Class 7 Chapter 8 Maths Comparing Quantities Notes (NCERT) to make the chapter easier. I hope it helps you.

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