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.
(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.
Chapter Notes and Summary