Page 92 - ICSE Math 7

7 Ratio, Proportion and

Unitary Method

Key Concepts

• Ratio • Proportion
• Comparison of Ratios • Continued Proportion
• Compound Ratio and Continued Ratio • Unitary Method
• Increase or Decrease in a Given Ratio • Variation
• To Divide a Given Quantity in a Given Ratio • Time and Work

In our everyday life, we often need to compare two quantities in terms of their magnitudes. Comparison
between two things can either be done by finding their ratio or by calculating their percentage.
Suppose we need to compare the speed of a helicopter with that of a fighter jet.

Helicopter Fighter jet
Speed of helicopter = 350 kilometres per hour Speed of fighter jet = 2,485 kilometres per hour

The speed of the fighter jet is approximately seven times the speed of Maths Info
the helicopter. Equivalently, the speed of the helicopter is approximately
1 We can compare two quantities
7 times the speed of the fighter jet. if and only if their units are
Ratio same.

The ratio of two quantities expressed in the same units and of the same kind is a fraction that shows
how many times one quantity is of the other.
a
The ratio of any two non-zero numbers a and b is a ÷ b = b . The usual notation to represent ratio

of a and b is a : b. The symbol ‘:’ stands for ratio and we read it as ‘is to’. Also, the first term a is
known as antecedent and the second term b is known as the consequent.

Suppose Reema got 70 marks and Meenu got 50 marks in an English test.
Reema’s marks 70 7
We can say that, = =
Meenu’s marks 50 5
We say that Reema’s marks and Meenu’s marks in the ratio 7 : 5. We read 7 : 5 as seven is to five.
In the ratio 7 : 5 the numbers 7 and 5 are terms of the ratio. The first term or antecedent is 7 and the
second term or consequent is 5.

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