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Published on January 26th, 2011 In category Education | Maths

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Working with fractions for problem solving

Questions on fractions are often asked in competitive exams, here we will learn the concept of fractions for problem solving in examination like CAT, XMAT etc. So what are fractions, fractions are part of rational numbers that can presented in the form of dividing one integer over another say of the form a/b, it is also represented as ab.cd as decimal form. In this section of fractions we cover the topics of converting decimals to fractions, how to add, subtract, multiply or divide the fractions, fractions as power and reciprocals. Starting with

The integer at the top represneted as a in a/b is called nominator

The integer at the bottom represented as b in a/b is called denominator

1. How to convert decimals to fractions : There are 2 types of decimal numbers recurring  ( for ex. 3.33333 …… ) and non-recurring   (5.50) the method to convert them into fractions are same.  Remove the decimal and represent the full number as nominatior and include 1 in the denominator and include as many zeros as number after the decimal for ex. 5.50 will represented as 550/100

2. Operations of fractions :  Adding, subtracting, multiplying and dividing the fractions

Adding or Subtracting:  If the denominators are same then just add the numerators for ex. a/b + c/b  = (a + c)/b if the denominators are not same then  a/b + c/d    =  (a x d ) + (c x b) / b x d

Multiplication: Quite simple numerator multiples numerator and denominatior multiples denominatior for ex. (1/2)  x (5/6) = (5/12)

Division : Almost similar to multiplication. However the multiplcation is with reciprocal of other fraction. For (a/b)  divided by (c/d)  = (a/b) x (d/c)

3. Reciprocal of fraction : The reciprocal of number a/b is represented as b/a, i.e. interchange numerator and denominator

4. Converting improper fraction to proper fraction : Improper fractions are the one that are top heavy. i.e numerators are bigger than denominator. How to reduce them to proper fractions: quite easy… divide the numerator by denominator and then represent the remainder as numerator  and denominator remains same. Factor obtained moved as integer. See this example 7/4 this can represented as 1 and 3/4  or

5. Fractions as power: fractions to the powers

 

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