His approach to solve the problem was perfect. After a minute, there was a need to add the two fractions:

3/4 + 1/20

He started doing some '

*cancellation*' .. I could hear his mumbling - '*four fives are 20'*... So after couple of seconds, he provided me his answer -
4/9

Right Sir?

He was waiting for my response, but there was only silence for few seconds. I kept staring at his solution. He was surprised with this strange kind of response :)

I am sure this is not a new situation to many maths teachers.. We have come across many interesting inventions of fraction arithmetic procedures by our students, isn't it? :-)

So then what happened next ? How did I respond ?

Why did you do this 'cancellation -- 4 fives are 20?'

Teacher has taught us this way...!

Okay... but why to do this way? How do you know if this answer is correct?

He stared at me with a surprising look....

My answer is not right, Sir ?

After thinking for a while, I inquired -

Okay, How much is Half + Quarter?

Three fourths.

How is it written?

3/4

Can you write down the entire equation?

1/2 + 1/4 = 3/4

I am quite surprised that you did not add the two fractions here, the way you did in the first problem... You did not do any cancellation here.....?

Sir, this was very simple.. I already knew that Half & Quarter adds to Three-fourths.

Hmmm... But how do you get these numbers 3 and 4 in the answer?

He thought for a while... and responded this way --

Half is made up of 2 one-fourths. So adding one more 1/4th gives 3/4.

Great ! So Can we add the two fractions in the first problem too

**with such an Understanding**?
I doubt if you will believe me, but he took less than 8-10 seconds to solve this:

He reasoned it this way --

There are 5 one-twentieths in 1 one-fourth.

So 3 one-fourths will have 15 one-twentieths....

Adding 1 more one-twentieth to them, gives 16 pieces of one-twentieth....

So answer is 16/20

He again asked me for validation...

I asked him back - "What do you think?"

And this time, he replied with confidence and even a wide smile :)

"Yes Sir, this answer is correct!"

Thanks and Regards

Rupesh Gesota

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