Divide proper fraction calculator

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Proper fraction division formula

\frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c}

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More about proper fraction division

Tricks

1. Cancel out common factors between numerators and a denominators before performing division.
2. Also cancel out common factors across the numerator of one fraction with the denominator of another to simplify calculations.
3. Ensure that the result is always greater than the original numerator but less than the original denominator, because the result represents how many times one fraction fits into another.

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 proper fraction division

Examples

Example 1: Find the proper fraction division of 1/2 ÷ 2/3.
Solution: Reciporcal of second fraction i.e 3/2
Multiply first fraction to reciprocal i.e 1/2 × 3/2 = 3/4
Proper fraction division of 1/2 ÷ 2/3 = 3/4.

Example 2: Find the proper fraction division of 7/12 ÷ 6/15.
Solution: Reciporcal of second fraction i.e 15/6
Multiply first fraction to reciprocal i.e 7/12 × 15/6 = 35/24
Proper fraction division of 7/12 ÷ 6/15 = 35/24.

Example 3: Find the proper fraction division of 11/13 ÷ 8/9.
Solution: Reciporcal of second fraction i.e 9/8
Multiply first fraction to reciprocal i.e 11/13 × 9/8 = 99/104
Proper fraction division of 11/13 ÷ 8/9 = 99/104.

Example 4: Find the proper fraction division of 6/7 ÷ 5/16.
Solution: Reciporcal of second fraction i.e 16/5
Multiply first fraction to reciprocal i.e 6/7 × 16/5 = 96/35
Proper fraction division of 6/7 ÷ 5/16 = 96/35.

Example 5: Find the proper fraction division of 5/7 ÷ 6/18.
Solution: Reciporcal of second fraction i.e 18/6
Multiply first fraction to reciprocal i.e 5/7 × 18/6 = 15/7
Proper fraction division of 5/7 ÷ 6/18 = 15/7.

Exercise

Divide proper fraction calculator FAQ

What is a proper fraction?

Proper fractions are fractions in which the numerator is less than the denominator. Decimal value of a proper fraction is always less than 1.

Can I cross-cancel when dividing proper fractions?

Yes, cross-canceling can help simplify the fractions before multiplication. If there are common factors between the numerator of one fraction and the denominator of the other, you can cancel them out before multiplying.

What are the steps to find proper fraction division?

Step 1: Keep - Change - Flip
Keep the dividend the same.
Change the division sign to multiply.
Flip the divisor by writing its reciprocal.
Step 2: Multiply the fractions
Step 3: If the resulting fraction can be simplified, simplify it.

Can the result of dividing proper fractions be a mixed number?

Yes, the result can be a mixed number if the numerator is greater than or equal to the denominator after simplification. Otherwise, it remains an improper fraction.

Could you provide examples from real-life scenarios where the division of proper fractions is commonly applied?

Division of proper fractions is commonly applied in various fields like cooking, construction, financial calculations, healthcare, measument, time management and production. For example, in measument, if their is rectangular piece of land that measures 3/4 of an acre and need to divide into equal piece where each piece should be 1/5 acre, by dividing 3/4 by 1/5 we get a equal pieces of 15/4 acre.

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