Page 78 - Start Up Mathematics_7

(b) If two rational numbers have the same sign, we find their equivalent forms with
denominator of each equal to the LCM. Now we compare their numerators. The number
having a greater numerator is greater.

8. Absolute value of a rational number is always positive. It is also known as numerical value
and gives the distance of the rational number from the origin.
p r
9. Addition of rational numbers: If and are to be added we add their numerators keeping
q q
p r p + r
the denominator same, i.e., + = . In case the denominators are different, we find
q q q
equivalent rational numbers with denominator equal to their LCM and add as above.

10. Subtraction of rational numbers: To subtract two rational numbers, we add the additive
inverse of a rational number that is to be subtracted.
11. Multiplication of rational numbers: To multiply two rational numbers, we multiply the
numerators and denominators separately.

p
12. Reciprocal of a rational number is same as its multiplicative inverse, i.e., reciprocal of q
q
is provided p ≠ 0, q ≠ 0.
p

13. Division of a rational number: To divide one rational number by another non-zero rational
number, we multiply the rational number with the reciprocal of the other.
14. Decimals are of two types—terminating and non-terminating decimals. Non-terminating
decimals are further of two types—non-terminating recurring (or repeating) and non-terminating
non-recurring decimals.

15. Every rational number is either terminating or non-terminating repeating decimal number.
Every irrational number is non-terminating, non-repeating decimal number.

Reason It Out!

2
(a) What is the 100th digit in the decimal part of ?
7
2
[Hint: = 0.285714285714...]
7
(b) Is every finite decimal equal to some infinite decimal? If yes, justify and if no, give
an example to contradict the statement.

Brainstorming

An old man wanted to distribute 34 gold coins among his 3 sons during his lifetime. He
1 1
wanted that the eldest one should get of the coins, the middle son should get of the coins
2
3
1
and his youngest son should get of the coins. But the gold coins could not be divided as
9
per his desire, so he took his sons to a goldsmith friend, who lent them 2 gold coins so that
the coins could be distributed as per the wish.

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