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Print Numerical / Quantitative Reasoning Best Practices #3: Manipulating Fractions

 

When I was at school, more years ago than I care to remember, we were taught to use fractions long before we were shown numbers with decimal points in them. There was some talk of Britain going decimal and fractions would no longer be used but it hasn’t happened.

Moreover, there seems to be a lot of occasions when fractions are more useful and easier to use than their decimal equivalents.

A lot of the numerical problems in these exams can often be solved more easily and more quickly using fractions but you need to know how to manipulate them. Here are a few quick rules.

Magic Multiplication

When multiplying fractions first multiply the numerators (the bits above the line) and then multiply the denominators (the bits below the line). For example:

 

 

Delightful Division

To divide a number by a fraction, and the number itself can be a fraction, then invert the fraction and multiply as above. Eg:

 

 

Addition and Subtraction

To add or subtract fractions then the denominator parts of the fractions need to be the same and then the numerators are added or subtracted as required.

 

 

However, if the denominators are not equal, this can be rectified but within the scope of these job application tests it is probably simpler to resort to the calculator at this point.

Cancellation and Reduction

A key feature of fractions is the ability to cancel out terms or parts of the fraction that are common throughout the sum. For example:

 

 

From the rule above we should multiply the tops and bottoms and get the answer 3/12 which can be reduced to ¼ but because we have a 3 on both the top and the bottom we can cancel them out altogether and we are simply left with the answer of ¼.

 

A Practical Example

Suppose we had to evaluate:
 


 

You may be able to do this in your head and get the answer 21/168 but hold on: there might be an easier way. There is a 7 on the top and a 14 on the bottom so we can reduce these by dividing by 7 and replacing them with 1 and 2 respectively. Similarly, 3 and 12 can be reduced to 1 and 4 respectively reducing the sum to:
 


 

…which is an awful lot easier!

Wish to practice more numerical reasoning? Check our free demo exams!

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