3/3 (1 3)/(4 3) 3/12; therefore, the equivalent fraction in this case is 1/4
3/12 (the equal sign is used to represent equivalent fractions).
What is the reciprocalof a number?
The reciprocal of a number is obtained when a given number is divided into 1: the
results are called the reciprocal of that number. For example, the reciprocal of 6 is 1
divided by 6, or 1/6. Reciprocals come in most handy when dividing fractions (see
above to learn more about dividing fractions).
101
MATH BASICS
What are unit fractions and how are they tied to ancient Egypt?
A
unit fractionis one that has a numerator of 1, such as 1/2, 1/4, and 1/43545.
One of the earliest discussions of unit fractions—a table of representations
of 1/n—was found on the famous Rhind papyrus (also called the Rhind Mathe-
matical Papyrus), dated to around 1650 BCE. This record—a table copied by the
Egyptians from another papyrus dated 200 years earlier—represented a sum of
distinct unit fractions for odd “n” numbers between 5 and 101. To write a certain
fraction, they would add combinations of 1/n. For example, instead of writing
2/5, they wrote 1/3 1/15; for 2/29, they wrote 1/24 1/58 1/174 1/232.Because of the Rhind papyrus discovery, the sums of unit fractions are now
called Egyptian fractions. No one truly knows why the Egyptians chose this
method for representing fractions, but some historians believe it was a “wrong
turn” in Egyptian mathematical history. Whatever the reason, the Egyptians
(apparently successfully) used this system for 2,000 years. (For more informa-
tion about the Rhind papyrus, see “History of Mathematics.”)