Page 137 - Mathematics Coursebook

7.1 Simplifying fractions
14 Ratio and proportion

A ratio is a way of comparing two or Key words
Key words
more numbers or quantities.

!e symbol : is used to show ratio. Make sure you learn and
understand these key words:
Ratios were used long before the ratio
symbol we use today was invented. simplify
Pythagoras was a famous Greek simplest form
mathematician who lived around highest common factor
500 BC. divide
Historians and mathematicians believe share
that he discovered the golden ratio. Pythagoras (about 596 direct proportion

If the lengths of the sides of a rectangle BC to 475 BC). unitary method
are in the golden ratio, the rectangle is called the
golden rectangle. Some sizes of paper, such as A4, are based
on the golden rectangle.
A rectangle is golden if, when you cut a square from it, the

piece le# over is mathematically similar to the original. !is

means that the sides are in the same proportion.
If you divide a rectangle in this way several times, you will
see that a spiral shape forms.

!is spiral shape can be seen in nature, for example, in the
shell of a chambered nautilus. !e golden rectangle.

It can also be seen in architecture, such as the Parthenon
in Athens.

Today we use ratios in everyday life, o#en without
knowing it! Builders use ratios when mixing sand and
cement for concrete. Chefs use ratios when mixing
ingredients for cakes.
In this unit you will learn how to use ratio and direct
proportion.

136 14 Ratio and proportion