CLASSIFICATION OF FRACTIONS 1. Proper Fraction : A Proper fraction is one whose numerator is less than its denominator. 1 eg., 3

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1 CLASSIFICATION OF FRACTIONS. Proper Fraction : A Proper fraction is one whose numerator is less than its denominator. eg.,. Improper Fraction : An improper fraction is one whose numerator is equal to or greater than its denominator eg.,. Mied Fraction: A mied fraction is a quantity consisting of two parts, one a whole number and other a proper fraction. eg., A mied fraction can always be epressed as an improper fraction. ( ) eg. Similarly an improper fraction can always be epressed as a mied fraction. For that divide the numerator by the denominator and write the quotient as the whole number part of the mied fraction, the remainder as the numerator and the divisor as the denominator. eg. ; Basic Property of Fractions. The value of a fraction is not altered by multiplying the numerator and denominator by the same number. ie. a ac ac b bc bc. The value of a fraction is not altered by dividing the numerator and the denominator by the same number. ie a a c. b b c Reduction of a fraction to its lowest terms To change a fraction to its lowest terms, divide its numerator and denominator by the H.C.F. of the numbers. eg. Reduce to its lowest terms. (Since H.C.F. of and is ) Reducing fractions to their common denominators To reduce fractions to their common denominators, change the denominators into their L.C.M. eg., L.C.M. of and = 0 To convert the denominator of into 0, multiply it by. To convert the denominator of into 0, multiply it by. (ie) ; ( ie) ; 0 0 Comparing Fractions

2 Let a c and b, be two fractions with same denominator c. c Then a c a c b if a>b eg. c b if a<b eg. c a c b if a=b eg. c Addition and Subtraction of Fractions Method : Convert the fractions with the same denominator by taking L.C.M. and then add or subtract. Eamples...? L.C.M. of, =.? L.C.M. of, and is = ? ( ) = 0 0 = ? L.C.M. of,, and is = ( 0 )

3 0 = 0 Multiplication of fractions. To multiply a fraction by a whole number, multiply the numerator by the whole number. ( ) eg.. To multiply a fraction by another fraction multiply corresponding numerators and denominators and then simplify. eg. Division of Fractions. To divide a fraction by a whole number, multiply the denominator of the fraction by the whole number. eg.. To divide a fraction by a fraction, find the reciprocal of the divisor and then multiply. eg. 0 Note: Cancellation can be performed only to multiplication and division of fractions; it can not be perfomed in addition or subtraction of fractions. Point to remember:. To multiply a whole number and a mied fraction together, perform separate multiplication and then add the results. eg. ( ) 0 0. To divide a mied fraction by a whole number divide the whole number part of the mied fraction by the divisor (let the quotient be. Reduce the remainder to a single fraction and divide this single fraction by the divisor. (Let the quotient be. Now the required result is a+b. eg. ) ( 0 Now More Solved Eamples. There are 0 students in a class. One day only 0 absentees on that day. th of total students were present. Find the number of

4 Number of absentees = Fraction of absentees Total number = 0 0 students. A man spends of his salary on food, 0 of his salary on house rent and of the salary on clothes. He still has Rs.,00 left with him. Find his total salary. Totally he spends 0 of his total salary. He saves 0 part of his salary. 0 total salary = 00 (ie) 0 total salary = 00 total salary = 00 0 Rs In an eamination, a studnet was asked to find of a certain number. By mistake, he found answer was 0 more than the correct answer. Find the given number. Let the given number be, then of it. His 0 = 0. By how much is of 0 less than of? 0. part of what amount will be equal to Let the amount be Rs.y part of Rs. 00. of y of 00 y 00 y 00 y 00 Decimal Fractions Fractions that have powers of 0 in the denominators are called decimal fractions.

5 (ie) Fractions whose denominators are 0, 0, 0, 0... are called decimal fractions. Here eg. 0., 0.0,. etc. 0. = ;. ;. 000 Addition 00 Anneing zeros to the etreme right of decimal fraction does not change its value. 0. = 0.0 = 0.00 etc. For adding a decimal number with another decimal number or with another whole number write the given number in such a way that the number of decimal places are equal for all the numbers. eg Here maimum number of decimal place= Convert all the numbers to decimal places = =. Subtraction In subtraction also, the given numbers are to be written in such a way that the number of decimal places become equal for all numbers. eg Maimum number of decimal place = (in 0.) ie. -0.= =. Multiplication. Multiplication of a Decimal Fraction by a power of 0: Shift the decimal point to the right by as many places of decimal as the power of 0. eg.. 00 =.. Multiplication of two or more decimal fractions : =? Step : Step : Multiply the given numbers as if they are without any decimal point. ie. = 0 Add the total number of decimal places in the given numbers ie ++ = Step : Write the result of step and convert it to a number whose number of decimal places is same as the number obtained in step by shifting the decimal point to the left = = Division. While dividing a decimal fraction by powers of 0, the result is obtained by shifting the decimal point to the left by as many places of decimal as is the power of 0. eg.. 0 = =.. While dividing a decimal fraction by a natural number, divide the given fraction without the decimal point by the given natural number. In the answer thus got, place the decimal point to the left as many places of decimal as are there in the dividend. eg..?

