbers -

Example 1. Let’s say we want to Multiply 2/5 by 3.

  • Change 3 into a fraction: 3 = 3/1
  • Multiply the top numbers: 2 × 3 = 6
  • Multiply the bottom numbers: 5 × 1 = 5
  • Write the result as a fraction: 6/5
  • Since 6/5 is an improper fraction, change it to a mixed number:

6/5 equals 1 with a remainder of 1, which is 1 1/5.

Answer: 1 1/5

Note: In case of mixed fraction, we need to change the mixed fraction into normal fraction and continue the same process after that.


Example 2. Let’s say we want to multiply 3 2/5 by 2.

Change the mixed fraction to an improper fraction:
3 2/5 = (3 × 5 + 2)/5 = (15 + 2)/5 = 17/5

Change 2 to a fraction:
2 = 2/1
Multiply the top numbers:
17 × 2 = 34
Multiply the bottom numbers:
5 × 1 = 5
Write the result as a fraction:
34/5
Change to a mixed number:
34/5 = 6 with a leftover of 4,
so it becomes 6 4/5.

Final Answer: 6 (4/5)

Solved Questions on Multiplication of Fractions with Whole Numbers

Question 1. Multiply 2/3 by 4

Solution:

Change 4 to a fraction: 4/1
Multiply the top numbers: 2 × 4 = 8
Multiply the bottom numbers: 3 × 1 = 3
Result: 8/3 (This is an improper fraction. To convert it to a mixed number, divide 8 by 3.)
8 divided by 3 equals 2 with a remainder of 2.

Final answer: 2 (2/3)

Question 2. Multiply 5/6 by 3

Solution:

Change 3 to a fraction: 3/1
Multiply the top numbers: 5 × 3 = 15
Multiply the bottom numbers: 6 × 1 = 6
Result: 15/6
Simplify: Both 15 and 6 can be divided by 3. So, 15/6 = 5/2.

Final answer: 2 (1/2)

Question 3. Multiply 1/2 by 5

Solution:

Change 5 to a fraction: 5/1
Multiply the top numbers: 1 × 5 = 5
Multiply the bottom numbers: 2 × 1 = 2
Result: 5/2 (This is an improper fraction. To convert it to a mixed number, divide 5 by 2.)
5 divided by 2 equals 2 with a remainder of 1.

Final answer: 2 (1/2)

Question 4. Multiply 3/5 by 6

Solution:

Change 6 to a fraction: 6/1
Multiply the top numbers: 3 × 6 = 18
Multiply the bottom numbers: 5 × 1 = 5
Result: 18/5
Convert to a mixed number: 18 divided by 5 equals 3 with a remainder of 3.

Final answer: 3 (3/5)

Question 5. Multiply 4/7 by 2

Solution:

Change 2 to a fraction: 2/1
Multiply the top numbers: 4 × 2 = 8
Multiply the bottom numbers: 7 × 1 = 7
Result: 8/7
Convert to a mixed number: 8 divided by 7 equals 1 with a remainder of 1.

Final answer: 1 (1/7

Question 6. Multiply 7/8 by 5

Solution:

Change 5 to a fraction: 5/1
Multiply the top numbers: 7 × 5 = 35
Multiply the bottom numbers: 8 × 1 = 8
Result: 35/8
Convert to a mixed number: 35 divided by 8 equals 4 with a remainder of 3.

Final answer: 4(3/8)

Question 7. Multiply 3/10 by 4

Solution:

Change 4 to a fraction: 4/1
Multiply the top numbers: 3 × 4 = 12
Multiply the bottom numbers: 10 × 1 = 10
Result: 12/10
Simplify: Both 12 and 10 can be divided by 2. So, 12/10 = 6/5.

Final answer: 1 (1/5)

Question 8. Multiply 5/12 by 3

Solution:

Change 3 to a fraction: 3/1
Multiply the top numbers: 5 × 3 = 15
Multiply the bottom numbers: 12 × 1 = 12
Result: 15/12
Simplify: Both 15 and 12 can be divided by 3. So, 15/12 = 5/4.

Final answer: 1 (1/4)

Question 9. Multiply 2/9 by 7

Solution:

Change 7 to a fraction: 7/1
Multiply the top numbers: 2 × 7 = 14
Multiply the bottom numbers: 9 × 1 = 9
Result: 14/9
Convert to a mixed number: 14 divided by 9 equals 1 with a remainder of 5.

Final answer: 1 (5/9)

Question 10. Multiply 6/11 by 2

Solution:

Change 2 to a fraction: 2/1
Multiply the top numbers: 6 × 2 = 12
Multiply the bottom numbers: 11 × 1 = 11
Result: 12/11
Convert to a mixed number: 12 divided by 11 equals 1 with a remainder of 1.

Final answer: 1 (1/11)

Question 11. Multiply 1/4 by 8

Solution:

Change 8 to a fraction: 8/1
Multiply the top numbers: 1 × 8 = 8
Multiply the bottom numbers: 4 × 1 = 4
Result: 8/4
Simplify: Both 8 and 4 can be divided by 4. So, 8/4 = 2.

Final answer: 2

Question 12. Multiply 2/5 by 10

Solution:

Change 10 to a fraction: 10/1
Multiply the top numbers: 2 × 10 = 20
Multiply the bottom numbers: 5 × 1 = 5
Result: 20/5
Simplify: Both 20 and 5 can be divided by 5. So, 20/5 = 4.

Final answer: 4

Practice Questions on Multiply Fractions with Whole Numbers

Question 1. Multiply 1/3 by 9

Question 2. Multiply 4/5 by 6

Question 3. Multiply 3/8 by 5

Question 4. Multiply 2/7 by 12

Question 5. Multiply 5/9 by 4

Question 6. Multiply 7/10 by 3

Question 7. Multiply 1/2 by 14

Question 8. Multiply 2/3 by 15

Question 9. Multiply 6/5 by 2

Question 10. Multiply 3/4 by 8

Answer Key

  1. 3
  2. 24/5 = 4 \frac{4}{5}
  3. 15/8 = 7\frac{1}{8}
  4. 24/7 = 3\frac{3}{7}
  5. 20/9 = 2\frac{2}{9}
  6. 21/10 = 2 \frac{1}{10}
  7. 7
  8. 10
  9. 12/5 = 2 \frac{2}{5}
  10. 6

Conclusion

So, we can say that multiplying fractions with whole numbers is very easy once we understand the steps. First, we change the whole number into a fraction, then multiply the top and bottom numbers. After that, we simplify it, if possible. With more practice, it will become easier to solve these problems. Provided examples and practice questions will help us in understanding multiplication.

Read More,

Comment
Article Tags:
Mathematics
School Learning
Arithmetic

Explore