GMAT fractions are numbers in a form \(\pm\)\(\frac{x}{y}\). The top number is the numerator and the bottom number is the denominator and both are positive integers. The denominator indicates how many of the equal parts make up the whole, and the numerator provides the total number of equal parts. GMAT Fractions are integer numbers and division can also be demonstrated using fractions. The GMAT problem-solving section consists of GMAT fractions decimals and percents type of questions.

GMAT Fractions Rules

To solve GMAT problem solving questions, GMAT fractions rules must be followed. Here are a few rules discussed that are required to solve GMAT fractions:

Addition and Subtraction in GMAT Fractions

It is to be remembered: two fractions with the same denominators can be added or deducted in a swift manner – otherwise not.

ab + cd a+cb+d

Few instances to simplify it:

1. Test taker can add the numerators and keep the denominator the same:

\(\frac{3}{8}-\frac{2}{8}=\frac{1}{8}\)

\(\frac{5}{9}-\frac{1}{9}=\frac{4}{9}\)

2. If the need arises to add or deduct fractions not having similar denominators, perform the opposite function of simplifying and displaying them. It is equivalent to fractions having similar denominators. Till the time you multiply/divide the numerator or denominator with the same number. It will remain equivalent:

\(\frac{3}{8}*\frac{9}{9}=\frac{27}{72}\)

From here, we can narrow down a helpful algebraic expression:

\(\frac{x+y}{z}=\frac{x}{z}+\frac{y}{z}\)

3. When adding/deducting fractions possessing different denominators, multiply the fractions so that they display the least common multiple or LCM. For instance,

\(\frac{1}{3}+\frac{3}{4}\)

\(LCM=12\)

\(\frac{1}{3}*\frac{4}{4}=\frac{4}{12}\)

\(\frac{3}{4}*\frac{3}{3}=\frac{9}{12}\)

\(\frac{1}{3}+\frac{3}{4}=\frac{4}{9}+\frac{9}{12}=\frac{13}{12}=1\frac{1}{12}\)

Multiplication in GMAT Fractions

Multiplying fractions in the GMAT quant section is the rule of cross-canceling or canceling the numerator with the other denominator (not their own). The other method is to cancel that individual fraction’s numerator with the denominator.

\(Multiply:3\frac{1}{2}*\frac{4}{5}\)

Division in GMAT Fractions

The holistic dividing rule is, reciprocal to the fraction following the division sign which is also termed the divisor. This will result in the denominator becoming the numerator and vice versa, then multiply by that number.

For instance,

\(Divide:\frac{\frac{3}{5}}{2\frac{1}{10}}\)

This reciprocal is called inversion in mathematical terms.

Proportion in GMAT Fractions

A proportion and ratio are equal to each other. When we have two ratios or fractions set equal to each other it is then known as proportion. For instance,

x/12 = 33/28

Rules to remember here are:

Never overlook the vital rule of canceling before multiplying.

This leads to the next guideline which is – what we can and cannot cancel in proportion. The general proportion is a/b = c/d.

Now, we know that we can cross-cancel any numerator with its denominator and thus you can cancel out the mutual factors in ‘a’ and ‘b’, or in c and d. In fact, we can multiply or divide both sides of an equation with a similar thing. Therefore, we can cross out any numerators or ‘a’ or ‘c’, or denominators ‘b’ or ‘d’.

a/b= c/d

FOLLOW THIS:

x/12 = 33/28 = x/3 = 33/7 = x = 99/7

Learning Mixed Numbers in GMAT Fractions

What are mixed numbers? Mixed numbers are a mixture of whole numbers and a fraction. For instance \(3\frac{1}{2}\), here 3 is the whole number and ½ is the fraction. To modify the mixed number into a fraction, multiply the whole number by the denominator and add the outcome with the numerator.

\(3\frac{1}{2}\) = (3*2 +1)/ 2= 7/2

For the GMAT fractions, candidates must focus more on the overall practice of the GMAT quant in a rigorous manner. The GMAT exam is a tricky one and with chapters like fractions, they will try to confuse the candidates with easy yet tricky questions.

Conversion Rules for GMAT Fractions Decimals and Percents

GMAT fractions to memorize have different ways to express the same value. Here are a few rules to convert Fractions, decimals, and percents:

Conversion of Decimals to Fractions

To convert decimals to fractions, one must know the place value of the decimal. For example, .324 has digits in tenths’, hundredths’, and thousandths places. So, .324 would become 324/1000.

Conversion of Fractions to Decimals

To convert any GMAT fractions to a decimal includes long division. A fraction is a numerator divided by the denominator. So, 7/9 is simply 7 divided by 9, which you can work out by long division to be 0.77.

Conversion of Fractions to Percents

Any percentage when converted to fraction it becomes, n% is n/100. This refers to a fraction with 100 as the denominator. To find out what percent is a fraction candidates need to divide the fraction with 100 in the denominator to get the answer in percentage.

For instance, to convert 25/200 in percent. One needs to convert it to an equivalent fraction with 100 as the denominator.

Conversion of Percents to Fractions

Candidates know that n% equals n/100. So, if the examiner asks to convert 150% into a fraction. It would be 150/100, which makes the answer 1 ½.