Multiplying Mixed Numbers

Class 5Fractions (Grade 5)

In Class 5, students learn to multiply mixed numbers (mixed fractions). A mixed number has a whole part and a fraction part, such as 2 1/3. To multiply mixed numbers, we first convert them to improper fractions, multiply, and then simplify the result.

This skill is used in real-life situations like calculating areas (3 1/2 m × 2 1/4 m), scaling recipes, and finding portions of quantities.

What is Multiplying Mixed Numbers - Class 5 Maths (Fractions)?

Multiplying mixed numbers involves three steps:

Convert each mixed number to an improper fraction.
Multiply the numerators together and the denominators together.
Simplify the result and convert back to a mixed number if needed.

Multiplying Mixed Numbers Formula

Step 1: Convert mixed numbers to improper fractions
Step 2: Multiply: (a/b) × (c/d) = (a×c) / (b×d)
Step 3: Simplify and convert to mixed number

Solved Examples

Example 1: Example 1: Mixed number × whole number

Problem: Calculate 2 1/3 × 4.

Solution:

Step 1: Convert 2 1/3 to improper: (2×3+1)/3 = 7/3

Step 2: Multiply: 7/3 × 4/1 = 28/3

Step 3: Convert: 28 ÷ 3 = 9 remainder 1 → 9 1/3

Answer: 2 1/3 × 4 = 9 1/3

Example 2: Example 2: Two mixed numbers

Problem: Calculate 1 1/2 × 2 2/3.

Solution:

Step 1: Convert: 1 1/2 = 3/2 and 2 2/3 = 8/3

Step 2: Multiply: 3/2 × 8/3 = 24/6

Step 3: Simplify: 24/6 = 4

Answer: 1 1/2 × 2 2/3 = 4

Example 3: Example 3: With cancellation before multiplying

Problem: Calculate 3 1/4 × 1 1/3.

Solution:

Step 1: Convert: 3 1/4 = 13/4 and 1 1/3 = 4/3

Step 2: Cancel: 4 in numerator and 4 in denominator cancel to 1.

13/4 × 4/3 = 13/1 × 1/3 = 13/3

Step 3: Convert: 13/3 = 4 1/3

Answer: 3 1/4 × 1 1/3 = 4 1/3

Example 4: Example 4: Mixed number × proper fraction

Problem: Calculate 4 1/2 × 2/5.

Solution:

Step 1: Convert: 4 1/2 = 9/2

Step 2: Multiply: 9/2 × 2/5 = 18/10

Step 3: Simplify: 18/10 = 9/5 = 1 4/5

Answer: 4 1/2 × 2/5 = 1 4/5

Example 5: Example 5: Word problem — Area

Problem: A rectangular garden is 3 1/2 m long and 2 1/4 m wide. Find its area.

Solution:

Step 1: Convert: 3 1/2 = 7/2 and 2 1/4 = 9/4

Step 2: Area = 7/2 × 9/4 = 63/8

Step 3: Convert: 63/8 = 7 7/8

Answer: Area = 7 7/8 sq. m

Example 6: Example 6: Three mixed numbers

Problem: Calculate 1 1/2 × 1 1/3 × 1 1/4.

Solution:

Step 1: Convert: 3/2 × 4/3 × 5/4

Step 2: Cancel: 3 in numerator and denominator, 4 in numerator and denominator.

= 1/1 × 1/1 × 5/2 = 5/2

Step 3: Convert: 5/2 = 2 1/2

Answer: 2 1/2

Example 7: Example 7: Word problem — Recipe

Problem: A recipe uses 1 3/4 cups of flour. Priya wants to make 3 times the recipe. How much flour does she need?

Solution:

Step 1: Convert: 1 3/4 = 7/4

Step 2: Multiply: 7/4 × 3 = 21/4

Step 3: Convert: 21/4 = 5 1/4

Answer: Priya needs 5 1/4 cups of flour.

Example 8: Example 8: Word problem — Distance

Problem: An auto-rickshaw travels 2 1/2 km in one trip. How far does it travel in 6 trips?

Solution:

2 1/2 × 6 = 5/2 × 6 = 30/2 = 15

Answer: The auto-rickshaw travels 15 km in 6 trips.

Example 9: Example 9: Mixed number with large values

Problem: Calculate 5 2/7 × 1 3/4.

