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A fraction is either a proper fraction or an improper fraction.
•A proper fraction is a number representing a part of a whole. This whole may be a single object or a group of objects. An improper fraction is a number in which numerator is gr eater than denominator .
•A mixed fraction is a combination of a natural number and a proper fraction.
•Two fractions are multiplied by multiplying their numerators and denominators separately and writing the product as product of numerators product of denominators . For example, ××==×23236 . 545420
•A fraction acts as an operator ‘of’. For example,
13of 3 is 13× 3 = 1.
•The product of two proper fractions is less than each of the fractions, For example,
111236×=and16is less than both 12and 13.
•The product of a proper and an improper fraction is less than the improper fraction and greater than the proper fraction. For example, 1322×= 34and 34is less than 32but greater than 12.
•The product of two improper fractions is greater than the two fractions .For example, 3724×= 218and 218 is greater than both 32and 74.
•The reciprocal of a nonzero fraction is obtained by interchangingits numerator and denominator . For example, reciprocal of 32is23.
•While dividing a whole number by a fraction, we multiply the whole number with the reciprocal of that fraction .For example, 3 ÷ 1 2= 3 × 21.
•While dividing a fraction by a natural number, we multiply the fraction by the reciprocal of the natural number. For example, 14÷ 2 = 14× 12.
•While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal of the other. For example, 12÷ 13= 12× 31.
•While multiplying two decimal numbers, first multiply them as whole numbers. Count the number of digits to the right of the decimal point in both the decimal numbers. Add the number of digits counted. Put the decimal point in the product by counting the number of digits equal to sum obtained from its rightmost place. For example, 1.2 × 1.24 = 1.488.
•To multiply a decimal number by 10,100or 1000, we move the decimal point in the number to the right by as many places as many zeros (0) are the right of one. For example, 1.33 × 10 = 13.3.
•To divide a decimal number by a natural number , we first take thedecimal number as natural number and divide by the given naturalnumber. Then place the decimal point in the quotient as in the decimal number. For example, 1.24= 0.3
•To divide a decimal number by 10, 100 or 1000, shift the decimal point in the decimal number to the left by as many places as there are zeros over 1, to get the quotient. For example, 1.34100= 0.0134
Main Concepts and Results
• A fraction is a number representing a part of a whole. This whole may be a single object or a group of objects. • A fraction whose numerator is less than the denominator is called a proper fraction, otherwise it is called an improper fraction.
• Numbers of the type
5 4 13 ,8 ,27 9 5etc. are called mixed fractions (numbers).
• An improper fraction can be converted into a mixed fraction and vice versa.
• Fractions equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a non zero number.
• A fraction in which there is no common factor, except 1, in its numerator and denominator is called a fraction in the simplest or lowestform.
• Fractions with same denominators are called like fractions and if the denominators are different, then they are called unlike fractions.
• Fractions can be compared by converting them into like fractions and then arranging them in ascending or descending order.
• Addition (or subtraction) of like fractions can be done by adding (or subtracting) their numerators


























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