The document outlines key mathematical concepts such as equivalent fractions, ratios, and proportions, including direct and inverse relationships. It explains percentages, their conversion to fractions and decimals, and includes formulas for calculating profit, loss, and simple interest. Additionally, it provides insights on how to find percentage increase and decrease.

1. 1) Equivalent Fractions-> Ratios which have the same
value in their simple form.
2) Ratios are just the fraction form to compare numbers.
For eg->
2
3
𝑖𝑠 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 2: 3.
3) Inversely proportion or a∝
1
𝑏
is when ‘a’ ratio increases
but ‘b’ ratio decreases. The same is when ‘a’ decreases
but ‘b’ increases.
4) Direct proportion or a∝b is when the ‘a’ ratio and ‘b’
ratio increase and decrease together.
5) Percentages are Fractions with 100 in denominator.
a. Fraction in Percent->
𝑎
𝑏
× 100=P%
b. Decimal to Percent->D× 100=P%
c. Percent to Fraction->
𝑃
100
=
𝑎
𝑏
d. Percent to Decimal->
𝑃
100
= 𝐷
e. Ratio to Percent->1: 3 𝑖𝑛 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 = 1𝑥 + 3𝑥 = 4𝑥
then,
1𝑥
4𝑥
× 100 = 25%. 𝑆𝑎𝑚𝑒 𝑓𝑜𝑟 3𝑥. 1: 3 =
25%: 75%.
6) Per cent is derived from Latin word ‘per centum’
meaning ‘per hundred’.
7) Percentage of increase and decrease-
>
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡
× 100
8) Loss and Profit formulas->
a. Profit%=
𝑃
𝐶𝑃
× 100
b. Loss%=
𝐿
𝐶𝑃
× 100
c. Profit= SP-CP
d. Loss=CP-SP

2. e. CP=SP-Profit or SP+Loss
f. SP=CP+Profit or CP-Loss
g. CP=
𝑆𝑃×100
100−𝐿%
or
𝑆𝑃×100
100+𝑃%
h. SP=
100−𝐿%
100
× CP or
100+𝑃%
100
× CP
9) Simple Interest formulas->
a. SI=
𝑃×𝑅×𝑇
100
b. Amount=SI+P
c. SI=Amount-P
d. P=Amount-SI
e. P=
100×SI
𝑅×T
f. R=
100×SI
𝑃×T
g. T=
100×SI
𝑃×R