Page 219 - Ganit Kaushal

• Converting mixed fractions into improper fractions: To convert a mixed fraction into an improper
fraction, multiply the whole number by the denominator and add the numerator to the product to get the
numerator of the improper fraction. The denominator remains the same.

Remember

Re mainder
(i) Mixed fraction =Quotient
Divisor
Whole number × Denominator + Numerator
(ii) Improper fraction =
Dennominator

• Equivalent fractions: Fractions having the same part (or share of a whole) are called equivalent fractions.

• Simplest form or lowest form: A fraction is said to be in its lowest term or its simplest form if the only
common factor of the numerator and the denominator is 1.
• Like and unlike fractions: Fractions with the same denominator are called like fractions, and fractions
1 5 2
with different denominators are called unlike fractions. For example: ,, are like fractions and
1 , 2 3 are unlike fractions. 6 6 6
,
11 10 9
• Comparing like fractions: To compare two like fractions, it is enough to compare their numerators. In
like fractions (or fractions having the same denominator), the fraction which has the greater numerator
is greater.

• Comparing unlike fractions: To compare two unlike fractions, convert each fraction to an equivalent
fraction with a common denominator (the LCM of the denominators). The larger fraction is the one with
the greater numerator.
• Brahmagupta’s method for adding/subtracting fractions: When adding/subtracting fractions, convert them
into equivalent fractions with the same fractional unit (i.e., the same denominator), and then add/subtract
the number of fractional units in each fraction to obtain the sum/difference. This is accomplished by
adding/subtracting the numerators while keeping the same denominator.

Fractions 217