Q. 2

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

Answer :

On observing the pattern we get general formula as

To prove this algebraically,

We know that so,

Hence, proved!

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Find fractions of denominators which are power of 10, getting closer and closer to each of the fractions below and then write their decimal form.

Kerala Board Mathematics Part-1

Find fractions of denominators which are power of 10, getting closer and closer to each of the fractions below and then write their decimal form.

Kerala Board Mathematics Part-1

i) Explain using algebra, that the fractions gets closer and closer to

ii) Using the general principle above on single digit numbers, find the decimal forms of (why are left out in this?)

iii) What can we say in general about those decimal forms in which a single digit repeats?

Kerala Board Mathematics Part-1Find the fraction of denominator is a power of 10 equal to each of the fractions below, and then write their decimal forms:

Kerala Board Mathematics Part-1

During rainfall, the volume of water falling in each square metre may be considered equal.

Explain why the heights of rainwater collected in different sized hollow prisms kept near one another are equal.

Kerala Board Mathematics Part-2For each pair of quantities given below, check whether the first is proportional to the second. For proportional quantities, calculate the constant of proportionality.

The volume of water poured into a hollow prism and the height of the water level.

Kerala Board Mathematics Part-2From 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?

Kerala Board Mathematics Part-1For each pair of quantities given below, check whether the first is proportional to the second. For proportional quantities, calculate the constant of proportionality.

The distance travelled and the number of rotations of a circular ring moving along a line.

Kerala Board Mathematics Part-2