Q1 of 21 Page 38

Find the general principle of each of the patterns below and explain it using algebra.

On observing the pattern we get general formula as,

To prove this algebraically,

We know that so,

Using, (a-b)(a + b) = a² – b²

Hence, proved!

i) Find three fractions larger than and smaller than

ii) Find three such fractions, all with the denominator 24.

iii) Find three such fractions, all with the numerator 4.

From a fraction, a new fraction is formed by adding the same natural number to both the numerator and the denominator.

i) In what kind of fractions does this give a larger fraction?

ii) In what kind of fractions does this give a smaller fraction?

Find the general principle of each of the patterns below and explain it using algebra.

Questions · 21

2. Fractions

1 2 3 1 2 3 4 1 2 3 4 1 2 3 4 1 2 2 2 2 3