Page 286 - ICSE Math 7

Formula Sheet

SET THEORY

• For a set having n elements: • For any non-empty sets A and B, we have
Number of subsets = 2 n (a) n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
n
Number of proper subsets = 2 – 1 (b) n(A – B) = n(A) – n(A ∩ B)
(c) n(B – A) = n(B) – n(A ∩ B)

RATIO, PROPORTION AND UNITARY METHOD

• If the ratio of original quantity to final quantity is a : b, then
b
Final quantity = × Original quantity
a
• Dividing a quantity ‘A’ in the given ratio x : y
 x   y 
First part =   × A Second part =   × A
 x + y   x + y 
• Dividing a quantity ‘A’ in the given ratio x : y : z
 x   y   z 
First part =   × A Second part =   × A Third part =   × A
 x + y + z   + x + y z   x + y + z 
• Four quantities p, q, r and s are in proportion, i.e., p : q = r : s p × s = q × r
1
• Full work is taken as 1, then one day’s work =
Number of days requred to complete the work
1
• Number of days required to complete the work =
One day's work
Work to be done
• Time required to do a certain work =
Wrok done in unit time
PERCENTAGE

Conversion Method Example(s)
Converting a fraction or a Multiply the given fraction or decimal by 100 and 7 = 7 × 100% = 28%
decimal into percentage put the percentage symbol (%) 25 25
0.38 = 0.38 × 100 = 38%
76 = 19
Converting a percentage Remove the symbol from the given percentage and 76% = 100 25
into a fraction or decimal then divide it by 100 39
39% = = 0.39
100
3
Converting a ratio into a Write the given ratio as fraction and then multiply it 3 : 5 = × 100%
percentage by 100 and put percentage symbol 5
= 60%
78 39
Converting a percentage Convert the given percentage into a fraction in the 78% = =
into a ratio simplest form and then write it as a ratio 100 50
= 39 : 50
To express a quantity X X 7 p as a percentage of ` 4
as a percentage of other × 100% = 7 × 100% = 1.75%
quantity Y Y 400
28% of 52 m
To find the given Given percentage × X 28
percentage of a quantity X 100 = × 52 m = 14.56 m
100

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