Solution:

Step 1: Convert: 5 2/7 = 37/7 and 1 3/4 = 7/4

Step 2: Cancel: 7 in numerator and 7 in denominator.

37/7 × 7/4 = 37/4

Step 3: Convert: 37/4 = 9 1/4

Answer: 5 2/7 × 1 3/4 = 9 1/4

Key Points to Remember

Always convert mixed numbers to improper fractions before multiplying.
Multiply numerators together and denominators together.
Cancel common factors before multiplying to keep numbers small.
Simplify the final answer and convert back to a mixed number.
A whole number can be written as a fraction with denominator 1 (e.g., 5 = 5/1).
The product of two mixed numbers greater than 1 is always greater than either number.
Multiplying a mixed number by a proper fraction gives a result smaller than the mixed number.

Practice Problems

Calculate 3 1/5 × 2.
Calculate 2 1/4 × 1 1/3.
Calculate 4 2/3 × 3/7.
A rope is 5 1/2 metres long. Aman needs 3 such ropes. Find the total length.
Calculate 1 5/6 × 2 2/5.
A plot of land is 4 1/3 m long and 3 1/2 m wide. Find its area.
Calculate 2 1/2 × 3 1/3 × 1 1/5.
Meera walks 1 3/4 km each day. How far does she walk in 5 days?

Frequently Asked Questions

Q1. How do I multiply mixed numbers?

Convert each mixed number to an improper fraction, multiply the numerators and denominators, simplify, and convert back to a mixed number. Example: 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 10/3 = 3 1/3.

Q2. Why must I convert to improper fractions first?

You cannot directly multiply the whole parts and fraction parts separately. 2 1/2 × 3 is NOT (2×3) + (1/2 × 3). Converting to improper fractions ensures the multiplication is done correctly.

Q3. What is cancellation and when should I use it?

Cancellation means dividing a numerator and a denominator by a common factor before multiplying. For example, in 3/4 × 8/9, divide 3 and 9 by 3, and 4 and 8 by 4 to get 1/1 × 2/3 = 2/3. This keeps numbers small.

Q4. Is the product of two mixed numbers always larger than both?

If both mixed numbers are greater than 1, then yes, the product is larger than both. But if one of them is a proper fraction (less than 1), the product will be smaller than the other number.

Q5. Can I use a calculator to check my answer?

Yes. Convert mixed numbers to decimals: 2 1/2 = 2.5, 1 1/3 = 1.333... Multiply: 2.5 × 1.333... = 3.333... = 3 1/3. This confirms your fraction answer.

Q6. How do I multiply a mixed number by a whole number?

Convert the mixed number to an improper fraction and write the whole number as a fraction over 1. Then multiply normally. Example: 3 1/4 × 5 = 13/4 × 5/1 = 65/4 = 16 1/4.

Q7. What if the answer is an improper fraction?

Always convert improper fractions back to mixed numbers for the final answer, and simplify if possible. For example, 28/6 = 4 4/6 = 4 2/3.

Q8. Can I multiply three mixed numbers at once?

Yes. Convert all three to improper fractions, cancel common factors across all numerators and denominators, then multiply everything together. Example: 1 1/2 × 1 1/3 × 1 1/4 = 3/2 × 4/3 × 5/4 = 5/2 = 2 1/2.

Multiplying Mixed Numbers

What is Multiplying Mixed Numbers - Class 5 Maths (Fractions)?

Multiplying Mixed Numbers Formula

Solved Examples

Example 1: Example 1: Mixed number × whole number

Example 2: Example 2: Two mixed numbers

Example 3: Example 3: With cancellation before multiplying

Example 4: Example 4: Mixed number × proper fraction

Example 5: Example 5: Word problem — Area

Example 6: Example 6: Three mixed numbers

Example 7: Example 7: Word problem — Recipe

Example 8: Example 8: Word problem — Distance

Example 9: Example 9: Mixed number with large values

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. How do I multiply mixed numbers?

Q2. Why must I convert to improper fractions first?

Q3. What is cancellation and when should I use it?

Q4. Is the product of two mixed numbers always larger than both?

Q5. Can I use a calculator to check my answer?

Q6. How do I multiply a mixed number by a whole number?

Q7. What if the answer is an improper fraction?

Q8. Can I multiply three mixed numbers at once?

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