**Chapter Notes and Summary**

• **Ratio of numbers : **ratio of two non-zero numbers a and b is fraction a b and we write it as a :** **b read as ‘a** **is to b’.In ratio a : b, we call a first term or antecedent and b second term or consequent.

• So, a ratio does not change when its first and second terms are multiplied or divided by same non-zero number. e.g., 2 : 3 = 2 3 = 2×4 3×4 = 8 12 = 8 : 12

•

**Equivalent ratios :**On multiplying (or dividing) each term of a ratio by same non-zero number, we get a ratio

**equivalent to given ratio.**

**e.g., : As shown above, 2 : 3 and 8 : 12 are equivalent ratios.**

•

**Ratio in simplest form : ratio a :**b is said to be in simplest form if HCF of a and b is 1.

e.g., ratio 11

**:**15 is in simplest form since HCF and 11 and 15 is 1.

**•**

**To convert a given ratio to its simplest form :**To convert a given ratio a :

**b to its simplest form, we divide each**

**term by HCF of a and b.**

**•**

**Proportion :**If two ratios are equal, we say that they are in proportion and use symbol ‘: : ‘ or ‘=’ to equator two ratios.

**•**

**Four numbers in proportion :**Four numbers a, b, c, d are said to be in proportion if a : b = c : d and we write a : b : : c : d.

We read it as ‘a is to b as c is to d’.

Here a, b, c, d are respectively known as first, second, third and fourth terms of given proportion.

**The 1st and 4th terms are called**

**extreme terms**or

**extremes.**

The 2nd and 3rd terms are called

**middle terms**or

**means.**

In a proportion a : b : : c : d, we always have (a × d) = (b × c).

**i.e., product of extremes = product of means.**

**•**

**Three numbers in proportion :**Three numbers a, b, c are said to be in proportion if a, b, c in proportion.

**a, b, c are in proportion ⇒ a, b, b, c are in proportion ⇒ a : b : : b : c ⇒ b2 = ac.**

•

**Unitary method :**method in which first we find value of one unit and then value of required number

**of units is known as**

**unitary method.**

The simple rules used in this method are :

(i) to get more, we multiply.

The simple rules used in this method are :

**(ii) to get less, we divide.**

**•**

**Some other important facts :**

(i) more is number of articles, more is cost.

**cost of any number of articles = (cost of 1 article) × (number of articles)**

**(ii) Less is number of articles, then less is cost.**

**cost of 1 article =**

**cost of a given number of articles**

**number of articles**

**(iii) method of finding first value of one quantity from value of some given quantities and then**

**finding value of required quantities is called unitary method.**

**(iv) ratio of two quantities in same unit is a fraction that one quantity is of other.**

**(v) A ratio is said to be in its simplest form if first and second terms have no common factor other than 1.**

**(vi) A ratio has no units in itself.**