Dividing Fractions

[KWF]

I saw the following method for dividing fractions:

3/4 ÷ 4/5 = ?


1. 3/4 ÷ 5/5 = 3/4
2. 3/4 ÷ 1/5 = 5 times 3/4 = 15/4
3. 3/4 ÷ 4/5 = 1/4 of 15/4 = 15/16

Answer: 15/16

What is the logic or explanation for this method or calculation? What is the purpose of 5/5, 1/5, and 1/4? And also, why are "times" and "of' used?


　

　

 

[ForeverDarkrai]

Explanation

Hi

When you have got this sort of question, think of an easier example:

Solve 1/3 ÷ 1/2

When you divide by a fraction, the rule is that you change the divide sign to a multiply and flip the second fraction.

So, the above become 1/3 x 2/1

When multiplying fractions, you multiply the top parts (numerators) together to form the new numerator, and then multiply the bottom parts (denominator) together.

So, for this, the numerator will be 2 x 1 = 2, and the denominator will be 3 x 1 = 3 - so your answer would be 2/3

Using the same logic behind your question:

3/4 ÷ 4/5

So, change the divide sign into a multiply sign and flip the second fraction:

3/4 x 5/4

Then, multiply the numerators and denominators together to form the new fraction:

Numerator: 3 x 5 = 15
Denominator: 4 x 4 = 16

Therefore, your answer is 15/16

If you have any other questions, please feel free to ask

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[stapel]

What is the logic or explanation for this method or calculation? What is the purpose of 5/5, 1/5, and 1/4? And also, why are "times" and "of' used?

The reason for "times" and "of" (and, in this context, "of" means "times") is noted in the first reply; namely, that division by a fraction is usually done by "flipping and multiplying". But the method you were shown, as outlined in your post, seems very strange to me.

Where did you see this (very odd) method?