About: Fractions, GMAT, MBA, Quantitative
Understanding Fractions for the GMAT
Fractions are one of the most important things on the GMAT, most of the quantitative questions will contain some element of fractions to them. Understanding the basics of how fractions work is essential.
First of all is how fractions work in relation to each other:
Multiplication & Division of fractions:
Multiplications of fractions are the easiest way to work with fractions as it is the most logical.
Simply multiply the numerator of one fraction by the numerator of the other. Same with the denominators of the fractions, simply multiply one to the other. If you have a long string of fractions to multiply, the concept is the same for all.
For example:
1/3 x 3/4 = 3/12
1/2 x 3/2 x 5/3 x 4/5 = 60/60 ( =1/1 = 1 )
If you want to multiply fractions with negative values, the concept is the same.
For divisions, there is an extra step. if we were to try to divide: 1/3 ÷3/4 we would actually inverse one of the terms for example 3/4 so that we got 4/3 and then multiply the two fractions as described above, thus: 1/3 ÷3/4 = 1/3 x 4/3 = 4/9
Subtraction & Addition of fractions:
For the addition and subtraction of fractions, it is essential to first established what the lowest common denominator is.
For example: in 1/3 + 3/4, the lowest common denominator is 12. Once a common denominator is established, you have to convert the fractions to that common denominator. This means multiplying the nominator by the same amount as you would multiply the denominator to achieve the common denominator.
For example, in 1/3, if we want to bring this fraction to have a common denominator of 12, we need to multiply both the 1 nominator and the 3 denominator by 4, thus: 1/3 = 4/12. We do the same for 3/4 by multiplying the nominator and denominator to get a denominator of 12, in this case we multiply each by 3 so that we get: 3/4 = 9/12.
Now, we can multiply or subtract the fraction: 4/12 + 9/12 = 13/12
It is important to note that the lowest common denominator remains the same, only the numerator gets added or subtracted.
Hot Tip: Usually, the easiest way to find the common denominator is to multiply both denominators together. This doesn’t always give you the lowest but it gives you a common denominator you can reduce thereafter.
Reducing Fractions:
Once your fractions have been multiplied, divided, added or subtracted, you will often have absurdly large fractions that need to be reduced in order to get to your final GMAT answer.
For example: 125/225 sounds very complicated, to have a better idea of what number it represents we can try to reduce it. To do this we need to divide both the denominator and the numerator by the same number. In this case, both the numerator and the denominator can be divided by 5. This means that we end up with 25/45. This can be further divided by 5 to give us 5/9. Once you have a prime number in either the denominator or the numerator then its time to stop, you’ve reduced the fraction as far as it can go.
Simplifying fractions:
- To simply fractions, first of all, reduce them to the lowest common denominator.
- Then simply gather all the denominators and the nominators in a single fraction and cross off the corresponding numbers on the top and bottom
Further topics which are essential to know for the GMAT include
About: Fractions, GMAT, MBA, Quantitative
