EQUIVALENT FRACTIONS

Definition:– Equivalent fractions are fractions having the same

values.– It can be obtained by multiplying both the

numerator and the denominator of the given fraction by the same non-zero whole number.

Example :

Determining equivalent fractions

– To determine whether two fractions are equivalent, convert each fraction into fractions with a common (same) denominator. Then, compare the numerators.

Example :

– If two fractions have the same denominators, their values can be compared by comparingtheir numerators or by using a number line.

Example :

Comparing two fractions

– If two fractions have different denominators, convert both fractions into their respectiveequivalent fractions with the common denominator.

Example :

Arranging fractions in order

– To arrange fractions in order, convert the given fractions into equivalent fractions withthe common denominator and then compare the numerators.

Example :

Lowest terms

– To simplify a fraction to its lowest terms, divide the numerator and the denominator ofthe fraction by their HCF.

Example :

Mixed Numbers

Definition:– A mixed number is a number consisting of a whole

number and a fraction

Example :

Comparing and arranging mixed numbers

– Like fractions, mixed numbers can be arranged and compared on a number line. Any number on the number line is greater than numbers to its left.

Example :

PROPER FRACTIONS AND IMPROPER

FRACTIONS

• Definition:– A proper fraction is a fraction whose numerator is

less than the denominator

• example:

• Definition– An improper fraction is a fraction whose numerator is

equal to or greater than the denominator

• example:

• Changing mixed numbers into improper fractions

– To change a mixed number into an improper fraction, multiply the whole number by the denominator and then add the numerator to it. The denominator remains the same.

• example:

• Changing improper fractions into mixed numbers

– To change an improper fraction into a mixed number, divide the numerator by the denominator. The quotient obtained is the whole number part and the remainder is the numerator of the fractional part.

• example:

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ADDITION OF FRACTIONS

• Definition:– Addition of fractions is a process of finding the sum of

two or more fractions

• Adding two fractions with the same denominator– To add two fractions with the same denominator,

keep the denominator and add the numerators.

• Example 1:

• Example 2:

• Adding two fractions with different denominators– To add two fractions with different denominators,

convert both the fractions into their respective equivalent fractions with the same denominators.

• example:

• Adding whole numbers and fractions– A mixed number is produced when adding a whole

number and a fraction.

• example:

• Adding fractions and mixed numbers– To add a fraction and a mixed number, keep the

whole number part and add the fractionalparts like adding two fractions.

• example:

• Adding two mixed numbers– Convert mixed numbers into improper fractions. Then

perform the additionlike adding two fractions.

• example:

• Adding three fractions– Convert the fractions so that they have a common

denominator before performing the addition.

• example: