Page 152 - Start Up Mathematics_6

1
5. Mr Srinivas earns ` 10,00,000 per year and of his income is deducted in tax. He
1 1 3 1
spends of his income in clothes, on outings and for an orphanage. He also pays
6 5 10
` 1,80,000 to the person with whom he stays as a paying guest. He saves the rest of the
money.
(a) How much does he pay as tax?
(b) What fraction of his earning does he pay to the person with whom he stays as a
paying guest?
(c) What fraction of his earning does he save?

At a Glance
1. A fraction is a number representing a part of a whole. It can be represented on a number
line.

2. A fraction is said to be proper if its numerator is less than the denominator.
3. A fraction is said to be improper if its numerator is greater than or equal to the denominator.
4. Mixed fractions are combination of a whole number and a proper fraction. We can convert
a mixed fraction into an improper fraction as follows:
(Whole part × Denominator) + Numerator
Improper fraction =
Denominator
5. An improper fraction can be converted into mixed fraction by dividing the numerator by its
denominator and writing it as follows:

Remainder
Mixed fraction = Quotient
Divisor
6. Fractions having the same value are called equivalent fractions.
7. A fraction is said to be in simplest or standard form if the numerator and denominator are
co-prime (i.e., they have no common factors other than 1).
8. Comparison of fractions:

(i) When two like fractions are compared, the fraction having the greater numerator is greater.
(ii) When two fractions having same numerator are compared, the fractions having the
greater denominator is smaller.
(iii) When two fractions having different numerators and different denominators are to be
compared, we convert them into like fractions and proceed as above.

9. Addition and subtraction of fractions:
(i) To obtain the sum or difference of like fractions, we add or subtract their numerators
to get the numerator, and the denominator remains the same.
(ii) To obtain the sum or difference of unlike fractions, we first convert them into like
fractions with LCM of their denominators as the new denominator and then find the
sum or difference.
(iii) To obtain the sum of mixed fractions, we first convert them into improper fractions
and then proceed as above by taking the LCM of their denominators.

144