6 First step is While dividing a decimal fraction by a decimal fraction, shift the decimal point to the right of the dividend and the divisor both by equal number of digits such that the divisor is converted into a whole number. eg Epressing a decimal into a vulgar fraction Put in the denominator under the decimal point and anne with it as many zeros as is the number of digits after the decimal point. Remove the decimal point and reduce the fraction to its lowest terms. Thus If numerator and denominator of a fraction contain the same number of decimal places, then we may remove the decimal sign.. eg.. To multiply a decimal by any multiple of ten, move the decimal point as many places to the right as is the number of zeros in the multiplier. To divide a decimal by any multiple of ten move the decimal point as many places to the left as is the number of zeros in the divisor. When a divisor as well as dividend is a decimal, we multiply both the dividend and the divisor by suitable multiple of 0 to make the divisor a whole number and then proceed division. Solved Eamples:. Evaluate ++ Given epression is of the form a + b + ab = (a+ = ( ) ( 00) ? Given epression is Φa - b =Φ(a+ (a- = Φ( + 0) ( - 0) = Φ = Given epression is of the form a b a ab b

7 .....?.... Given epression is a b ( a cy dy ( c d) y (.. ) (.. ) ?. Given epression is a b a b = = 0.0 a b ? (. ) (. ) The given epression is a ab b a b = ( a a b (.. ) ( a ( a a b (.. ) 0 00 = =? The given epression is a - b - ab (a- = (a- =(0.-0.) =(0.) = 0.0. Simplify = = =

8 . Find the value of = = = = 0. Find the value of = =. Find the value of = = =. If y then find the value of y y y y y y

9 = = PRACTICE TEST. 0 -[-{+()} +] =? 0 d). +[+{(-) -()-}+]=? d). of + (-) =? d). d). ( )? d). of?. d)....? d) =? d) ? 0.. d) ? =? d) 0 d)

10 . ( 0. ) ( 0. 0) ( 0. ) ( 0. ) d) 0.? ? d)......? d) d) ( ) ( ) d). ( ) ( ) ( ) ( )? d) (.. ) (.. ) d)??? d) =? d) 0? ? d) 0. (. ) 0. 0? (. ) d).0?

11 d). 0.? d). of 0? d).? d) 0. of? of d). ( )? 0 d) 0. If a b, then b a b a is equal to d) 0....?

12 000 d) If a b a b, then the value of is a b - d). If, then the value of is d).? d).? 0 0 d) 0. If (a- is more than (c+d) and (a+ is less than (c-d), then (a- is d).0. The epression ( ) will be a perfect square for equal to d) The sum of the smallest si digit number and the greatest five digit number is 00 0 d) 0. The sum of two numbers is and their difference is. Find the product of the numbers. 0 d). The sum of squares of two numbers is 0 and the square of their difference is. The product of the two numbers is d) 0. The product of two numbers is 0. The sum of their squares is. The sum of the two numbers is 0 d) 0. The difference of two numbers is and one-fifth of their sum is. The numbers are:,0 0,, d),. The sum of two numbers is 0 and their product is 0. The sum of their reciprocals is

13 d). If the sum of two numbers eceeds their difference by 0, then the smaller of the two numbers is d). The simplification of of yields 0. Given that d).. 0. then... is equal to d) 0.. The simplification of yields d). The simplification of of yields d). The simplification of yields

14 d) ANSWERS TO PRACTICE TEST. (d). (. (. (. (d). (d). (. (. (d) 0. (. (. (. (. (d). (. (. (. (. (d) 0. (.(d). (. (d). (. (. (. (d). (.( 0. (d). (.(. (. (. ( (. (. (. ( 0.(. (d) ( (. (. (. (d). (.(

3.1 Dividing a Whole into Fractional Parts. 3.1 Dividing a Set into Fractional Parts. 3.2 Identifying Parts of Wholes.

3.1 Dividing a Whole into Fractional Parts. 3.1 Dividing a Set into Fractional Parts. 3.2 Identifying Parts of Wholes. . Dividing a Whole into Fractional Parts Fraction: represents a part of a whole object or unit Numerator: (top number) represents number of parts of the whole Denominator: (bottom number) represents how