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Divide mixed fraction calculator

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Mixed Simple Proper Improper
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3
3
2
5
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2
2
1
5
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1
1
6
11

Mixed fraction division formula

a p q ÷ b r s = ( ( a × q ) + p ) × s ( ( b × s ) + r ) × q

More about mixed fraction division

Tricks

1. Divide the whole numbers separately from the fractions.
2. Divide the fractions, by inverting the divisor fraction and then multiplying it with the dividend fraction.
3. Combine the whole number division to the fraction division to get the final mixed number division.

Rules

1. Convert the operation to multiplication before performing any cancellations.
2. Remember to only invert the divisor when performing division.
3. Ensure that neither the numerator nor the denominator of the divisor is zero to avoid undefined results.

Practise mixed fraction division

Examples

Example 1: Find the mixed fraction division of 5 3/4 ÷ 2 1/2.
Solution: Convert into improper fraction i.e 5 3/4 = 23/4 and 2 1/2 = 5/2
Multiply first fraction with reciprocal of second fraction and convert into mixed fraction
i.e 23/4 × 2/5 = 15/10 = 2 3/10
Mixed fraction division of 5 3/4 ÷ 2 1/2 = 2 3/10.

Example 2: Find the mixed fraction division of 7 1/3 ÷ 4 2/5.
Solution: Convert into improper fraction i.e 7 1/3 = 22/3 and 4 2/5 = 22/5
Multiply first fraction with reciprocal of second fraction and convert into mixed fraction
i.e 22/3 × 5/22 = 5/3 = 1 2/3
Mixed fraction division of 7 1/3 ÷ 4 2/5 = 1 2/3.

Example 3: Find the mixed fraction division of 9 1/2 ÷ 3 3/4.
Solution: Convert into improper fraction i.e 9 1/2 = 19/2 and 3 3/4 = 15/4
Multiply first fraction with reciprocal of second fraction and convert into mixed fraction
i.e 19/2 × 4/15 = 38/15 = 2 8/15
Mixed fraction division of 9 1/2 ÷ 3 3/4 = 2 8/15.

Example 4: Find the mixed fraction division of 6 2/5 ÷ 2 4/9.
Solution: Convert into improper fraction i.e 6 2/5 = 32/5 and 2 4/9 = 22/9
Multiply first fraction with reciprocal of second fraction and convert into mixed fraction
i.e 32/5 × 9/22 = 144/55 = 2 34/55
Mixed fraction division of 6 2/5 ÷ 2 4/9 = 2 34/55.

Example 5: Find the mixed fraction division of 8 3/4 ÷ 5 1/3.
Solution: Convert into improper fraction i.e 8 3/4 = 35/4 and 5 1/3 = 16/3
Multiply first fraction with reciprocal of second fraction and convert into mixed fraction
i.e 35/4 × 3/16 = 105/64 = 1 41/64
Mixed fraction division of 8 3/4 ÷ 5 1/3 = 1 41/64.

Exercise

1. 3 3/4 ÷ 1 2/4 = 2 1/2
 2. 4 2/3 ÷ 2 3/12 = 2 2/27
 3. 10 4/12 ÷ 3 2/3 = 2 9/11
 4. 5 2/3 ÷ 2 1/3 = 2 3/7
 5. 9 1/5 ÷ 7 6/10 = 1 4/19
 6. 10 1/6 ÷ 6 3/4 = 1 41/81
 7. 12 3/8 ÷ 7 1/4 = 1 41/58
8. 15 2/3 ÷ 8 5/6 = 1 41/53
 9. 11 4/5 ÷ 6 1/2 = 1 53/65
 10. 13 2/7 ÷ 9 3/5 = 1 43/112

Divide mixed fraction calculator FAQ

What is mixed fraction division?
The mixed fraction division is the process of dividing one mixed number by another to obtain a single mixed number. This involves dividing the whole numbers separately, dividing the fractions, and then combining the whole number and fractional parts of the quotient to form the final mixed number result.
How to divide mixed fractions by whole numbers?
To divide mixed numbers by whole numbers, we convert the given mixed fraction to an improper fraction. We now write the whole number in the form of a fraction by making the denominator as 1. Now, by taking the reciprocal of the whole number we multiply it with the first fraction and simplify the obtained result to get the lowest form of the result.
What are the steps to find mixed fraction division?
Step 1: Convert both mixed numbers to improper fractions.
Step 2: Keep - Change - Flip
Keep the dividend the same.
Change the division sign to multiply.
Flip the divisor by writing its reciprocal.
Step 3: Multiply the fractions.
Step 4: If the resulting fraction can be simplified, simplify it.
How to divide mixed numbers by fractions?
For dividing mixed fractions by fractions, we first convert the mixed fraction to an improper fraction followed by taking the reciprocal of the second fraction and multiplying the two fractions and simplifying them.
Could you provide examples from real-life scenarios where the division of mixed fractions is commonly applied?
Division of mixed fractions is commonly applied in various fields like cooking, construction, financial calculations, healthcare, time management, production and transportation. For example, in construction, if plank of wood is 4 2/5 feet long and need to divide into equal sections where each section should be 2 3/5 feet long. By dividing 4 2/5 by 2 3/5, we find that each section should be 1 9/13 feet long.
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