Checking Whether Two Fractions Are Equal

We want to distribute 36 marbles from one packet equally among four people and 27 marbles from another packet among three people. It is easy to see that each person will receive 9 marbles in both of these distributions, as $\frac{36}{4}=9$ and $\frac{27}{3}=9$. The two fractions $\frac{36}{4}$ and $\frac{27}{3}$ represent the same number, so we say that they are equal. We can see this by working out the divisions 36 ÷ 4 and 27 ÷ 3.

I. Using a calculator

If we have a calculator (e.g., the one on a computer), we can see whether two fractions are equal by looking at the quotients obtained.


For example, the fractions $\frac{102}{6}$ and $\frac{119}{7}$ are equal, since
102 ÷ 6 = 17 and 119 ÷ 7 = 17.

II. Without using a calculator

In this case, recognizing two equal fractions assumes that we know how to establish that a fraction is equal to a given fraction.


To do this, we use the following rule: To establish that a fraction is equal to a given fraction, simply multiply or divide its numerator and its denominator by the same natural number (not zero).


For example, the fractions $\frac{15}{20}$ and $\frac{21}{28}$ are equal, since: $\frac{15}{20}=\frac{15+5}{20+5}=\frac{3}{4}$
 and $\frac{21}{28}=\frac{21+7}{28+7}=\frac{3}{4}$.