Carl Friedrich Gauss was the famous 17th century German Mathematician.
His mathematical skills were clearly visible from a very young age. His elementary teacher Büttner, one day asked all his students to add numbers from one to hundred. this was to keep them engaged for some time. So the students started summing up the numbers,
1 + 2 + 3 + 4 + ............... + 100
Within minutes Gauss was sitting idle. The teacher asked why he was not doing the sum, for which he replied he's already finished it! and the answer is 5050.
Wonder how he did that? Gauss observed that there is a pattern in these numbers,
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
.
.
.
.
50 + 51 = 101
so there are 50 pairs of 101. i.e 50 x 101 = 5050. interesting isn't it?
Now try this,
Find the sum of integers from -10 to 10. what will be your approach?
Can you apply the same for adding consecutive fractions? what do you observe?
We are going to study more operations on fractions and integers combined together, called Rational Numbers (Q). Hope you remember the Number System and where Rational numbers fall!.
His mathematical skills were clearly visible from a very young age. His elementary teacher Büttner, one day asked all his students to add numbers from one to hundred. this was to keep them engaged for some time. So the students started summing up the numbers,
1 + 2 + 3 + 4 + ............... + 100
Within minutes Gauss was sitting idle. The teacher asked why he was not doing the sum, for which he replied he's already finished it! and the answer is 5050.
Wonder how he did that? Gauss observed that there is a pattern in these numbers,
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
.
.
.
.
50 + 51 = 101
so there are 50 pairs of 101. i.e 50 x 101 = 5050. interesting isn't it?
Now try this,
Find the sum of integers from -10 to 10. what will be your approach?
Can you apply the same for adding consecutive fractions? what do you observe?
We are going to study more operations on fractions and integers combined together, called Rational Numbers (Q). Hope you remember the Number System and where Rational numbers fall!.
A rational number is a number that can be expressed as a fraction 
where 
and 
are integers and 
. A rational number 
is said to have numerator 
and denominator 
. Here, the symbol 
derives from the German word Quotient, which can be translated as "ratio,"
where and are integers and . A rational number is said to have numerator and denominator . Here, the symbol derives from the German word Quotient, which can be translated as "ratio,"
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